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Artificial Life as a Tool for Biological Inquiry
Charles Taylor
Department of Biology
University of California at Los Angeles
Los Angeles, CA 90024
taylor@cs.ucla.edu
David Jefferson
Department of Computer Science
University of California at Los Angeles
Los Angeles, CA 90024
jefferson@cs.ucla.edu
Keywords
artificial life, evolution, natural selection, origin of life, development, wetware,
emergent properties
Abstract Artificial life embraces those human-made systems that possess some of the key properties of
natural life. We are specifically interested in artificial systems that serve as models of living systems for
the investigation of open questions in biology. First we review some of the artificial life models that
have been constructed with biological problems in mind, and classify them by medium (hardware,
software, or ''wetware") and by level of organization (molecular, cellular, organismal, or population).
We then describe several "grand challenge" open problems in biology that seem especially good
candidates to benefit from artificial life studies, including the origin of life and self-organi- zation,
cultural evolution, origin and maintenance of sex, shifting balance in evolution, the relation between
fitness and adaptedness, the structure of ecosystems, and the nature of mind.
The question of what the major current problems of Biology are cannot be answered, for I do not know of a single
biological discipline that does not have major unresolved problems.... Still, the most burning and as yet most
intractable problems are those that involve complex systems.
Ernst Mayr [42]
1 Introduction
Natural life on earth is organized into at least four fundamental levels of structure: the molecular level,
the cellular level, the organism level, and the population-ecosystem level. A living thing at any of these
levels is a complex adaptive system exhibiting behavior that emerges from the interaction of a large
number of elements from the levels below. Understanding life in any depth requires knowledge at all
these levels.](https://image.slidesharecdn.com/28194266-250517172049-c19ec913/85/Artificial-Life-An-Overview-Christopher-G-Langton-15-320.jpg)
![To deal with this multilevel complexity, a broad methodological shift is in progress in the biological
sciences today as a new collection of Artificial Life models of natural biological systems become
available for the first time. These modeling tools, some expressed as software, some as hardware, and
some as wet-bench lab techniques (wetware), are powerful enough to capture much of the complexity of
living systems, yet in a form that is more easily manipulable, repeatable, and subject to precisely
controlled experiment than are the corresponding natural systems.
In Artificial Life there is a major intellectual divide, similar to the one in the field of Artificial
Intelligence, between "engineered" systems designed to accomplish some complex task by any means
the designer can devise, even if only distantly related to the way natural systems accomplish it, and
systems meant to accurately model biological
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systems and intended for testing biological hypotheses. For example, most of the literature on genetic
algorithms [26] has centered on function optimization, and the technical concerns have been about
which algorithm variations are most efficient for which class of optimization problems. While these
issues are important for many purposes, they are not central to the behavior of living systems.
We are specifically interested in those Artificial Life systems that tell us something about natural life. In
this review, we will describe some of the modeling techniques under development for biological
problems in order to survey the breadth of research in those areas. Then we will describe a number of
open problems in biology that seem especially good candidates to benefit from the tools that Artificial
Life is beginning to offer.
2 Brief Survey of Artificial Life Models Applied to Problems in Biology
Researchers have produced Artificial Life models at each of the levels of organization recognized in
natural life, from the molecular to the population level, sometimes covering two or three levels in a
single model. At present there is a tendency to study the molecular level through wetware experiments,
the cellular and population levels with software experiments, and the organismic level with hardware
(robotic) studies, although that may change in the future. We will classify the Artificial Life systems we
discuss by medium: wetware, hardware, or software.
2.1 The Molecular Level: Wetware Systems](https://image.slidesharecdn.com/28194266-250517172049-c19ec913/85/Artificial-Life-An-Overview-Christopher-G-Langton-16-320.jpg)
![Wetware Artificial Life systems are the most similar to natural life and indeed are actually derived from
natural life, today at least. Most of the experiments are attempts to direct an artificial evolutionary
process toward the production of ribonucleic acid (RNA) molecules with specific catalytic properties.
Experiments typically begin with a pool of 1013 to 1015 variant RNA molecules, placed in a solution of
substrates for a specific reaction that the experimenter wishes to catalyze. Because initially the
sequences are almost all distinct, and there are trillions of them, some will presumably "accidentally"
catalyze the reaction at least weakly. The more "successful" RNA molecules, those that promote the
target reaction more strongly than others, are then selected and separated from the "unsuccessful" and
replicated many times, with mutations inserted, by using a variant of the polymerase chain reaction
(PCR)—a relatively new technique for creating vast numbers of copies of nucleic acid sequences. These
new daughter sequences are then tested and selected again, and the whole cycle is repeated for a number
of generations until RNA sequences with sufficiently strong catalytic properties are evolved.
Examples of wetware research along these lines include work by (a) Beaudry and Joyce, where RNA
ribozymes that normally cleave specific RNA sites were evolved to cleave DNA as well; by (b) Bartel
and Szostak [2], who evolved catalytic RNAs from a pool of random-sequence RNAs; and by (c)
Lehman and Joyce [36], who evolved RNA sequences to work with different metal ions than they
normally would. So far the RNA sequences produced artificially have been similar to natural sequences;
however, they have enzymatic functions not possessed by any preexisting natural RNA, so far as we
know, indicating an obvious potential for evolving chemically useful RNA molecules. And someday,
perhaps, if the RNA molecules are selected not on the basis of their own catalytic behavior but on that of
the proteins they code for, then we can look forward to evolving artificial genes for medically useful
protein molecules.
If we view the direct goal of these experiments as producing some particular catalytic properties in
RNA, the experiments are not biological modeling as we have defined it. But taken collectively, they do
have a biological significance well beyond their potential economic and medical value. They help us
calibrate the degree to which RNA can catalyze biochemical reactions, a job normally done by proteins,
and they lend strong](https://image.slidesharecdn.com/28194266-250517172049-c19ec913/85/Artificial-Life-An-Overview-Christopher-G-Langton-17-320.jpg)
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credibility to the hypothesis of the "RNA world" [30], one of the most important theories about the
origin of life. This RNA world hypothesis asserts that there was a time early in the earth's history when
there were few if any deoxyribonucleic acid (DNA) or protein molecules, and the primordial soup was
instead dominated by RNA molecules that were able to accomplish both replication and catalysis. By
demonstrating that pure replicating RNA systems are capable of evolving specific catalytic behaviors,
these Artificial Life studies are providing evidence for the plausibility of the RNA world that is more
direct than any other line of research so far.
2.2 The Cellular Level: Software Systems
It is customary to distinguish between chemical evolution, which refers to evolutionary history from the
stage of self-replicating molecules to the stage of encapsulated cells, and organic evolution, which refers
to evolution since life became organized almost exclusively into cells that, either alone or in
assemblages, behave and reproduce as clearly defined units. Much research in Artificial Life is directed
at understanding just how a differentiated multicellular assemblage can replicate itself, and how such
replication might have evolved.
John von Neumann was the first to characterize conditions for self-replication in cellular automata
systems [6, 58]. He constructed self-replicating systems that possess the full computational power of
universal Turing machines using a very large number of cells, each with 29 possible states. Langton [33]
dropped the requirement of universality (after all, natural cells do not seem to have that) and found very
much simpler systems that are capable of self-replication, nicely displayed in Langton [34]. Reggia,
Armentrout, Chou, and Peng [53] have identified a number of even simpler self-replication patterns in
cellular automata.
Whatever the first self-replicating molecules may have been, their organization into cells must have
required the evolution of mechanisms for spatial segregation in a chemical environment. How this
occurred has been an open question in chemical evolution since Oparin posited a role for coacervates in
the 1920s (see Chang, DeMarais, Mack, Miller, & Strathern [8]). Recently Boerlijst and Hogeweg [4]
have studied cellular automata that generate hypercycles and seem to generate spatial diversity
spontaneously. While it is still too early to know just how directly this corresponds to the actual
evolution of cells, these studies serve to enlarge the set of possible explanations.](https://image.slidesharecdn.com/28194266-250517172049-c19ec913/85/Artificial-Life-An-Overview-Christopher-G-Langton-18-320.jpg)
![It took only 1 billion years or so for the first cells to form on earth but about 3 billion more years for
these to evolve into metazoans (multicellular organisms) shortly before the Cambrian period. There are
many questions about how this might have been accomplished, and it appears that several major steps
were involved. One step was the formation of endosymbiotic associations, where distinct types of cells
associate, with one inside the cell membrane of the other (as apparently happened in the formation of
chloroplasts and mitochondria within eucaryotic cells). Another step was the association of genetically
related cells to form multicellular organisms, in which only some of the cells reproduce. These issues are
only partly understood. While there have been a number of fine studies on symbiotic associations
generally (e.g., [28,59]), there has been much less work directed at endosymbiosis, although there has
been some [56]. And while there have been several studies of how individual cells might reproduce to
form the next higher level of organization [37,44,51], these have been clearly exploratory. The cellular
level of life is an area where it would seem that artificial life research has only begun.
2.3 The Organism Level: Hardware Systems
To model the behavior of living things at the organism level, for example, of insects, one must model
the organism's sensory and nervous system, its body, and its envi-
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ronment. Although we are quite used to thinking of nervous systems as fantastically complex, we tend to
ignore the fact that animals' bodies are highly complex as well, with extremely complicated geometries,
mechanical, dynamical and thermal properties, energy constraints, growth and developmental programs,
etc.
In principle all of the components of an animal—nervous system, body, environment—can be simulated
in software. In practice, however, the amount of computation required to reasonably model the
properties of sound or light in a complicated environment, or the mechanical properties of an organism
with 100 coupled elastic parts, is vast and effectively beyond the capacity of computational technology
for some time to come.
However, it is now becoming possible to let the real physical environment model itself, and to represent
the bodies of animals and their interactions with the environment by using small, computer-controlled,
autonomous mobile robots (mobots). With this technology, we can now model how organisms
accomplish the integration of various perceptual modalities, how they navigate in space, how they
control their senses and muscles to accomplish precisely coordinated movements, and how they do all
these things in real time.](https://image.slidesharecdn.com/28194266-250517172049-c19ec913/85/Artificial-Life-An-Overview-Christopher-G-Langton-19-320.jpg)
![One research project of this kind involved the mobot Genghis, developed by Angle [1] and programmed
by Maes and Brooks [41] to learn to walk. Genghis is a six-legged robot, approximately 1 foot long and
1 food wide, designed to traverse rugged terrain. Each leg is powered by two motors and there are two
sensors, one in front and one in back, to detect whether the body is touching the ground, and another
sensor to measure the distance Genghis has traveled. In most such systems, coordination for tasks such
as walking is statically programmed; Genghis, however, has to learn to walk. The leg modules are
coordinated by a network of finite automata that receives feedback from the sensors about stability and
forward movement, and produces output to the motors. Starting from a random neural network, Genghis
learns how to achieve a reliable tripod gait in just few minutes.
Several features of the Genghis experiments and others like it are worth noting: (a) Emergent
functionality of control: Control of Genghis' gait is an emergent property, in that no individual part of
the neural net "knows" how to walk. (b) Task-level decomposition: The agents that govern behavior are
essentially autonomous. At the lowest level, one simple task is accomplished (e.g., standing up), upon
which is superimposed the next layer (e.g., moving), upon which is superimposed another (e.g., obstacle
avoidance), and so on. This layering of behaviors, each one making use of others that preexist, is
analogous to the way that task proficiency might be accomplished by evolution in natural life. (c) Low-
level processing: Because there is no global model, much of the reasoning is accomplished at a low
level, close to the perception level, in much the same way that visual information seems to be processed
in the mammalian retina. These points are discussed in Maes [40] and Brooks [5]. Adherents to this
approach make the narrow claim that it is a good way to control mobile robots for complex tasks, and
the broader claim that it is a good way to engineer intelligent systems generally. If so, then using mobots
to model animals will aid in extracting some of the principles of intelligent behavior generally, whether
natural or artificial.
2.4 Software Life at the Population Level: Equational Models versus Artificial Life Models
Models of population behavior for the study of ecosystem organization, population genetics,
macroevolution, geographic dispersal, etc. have traditionally been expressed formally as systems of
algebraic or differential equations. Unfortunately, equational models are subject to many limitations. For
example, in many models it is common to refer to the derivative of a variable with respect to population
size N. This in turn](https://image.slidesharecdn.com/28194266-250517172049-c19ec913/85/Artificial-Life-An-Overview-Christopher-G-Langton-20-320.jpg)
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implies the assumption of very large populations in order for such a derivative to make sense, which has
the effect of washing out small population effects, such as genetic drift, or extinction. Another difficulty
is that it would take tens to hundreds of lines of equations to express even a simple model of an
organism's behavior as a function of the many genetic, memory, and environmental variables that affect
its behavior, and there are simply no mathematical tools for dealing with equational systems of that
complexity. Furthermore, equational models are generally poor at dealing with highly nonlinear effects
such as thresholding or if-then-else conditionals, which arise very frequently in the description of animal
behavior.
One of the most fundamental and successful insights of the field of Artificial Life has been the
development of an alternative population modeling paradigm that dispenses with equations entirely, and
represents a population procedurally, that is, as a set of coexecuting computer programs, one for each
cell or one for each organism. We consider this feature, the representation of organisms by programs, to
be the defining feature of "artificial life" models of population behavior, the property that distinguishes
them from other mathematical or computational models of populations.
Artificial Life models offer the advantage of coding an organism's behavior explicitly as a program,
rather than implicitly as the solution to equations that must be integrated. This directness of encoding
typically makes Artificial Life systems much easier to use and modify, as new information is obtained or
new hypotheses are entertained, than is possible with equational models. Today most Artificial Life
models represent each organism as a Lisp program, a finite automaton, or a neural net. The genes of the
organism are represented variously as bit strings, character strings, or list structures, either contained
within the organism or stored as a separate data object that serves to encode the structure or behavior of
the organism. Software organisms can reproduce either asexually, with point mutations altering the
genetic data passed from parent to child, or sexually, with the child's genome derived by combining
information from two parent genomes.
An early example of the artificial life modeling approach is the RAM system [55], developed by Taylor,
Jefferson, Turner, and Goldman, in which animal-like processes (parameterized Lisp programs) and
environment-like processes could execute concurrently and synchronously. A RAM animal's program is
a Lisp routine whose parameters serve as genes. RAM animals reproduce asexually but live in a
common environment in which they interact and compete ecologically. The RAM system was relatively
limited in two ways: (a) The "genes" defined a relatively small parameter space within which variation
could occur, leaving limited scope for innovation and evolution; and (b) because at the time it was built
only a few hundred individuals could be simulated for a few tens of generations per hour of workstation
time, so the process of natural selection was subject to drift unless the selection forces were
exceptionally strong.](https://image.slidesharecdn.com/28194266-250517172049-c19ec913/85/Artificial-Life-An-Overview-Christopher-G-Langton-21-320.jpg)
![Jefferson et al. [291 drastically extended and scaled up the idea of representing organisms as programs
with such systems as Genesys. In that system, executed on a Connection Machine, animals were
represented as neural nets in some cases or as finite automata in others. The genes of each organism
were represented as bit strings that encoded either the weights of a neural net, or the transition table of a
finite automaton. With a population of 64K individuals evolving at the rate of one generation per
minute, and starting from a population of random bit strings, Genesys was able to evolve the ability to
follow a broken rectilinear trail in a grid environment in 100-200 generations.
Since RAM and Genesys, many other systems representing organisms as programs have been developed
to explore problems in biology. We can illustrate the diversity of this approach by classifying these
systems according to the general purposes for which they were developed—the study of evolution,
behavior, ecology, developmental biology, or teaching.
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Evolution. Artificial Life models are especially well suited for studying the dynamics of natural
evolution and were originally invented for this purpose. Imagine a genetic algorithm in which each
genome encodes a computer program, and the programs in the population are selected and bred on the
basis of their ability to survive and prosper in some environment. One would expect that the future
generations of programs will perform better than their progenitors, and, indeed, in practice this is
typically the case—although it depends on how the programs are represented, as Collins and Jefferson
[10] have argued. For a number of reasons, artificial neural networks, encoded in various ways into bit
strings, seem to be especially good representations for evolution.
Sexual selection is an evolutionary phenomenon recognized by Darwin and emphasized by Fisher [19]
in the 1930s. If a female produces sons who are extreme for some trait (e.g., wattle color) and also
daughters who have a preference for that extreme— through linkage, pleiotropy, or some other
mechanism—then that trait will be selected to a high frequency in the population even if it has very
disadvantageous side effects. It has been suggested that chance differences in traits subject to such
runaway selection might underlie the tremendous diversity of secondary sexual characters in many
tropical birds. The mathematical analysis of this phenomenon, however, requires a system of several
nonlinear differential equations, so it is very complex and has been successful for only a few special
cases.
Collins and Jefferson [11] constructed an Artificial Life model of sexual selection, endowing the
organisms with the relevant heritable traits and preferences. They explored this system in some
generality, identifying where such explanations are plausible and where they are not. In particular, they
were able to show that certain propositions that had been demonstrated analytically under very
restrictive assumptions were actually true under a much broader set of circumstances than was provable
by mathematical analysis. There are many other problems in sexual selection (see, e.g., Williams [60])
where similar methods would appear to be useful.](https://image.slidesharecdn.com/28194266-250517172049-c19ec913/85/Artificial-Life-An-Overview-Christopher-G-Langton-22-320.jpg)
![Behavior. Even Darwin was impressed by how exquisitely adapted animals seem to be to their
environments. Indeed, when it has been possible to develop models of optimal behavior from theoretical
principles and then compare these to the way animals actually behave, the fit is often striking. How is
that accomplished? Do animals figure out the relevant formulae, differentiate them, and solve for zero?
Koza, Rice, and Roughgarden [32] have recently examined the feeding behavior of Anolis lizards, a
small, well studied group that inhabits the Caribbean region, and compared their actual foraging
behavior to optimal foraging behavior as determined by a theoretical analysis, noting that the fit was
quite close. They then compared that to the foraging behavior of simulated lizards that they evolved via
genetic algorithms, and found that it was not difficult for the evolution to endow the lizard with
behavioral strategies that closely approximate the optimal.
In a similar vein, Gibson, Taylor, and Jefferson [22] used the RAM system described earlier to model
the peculiar mating behavior of sage grouse in which the females choose from among male suitors.
Dozens of males will gather to form leks (local mating markets) in which they display and attract the
attention of females. Gibson et al. were trying to discover what influenced the females in selecting
males. By searching a space of parameterized Artificial Life models, they found that if females, when
choosing a mating lek, considered the distance from their nest, the number of males there, and the
expected waiting time for the top male, most of the variance in their observed behavior was explainable.
Similar work by Denoubourg, Theraulaz, and Beckers [15] on "swarm intelligence" has identified
plausible sets of rules that are sufficient to explain much of the complex behavior used by ants and other
social insects.
In a more theoretical direction, Lindgren and Nordahl [39] examined how the outcomes of iterative
games of the Prisoner's Dilemma, a widely used model for the evo-
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lution of cooperation, might differ when there is misinformation among the players. Their analysis is
remarkable because it lends credence to the position that social behavior will by itself lead to increased
complexity in participant behavior. This approach is described more fully in Lindgren [38].
Ecology. Behavioral and ecological phenomena are often closely related, and both are rich with
examples of collective action and emergent phenomena. At an abstract level, Ray [52] has shown how
several trophic levels might emerge as a general property of ecological systems. Similarly, Ikegami [27]
used variations of the Prisoner's Dilemma analogous to symbiosis and host/predator or predator/prey
interactions to examine this evolution of interspecies associations.
Toquenaga, Ichinose, Hoshino, and Fuji [57] and Fry, Taylor, and Devgan [21] have used Artificial Life
models to examine complex modes of behavior and population growth. By programming empirically-
derived rules of behavior into the artificial animals, they observed the consequences of the collective
behavior that was exhibited by ensembles of animals and the environments with which they interacted.](https://image.slidesharecdn.com/28194266-250517172049-c19ec913/85/Artificial-Life-An-Overview-Christopher-G-Langton-23-320.jpg)
![Developmental biology. Emergent phenomena are nowhere more evident than in developmental biology,
where large numbers of cells, following presumably simple rules of behavior, collectively generate
complex and interesting patterns. Prusinkiewicz [50] has explored the use of algebraic formulae for cell
division and differentiation. These generate some stunning visual representations as well as realistic
botanical patterns. Recently, Fleischer and Barr [20] have developed a system where cells change state
and/or produce fields that mimic diffusion of growth regulators.
Because there is such a large amount of new information accumulating, consistent with simple collective
behavior both within and between cells, it seems likely to us that Artificial Life systems will prove
invaluable in the future for precisely formulating and testing hypotheses about development.
Teaching. It is sobering to reflect that 40% of Americans do not believe in Darwinian evolution and that
this is true for 25% of all college-educated Americans as well. Religious convictions seem to be only
part of the problem. Rather, it appears that the major obstacle is failure to understand the theory of
evolution itself, aggravated by the fact that even many secondary school biology teachers have serious
misunderstandings. It is well established that students are less likely to understand and absorb when they
are passively presented with facts than when they are actively involved in construction and
experimentation.
Artificial Life, however, offers a student the possibility of watching evolution in action, actively
intervening with it and creating his or her own microworld. The Blind Watchmaker program by
Dawkins [14] is especially noteworthy in this regard, as are the efforts of Resnick [54] to explore how
children learn about collective behavior, and of the Apple Vivarium group (A. Kay [personal
communication]), who are exploring Artificial Life systems to provide better ways of teaching ecology,
evolution, and biology in general, in a classroom setting.
Papert [47], whose earlier Mindstorms was so influential for introducing computers to the K-12
classrooms, has recently advocated [48] a cybernetic approach to teaching science in the early grades.
The argument he makes is compelling, and if generally adopted, then we may see a major influence of
Artificial Life on the next generation of scientists.
3 Open Problems in Biology that Are Amenable to Study by Artificial Life Modeling
The opening quotation by Ernst Mayr concerns the need for understanding biological systems as
complex adaptive systems. In the past, despite several brave attempts,](https://image.slidesharecdn.com/28194266-250517172049-c19ec913/85/Artificial-Life-An-Overview-Christopher-G-Langton-24-320.jpg)
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disussion of holistic properties and emergence in biology typically devolved into mysticism or
obfuscation. The study of Artificial Life, if it accomplishes nothing else, is providing a platform for
more informed discussion of those issues.
We believe that several of the major outstanding problems in biology, especially in the study of
evolution, are likely to benefit from the study of Artificial Life. In this section a few such problems are
described. We will focus on evolution simply because it is the foundation upon which so much of
biology is based, because it is permeated with problems of emergence, and because we are more familiar
with this area.
3.1 Origin of Life and Self-Organization
Questions abound when one attempts to understand how life originated on earth and possibly elsewhere
in the universe as well. If we restrict our attention to the origin of life on earth, those problems involve
reconstructing the physical, chemical, geologic, and competitive forces that shaped the peculiar history
of life on earth, the sequence of chemical reactions that may have occurred, the manner in which they
became packaged and encapsulated so that organic evolution could supplant that which occurred
previously, etc. Work along theoretical lines, such as that by Langton [35]; Farmer, Kauffman, and
Packard [18,31]; or Eigen and Schuster [17] will be required, as well as experimental work [30]. As yet
there has been little research in Artificial Life directed toward the actual constraints that operate on the
other planets in our solar system and prevented (or at least constrained) the origin of life there. Most is
directed at learning the minimal chemical requirements for replication to get started.
3.2 Cultural Evolution
Ideas and other atomic particles of human culture often seem to have a life of their own—origination,
mutation, reproduction, spreading, and dying. In spite of several bold attempts to construct theories of
cultural evolution (e.g., [7,13]), an adequate theory remains elusive. The financial incentive to
understand any patterns governing fads and fashion is enormous, and because cultural evolution has
contributed so much to the uniqueness of human nature, the scientific motivation is equally great.
Much of the problem with cultural evolution is similar to that for prebiotic evolution— the difficulty of
identifying just what evolves (the "units of evolution"), how these units maintain their identity, and how
they interact with one another. This area would seem to benefit from the same sorts of considerations
that govern the origin of life.
3.3 Origin and Maintenance of Sex](https://image.slidesharecdn.com/28194266-250517172049-c19ec913/85/Artificial-Life-An-Overview-Christopher-G-Langton-25-320.jpg)
![Few problems in contemporary evolutionary theory are attracting as much attention as is the evolution
of sex, sometimes referred to as "the cost of meiosis" [43]. All else being equal, a female who
reproduces asexually will leave twice as many genes in her offspring as will a female who reproduces
with a male. This would seem to impose a tremendous hurdle for sexuality to overcome, yet it persists,
and sex is widespread in the natural world. Why? The answer almost certainly involves complex
interactions among linkage, pleiotropy, epistasis, parasitism, and nonlinear relations between genotype
and fitness. There are many qualitative theories but little in the way of testable quantitative research.
The ability to construct and examine large, but finite, populations with a variety of arbitrary constraints
makes Artificial Life systems an excellent platform from which to study the theoretical side of this
problem. We have observed, for example, that the ability of sexual systems to rid themselves of
maladaptive mutations (Muller's ratchet) can be significant in populations of bit strings that evolve by
genetic algorithm [12]. The genetic algorithm literature also has many examples where these issues are
addressed in the context of optimization problems [23].
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3.4 Shifting Balance Paradigm
Wright, in his four-volume treatise on population genetics [61], argued that the key issues in evolution
today had their roots in the disagreements of the 1930s-1950s among Fisher, Haldane, and himself. This
related particularly to how populations of organisms traversed their adaptive landscape—through
gradual fine-tuning by natural selection on large populations, or alternatively in fits and starts with a
good bit of chance to "jump" adaptive valleys in order to find more favorable epistatic combinations.
The traditional mathematical models of population genetics and evolution require extensive linearization
and so are not very good for exploring the nonlinear interactions that this problem requires. On the other
hand, Artificial Life models are ideal for studying this problem, and several studies have begun on the
importance of population size for evolving solutions with arbitrary degrees of epistasis. It may be that
the rules that govern adaptation in artificial systems are different from those for natural systems, but
these studies will certainly highlight which issues are most important, and there will certainly be some
generalizations that pertain to both worlds.
3.5 Fitness and Adaptedness](https://image.slidesharecdn.com/28194266-250517172049-c19ec913/85/Artificial-Life-An-Overview-Christopher-G-Langton-26-320.jpg)
![Even before Darwin, it was recognized that there is some degree of direction or progress toward more
complex forms over geologic time—the "chain of being," although how much direction there might be
and how that effect is produced by natural selection remain murky. This concern can be compressed
essentially into one question, What is the relation between adaptedness and fitness, that is, between
adaptation and what is selected for? This question has occupied some of the greatest evolutionists of this
century [16] and remains quite open [60]. It is now well understood that natural selection does not
necessarily maximize adaptedness, even in theory [45]. Yet field biologists are constantly impressed by
just how good the fit seems to be, and optimization arguments abound in population ecology (see Koza
et al. [32]). In a classic essay, Gould and Lewontin [24] assailed the widespread use of optimization,
pointing out that chance, structural necessity, pleiotropy, historical accident, and a host of other
contributors will detract from making this "the best of all possible worlds."
The analysis of artificially living systems is beginning to shed needed light on this issue. Miglino, Nolfi,
and Parisi [44] studied the evolution of generating functions that produced neural nets, which then
determined the behavior of organisms, which in turn determined the fitness of artificial organisms in
their environments. They found that a variety of genotypes coded for identical neural nets, that a variety
of neural nets coded for the same behavior, and that a variety of behaviors achieved the same fitness in
their system. However, the opportunities these various solutions offered for future evolution differed
significantly. Similar observations were made by Hinton and Nowlan [25] in their study of the Baldwin
effect in evolved learning by neural networks.
As research in Artificial Life acquires greater ability to capture development of organisms and
intervening levels of organization between molecules and populations, the field is likely to contribute to
the analysis of this problem that Dobzhansky characterized as "the most important theoretical problem
in the study of evolution" (personal communication).
3.6 Structure of Ecosystems
In natural ecosystems there are a number of patterns that seem fairly general. For example, in their study
of many food webs, Pimm, Lawton, and Cohen [49] observed a number of patterns, among them (a) the
average proportion of top predators, intermediate species, and basal species remained roughly constant;
(b) linkage density is approximately constant; and (c) the modal number of trophic levels is three to four.](https://image.slidesharecdn.com/28194266-250517172049-c19ec913/85/Artificial-Life-An-Overview-Christopher-G-Langton-27-320.jpg)
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There are others that also point to emergent properties of natural ecosystems. The reasons underlying
these regularities are seldom understood.
As Artificial Life develops and ecosystems are evolved, perhaps along the lines of Ray [52] or Holland
[26], it will be interesting to see if the same patterns evolve. Perhaps others will emerge, such as the
intermediate connectedness of complex adaptive systems and their posture near the edge of chaos
[31,35].
3.7 Mind in Nature
No problems in science are more venerable or profound than those surrounding the nature of mind. Will
it be possible to design or evolve robots that experience the same sensations that we do? Do radically
different life forms experience equally different forms of consciousness? Or is consciousness a universal
property that organisms experience to various degrees but fundamentally alike in kind (and how can we
tell)? How could mind and consciousness be produced by Darwinian evolution? Two recent and lucid
accounts of these problems are those by Nagel [46] and Churchland [9].
Like most people, we have our own views on these problems. But unless these views are subject to
rigorous definition, testing, and verification, they cannot be considered scientific. As the ability to
construct Artificial Life systems improves, it may well become possible to construct systems that exhibit
behavior that is typically ascribed to "mind." Such systems will, in a sense, play a role analogous to that
played by Escherechia coli or Drosophila melanogaster that have permitted manipulation and dissection
of mechanisms in natural living systems. If that happens, and we believe it will, then the field of
Artificial Life will have contributed to what is surely one of the scientific grand challenges of all time.
References
1. Angle, C. M. (1989). Genghis, a six-legged autonomous walking robot. Bachelor's thesis, Department
of EECS, Massachusetts Institute of Technology, Cambridge, MA.
2. Bartel, D. P., & Szostak, J. W. (1993). Isolation of new ribozymes from a large pool of random
sequences. Science, 261, 1411-1418.
3. Beaudry, A. A., & Joyce, G. F. (1992). Directed evolution of an RNA enzyme. Science, 257, 635-641.
4. Boerlijst, M., & Hogeweg, P. (1992). Self-structuring and selection: Spiral waves as a substrate for
prebiotic evolution. In C. Langton, C. E. Taylor, J. D. Farmer, & S. Rasmussen (Eds.), Artificial life II,
255-276. Reading, MA: Addison-Wesley.
5. Brooks, R. A. (1991). New approaches to robotics. Science, 253, 1227-1232.
6. Burks, A. (1970). Essays on cellular automata. Urbana, IL: University of Illinois Press.](https://image.slidesharecdn.com/28194266-250517172049-c19ec913/85/Artificial-Life-An-Overview-Christopher-G-Langton-28-320.jpg)
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taking advantage of others by acting according to short-term self-interest. In other cases, cooperation could be profitable
enough that it is dictated even by shortsighted selfishness.
In the early history of evolutionary theory, the emphasis appears to have been mostly on the struggle for existence. (See
Cronin [19] for a discussion.) Some early writers, such as the anarchist Kropotkin [47], did, however, stress the importance
of cooperative interactions both in a biological context and in society. A number of scenarios for how altruistic and
cooperative behavior could be established have later been suggested. The main difficulty in the evolution of altruistic
behavior and cooperation is explaining how this behavior could be stable against cheaters who enjoy the benefits without
giving something in return.
One case, which will not be discussed further in this article, is when the altruistic behavior is directed toward relatives (e.g.,
[34]). From the viewpoint of reproduction of genes, an individual is equivalent to two of his brothers or eight of his cousins.
In the terminology of biologists, this is called kin selection. A number of cases of altruistic behavior in biology, such as
eusociality among ants, bees, and wasps (e.g., [2]), have been claimed to at least in part depend on kin selection.
Another important mechanism is reciprocal altruism (e.g., [98]). In this case favors are given, and favors are expected back
in return. In many cases, this could be viewed as enlightened self-interest that takes the shadow of the future into account.
The game theoretic models discussed later mostly fall under this heading.
A third mechanism could be group selection, where selection can be viewed as operating at higher levels. A simple
mathematical example where clearly defined higher units of selection (different kinds of spiral waves) appear is the spatial
hypercycle model studied by Boerlijst and Hogeweg [10,11].
Another case where cooperative behavior can occur is when cooperation follows from immediate self-interest. This was
called by-product mutualism in Dugatkin, Mesterton-Gibbs, and Houston [24]; in a game theoretic framework, parameters
have changed so that the game is no longer a Prisoner's Dilemma (PD) (see section 2.1), but the trivial game where both
players prefer cooperation. For example, this could be the case if the profit of a group grows faster than linearly with the
number of participants. Cooperative hunting of larger prey among lions has been suggested as one example [24] (but see also
[18]).
Finally, explanations of cooperation in human society could take cultural as well as genetic transmission into account, and
could involve, for example, explicit modeling of societal norms (e.g., [5,14,93]).
This list of scenarios is undoubtedly incomplete, and many examples may be hard to classify as one scenario or the other.
Consider, for example, the case of cleaning symbiosis discussed in Trivers [98], where certain small fish (cleaners) clean
larger fish (e.g., a grouper, which serves as host) of ectoparasites.
The large fish appears to have very strong barriers against feeding on the cleaners— the cleaner, which is comparable in size
to the ordinary prey of the larger fish, even works in the mouth of its customer. Cleaners are identified, for example, by their
swimming pattern. Species that mimic cleaners but instead bite off pieces of the fins of the large fish also exist.
This is certainly a reciprocal relationship—both species obviously benefit from it. But whether the benefit (e.g., of having
parasites removed) is large enough that this is a case of an interaction in both players' short-term interest is not immediately
obvious. An IPD model would have the property that a single defection by the large fish ends the game; it also fails to
include evolution of signals that are clearly important. (An example of a model of mutualism where recognition is included
is given by Weisbuch and Duchateau [102]).](https://image.slidesharecdn.com/28194266-250517172049-c19ec913/85/Artificial-Life-An-Overview-Christopher-G-Langton-34-320.jpg)
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Table 1. Payoff Matrix M for the Prisoner's Dilemma.
In the rest of this section, we concentrate on models of the evolution of cooperation based on the IPD. The previous
examples should, however, serve as a reminder that the PD by no means covers all aspects of the evolution of cooperation.
2.1 The Prisoner's Dilemma
The Prisoner's Dilemma (PD) provides a useful framework for studying how cooperation can become established in a
situation where short-range maximization of individual utility leads to a collective utility (welfare) minimum. This is a two-
person game where the players simultaneously choose between the two actions ''cooperate" and "defect," which we denote
by C and D (or equivalently 1 and 0).
The game was first studied by Flood and Dresher at Rand Corporation in 1950 [30]. (An account of the first iterated
Prisoner's Dilemma-like game played can also be found in Poundstone [85].) The name is derived from an anecdote by
Tucker, which goes more or less as follows:
Two persons have been caught, suspected of having committed a crime together. Unless one of them confesses, there is no
evidence to sentence them. The prosecutor offers a reward to the one that confesses; the other will in this case get a severe
sentence. If both confess, they will be imprisoned, but for a shorter time. If they stay quiet, they will be released in the
absence of evidence.
The results of the players' choices are quantified by the payoff matrix of Figure 1. Here R is the reward for mutual
cooperation (i.e., keeping quiet), and T is the temptation to defect against a cooperating opponent, who then gets the sucker's
payoff S. In the case of mutual defection, both get the penalty P. The PD is defined by the inequalities T > R > P > S and
2R > T + S. R = 3, T = 5, S= 0, and P= 1 is a common choice in the literature. The PD is a non-zero-sum game, that is, the
total score distributed among the players depends on the actions chosen.
If the game is only played once, a player maximizes her score by defecting, regardless of the move of the opponent. Thus,
two rational players share the lowest total payoff for mutual defection. This is the Nash equilibrium of economic
theory—none of the players is willing to change to cooperation.
If, on the other hand, the game is played more than once, that is, there is a high probability that a player encounters the same
opponent again, cooperating strategies may be more successful. (We assume that the objective is maximizing the score,
rather than beating the opponent.) This is the iterated Prisoner's Dilemma (IPD).
A computer tournament arranged by Axelrod [3-5,8] showed that a very good strategy is given by cooperating unless your
opponent defected in the previous round. This strategy that mimics the opponent's last action is called Tit-for-Tat (TfT).
For a game consisting of a known fixed number of rounds, the cooperative behavior is destabilized [87]. In the last round, the
single-round dilemma appears, and both players should defect—but then the same reasoning applies to the next to last round,
and so on. In this particular situation, defection is the unique Nash equilibrium. This](https://image.slidesharecdn.com/28194266-250517172049-c19ec913/85/Artificial-Life-An-Overview-Christopher-G-Langton-35-320.jpg)
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somewhat pathological behavior can be avoided by considering an infinitely iterated game or by choosing the number of
rounds stochastically.
One complicating factor in a repeated game is the possibility of mistakes by the players (noise). These could be either
mistakes where the action performed by a player is different from the intended one, or misinterpretations of the opponent's
action (which leads to the players seeing different histories).
Noise in the iterated game destroys the cooperative pattern between two TfT players. An accidental defection causes a
sequence of alternating revenges; another mistake can then result in either mutual cooperation or defection. In the infinitely
iterated game, the score for TfT playing against itself drops from R to (R + S + T + P)/4 for any non-zero noise level.
A strategy that defects only if the opponent defects twice in a row (Tit-for-two-Tats, Tf2T) is stable against a low noise rate
but can be exploited by a strategy that cooperates only every second round. Another possibility is the strategy called
Simpleton by Rapoport and Chammah [87]: change action if the score received in the previous round was less than R, that is,
cooperate when the actions of the previous round are identical. For an accidental defection D* during a period of mutual
cooperation, the players return to cooperation after a single round of mutual defection, that is, (. . ., CC, CC, CD*, DD, CC,
CC,. . .).
Whether this strategy can be exploited or not depends on the payoff matrix. When T + P < 2R (to 0th order in the mistake
probability Perr), defection scores less than cooperation against Simpleton; for the standard parameter values, equality holds,
and Simpleton can be exploited by uncooperative strategies.
The strategies discussed so far depend only on a finite portion of the history of the game. TfT, Simpleton, and Tf2T can be
classified in terms of the maximal number of history bits used by the strategy as memory 1, 2, and 3, respectively. They are
also deterministic, which means that the history determines the action uniquely. Some successful deterministic strategies of
higher memory will be discussed below.
A strategy that makes a stochastic choice of action with probabilities depending on the history is called probabilistic. A TfT-
like strategy that forgives defections with a suitably tuned probability can both resist exploitation and cooperate with its own
kind in a manner stable against accidental defections [69,75]. Probabilistic strategies with tunable random number generators
appear to be rare in nature, however.
The PD has been applied to explain the emergence of altruistic behavior in a number of situations, both in biology and in
human society.
Axelrod [5] discusses cooperative behavior between British/French and German soldiers in the trench warfare of World War
I. During the first years of the war, the same units faced each other for long periods, which placed them in a situation
reminiscent of an IPD, and a TfT behavior was established (quotation from Hay [37]): "It would be child's play to shell the
road behind the enemy's trenches, crowded as it must be with ration wagons and water carts, into a bloodstained wilderness .
. . but on the whole there is silence. After all, if you prevent your enemy from drawing his rations, his remedy is simple; he
will prevent you from drawing yours."
In many other applications to human society, it is natural to consider a similar game with a larger number of players—an n-
person PD. One situation where this occurs is in the sharing of a common resource (the tragedy of the commons), such as air
and water in an environmental context.
Another situation, where cooperation is a less desirable outcome, is an oligopoly consisting of a small number of firms that
sell almost identical products (such as coffee, gasoline, or airline tickets), and compete by adjusting prices (e.g., [57]). Two
strategy tournaments for this situation modeled by a three-person generalized PD with continuous actions were organized at
MIT by Fader and Hauser; see [28] for details.](https://image.slidesharecdn.com/28194266-250517172049-c19ec913/85/Artificial-Life-An-Overview-Christopher-G-Langton-36-320.jpg)
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Game theory [100, 101] has found a number of applications in biology [62]. Some cases where interpretations of altruistic
behavior in terms of the PD have been attempted are food (blood) sharing among vampire bats [103,104], interactions
between breeding adults and nonbreeders in tree swallows [53], and cooperative inspection of approaching predators in small
fish such as sticklebacks [66]. The identification of the game and strategy followed (e.g., [67,76]) is often somewhat
uncertain in these examples.
In biological applications of game theory, the analysis has often focused on finding evolutionarily stable strategies. An
evolutionarily stable strategy (ESS) [62] is a strategy that cannot be invaded by any other strategy present in arbitrarily small
amounts. (Other, less intuitive definitions involving invasion by a group of strategies also appear in the literature [13].) A
distinction is often made between the case where strategies exist that achieve equal scores to the strategy in question, and can
invade through genetic drift, and the case where a strategy dominates strictly.
In the PD, a number of results about ESSs are known: In the error-free case, no deterministic strategy or finite mixture of
such can be an ESS in the infinitely iterated game [13,29]; for general probabilistic strategies, the same result has been
shown except in the still open case of no discounting of the future [54]. When mistakes occur, ESSs can exist ([12]; see also
later).
An analysis of a system in terms of evolutionary stability should not be viewed as complete. Knowledge of the fixed points
of a dynamical system and their stability is not the same as a complete understanding of the system. The artificial life
perspective could contribute to a greater understanding of the evolutionary dynamics of many different systems.
Let us finally remark that in some of the evolutionary models discussed later, the PD provides not only a model of the
evolution of cooperation, but it also generates an interesting example of a complex coevolutionary landscape [44, 71], which
can serve as a simple prototype model for the study of coevolutionary phenomena.
2.2 Evolutionary Dynamics
Evolutionary dynamics can be imposed on the space of strategies by viewing strategies as interacting individuals in a
population. All pairwise interactions in the population could be included, or individuals could interact only with some subset
of the population, such as their neighbors in space. Through these interactions, each individual receives a score that
represents the success in the game. We can introduce population dynamics by letting successful strategies produce more
offspring in the next generation. If strategies are represented as individuals, births and deaths could be given by a stochastic
process. Species could also be represented by their population size; in this case the dynamics is given by a set of differential
equations.
An evolutionary process requires a mechanism for generating variation as well as a mechanism for selection. This can be
arranged by including mutations in the step where strategies are reproduced. The exact nature of these will depend on the
representation scheme used.
A number of evolutionary simulations of this type have been performed for the IPD: Axelrod [6] applied a genetic algorithm
(e.g., [38]) to evolve PD strategies of fixed memory length 6. The strategies played games of 151 rounds against eight
selected strategies from his tournament [5]. A coevolutionary simulation, in which the strategies played against each other,
was also discussed.
In another experiment, Miller [68] represented strategies as 15-state finite automata with 148-bit genotypes. Here a
coevolutionary model, where each generation was evaluated by playing all pairwise games, was studied more extensively. A
population of 30 individuals was followed for 50 generations; games consisted of 150 rounds. Three cases were studied:
perfect information, and a probability for misunderstanding](https://image.slidesharecdn.com/28194266-250517172049-c19ec913/85/Artificial-Life-An-Overview-Christopher-G-Langton-37-320.jpg)
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of 0.01 or 0.05. No successful error-correcting strategies were discovered, possibly because of the very short evolutionary
time scale of the simulations.
Several other experiments of this kind have been performed. (We are probably not aware of them all; we also do not attempt
to discuss models of dynamics in strategy spaces containing only a small number of strategies.) Interesting examples are, for
example, the work by Fujiki and Dickinson [32], who used a representation in terms of Lisp programs (a representation later
used by Koza in his genetic programming approach [46]), the work by Marks [57] where strategies for the three-person
generalized PD discussed earlier also were considered, and work by Fogel [31] which suggested that the initial moves in the
game may become a tag that allows strategies to recognize each other.
A model introduced by one of us [49] uses the infinitely IPD with noise as an interaction between individuals and considers
the evolution of deterministic finite memory strategies with an initial population containing only memory 1 strategies. The
memory length is allowed to change through neutral gene duplications and split mutations.
The genomes in the model represent strategies in the game, which determine the next move of a player given the history
h = ((x0, y0), . . ., (xt, yt)) of the game. Here (xt, yt) are the moves of the player and the opponent at time t. We consider
deterministic strategies of finite memory m > 0. For m even, the strategy depends on the last m/2 moves of both players; for
m odd on the last moves of the opponent and the last moves of the player herself.
If we let 1 denote the action C, and 0 the action D, a strategy of memory m can be represented as a binary string s of length
2m (see Figure 1).
In the reproduction of a strategy, three types of mutations can occur: point mutations, gene duplications, and split mutations.
Point mutations flip single bits in the genome with frequency Pmut. Gene duplications increase the memory from m to m + 1
(with frequency Pdupl) while leaving the actual strategy unchanged. This corresponds to duplicating the genome, for example,
1011 → 10111011. Gene duplication is a neutral mutation, which increases the size of the evolutionary search space without
affecting the phenotype. Additional point mutations can then give rise to new strategies without shorter memory equivalents.
Finally, the split mutation keeps only a randomly chosen half of the genome with frequency Psplit.
Each strategy i has a real-valued population size xi. The population densities evolve in time according to
(1)
where the term (identical to the average score of the population)
(2)
ensures that the total population stays constant.
The interaction coefficient gij is the score obtained when strategy i plays the noisy infinitely iterated PD against strategy j.
The infinite game can be viewed as a Markov chain of finite memory, which means that the result of the game can be
calculated analytically. (See Lindgren [49] for details.)
At each time step, mutations act in the way described previously. In this way new species can be introduced. Species are
removed from the system if their population falls below a threshold value.](https://image.slidesharecdn.com/28194266-250517172049-c19ec913/85/Artificial-Life-An-Overview-Christopher-G-Langton-38-320.jpg)
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Figure 1. The representation of strategies in the model of Lindgren [49]
is illustrated for the memory 3 strategy 0001 1001.
Figure 2. A typical simulation of the coevolving strategy model of Lindgren [49]; 30,000
generations of the simulation are shown.
A typical example of a simulation of the model is shown in Figure 2. In general, a succession of stable periods separated by
periods of rapid evolution are seen (reminiscent of punctuated equilibria [26]).](https://image.slidesharecdn.com/28194266-250517172049-c19ec913/85/Artificial-Life-An-Overview-Christopher-G-Langton-39-320.jpg)
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Cooperation can be observed at several levels in the model. The elementary actions C and D represent cooperation at the
lowest level. In an application of the PD, they would be an abstraction of behavior with a more interesting substructure. The
average score tends to increase in the time evolution (although not monotonically), which indicates an increasing degree of
cooperation at the level of elementary actions.
But we also observe cooperative behavior at the level of strategies. Consider, for example, the first period of stasis, where
TfT (01) and ATfT (10) coexist. This coexistence is possible because TfT suppresses invasion attempts by AllD (00), which
otherwise would outcompete ATfT, and similarly ATfT suppresses invasion attempts by AllC (11), which could outcompete
TfT. In other words, the strategies cooperate through indirect effects where one suppresses the predators of the other, and
vice versa. However, TfT and ATfT do not manage to get very high scores in the game.
The stable period at memory 3 is dominated by a symbiotic pair of strategies. This is an example of mutualism where the
strategies achieve a fairly high score by cooperating to correct errors [49], something they cannot do when interacting with
themselves.
The evolution of error correcting mechanisms is an interesting example of emergent higher level behavior in the model. The
first error-correcting strategy that appears in the simulations is 1001 or Simpleton, which was discussed earlier. In case of an
accidental defection, two strategies of this type return to cooperation after a single round of mutual defection. For the
standard payoff matrix, this behavior is too forgiving, and defectors can invade. A strategy that defects twice before
returning to cooperation, however, is sufficiently punishing to avoid exploitation.
This type of strategy requires memory 4 (a history of two rounds) and often appears as a very stable final state for the
standard parameter values (see Figure 2). We denote this strategy type sl; it is defined by fixing seven of the positions in the
genome to lxx10xxx0xxxx001, where the symbol x stands for undetermined actions that occur infrequently (order )
when sl plays itself. Several strategies that fit this template can in fact be shown to be ESSs (under reasonable assumptions
about the allowed class of invading strategies for the infinite game).
The choices of representation and adaptive moves in this model, of course, are not unique. Another choice was made in the
model studied by Ikegami [40], where strategies were represented as trees of unequal depth representing all contexts where
the strategy defects. Mutations included genetic fusion [43], where a tree is attached to a leaf of another. This choice of
representation favors the evolution of noncooperative strategies.
Probabilistic strategies could also be considered. Nowak and Sigmund [75,76] have studied the coevolution of probabilistic
strategies in the memory 1 and memory 2 subspaces, respectively.
Extensions of the simple PD model are also possible, for example, in the form of tags and signals, communication, and
control over whom to play. Stanley, Ashlock, and Tesfatsion [94] have studied evolution of strategies for the noise-free IPD,
where strategies have the option of choosing and refusing partners depending on the results of the games between them.
Models of the evolution of cooperation that go beyond the standard framework of the IPD, both by extending it and by
focusing more in detail on actual mechanisms of interaction and cooperation so that a PD appears implicitly, are certainly
worth pursuing.
2.3 Spatial Games
The fact that the physical world has three spatial dimensions did not enter into the evolutionary models discussed in the
previous section. In some cases, this may be a reasonable approximation—we could consider organisms mobile enough that
in a generation, all individuals in the population have time to interact with each other.](https://image.slidesharecdn.com/28194266-250517172049-c19ec913/85/Artificial-Life-An-Overview-Christopher-G-Langton-40-320.jpg)
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Table 2. Different Paradigms for Spatial Dynamics.
individuals
discrete continuous
space-time discrete CA CML
continuous Gas/Swarm PDE
But in general the environment may provide barriers so that different evolutionary paths can be explored in different regions
of the world, and it is essential to take spatial effects into account. In the context of explaining speciation, Mayr [63, 64] has
argued for the importance of spatial separation (see also [26]). A typical case would involve a small founder population
capable of rapid evolution separated off from the region inhabited by the majority of its species, for example, on an island.
The spatiotemporal dynamics of the system can also be important. Even in a homogenous environment, the dynamics of the
system could generate spatial structure, which could influence evolutionary processes. As an example, Boerlijst and
Hogeweg [10,11] studied a cellular automaton model of the hypercycle model of Eigen and Schuster [25] and found spiral
wave dynamics that increased the stability against parasites. Selection for certain altruistic properties (catalytic support and
faster decay rates) was observed—the introduction of spatial degrees of freedom allows localized structures to form, and
selection can take place at the level of these structures as well.
The spatial dynamics could also affect the stability of ecological systems and in that way influence evolutionary processes.
As an example, space-time chaos can allow locally unstable systems to persist with essentially constant global population
levels (e.g., [35]).
Several different ways of introducing spatial degrees of freedom can be imagined. In Figure 2.3 we have classified these into
four groups, depending on whether space and time are treated as continuous or discrete, and whether we consider separate
individuals or a continuous local population density.
Let us first consider the case with discrete individuals and discrete space and time. In this case we obtain models that are
essentially cellular automata (CA) (e.g., [107]) or lattice Monte Carlo simulations, depending on whether sites are updated
simultaneously or asynchronously in random order.
One class of lattice games is obtained in the following way: Let each lattice site be occupied by a single strategy; empty
lattice sites are not allowed. All lattice sites are updated simultaneously in the following manner: First, the score of a site is
calculated as the sum of the average scores obtained when the strategy at the site plays the infinitely iterated game against
the strategies in the neighborhood N1 (e.g., the four nearest neighbors on a square lattice).
The score of a site is then compared to the scores in a neighborhood N2 (e.g., the von](https://image.slidesharecdn.com/28194266-250517172049-c19ec913/85/Artificial-Life-An-Overview-Christopher-G-Langton-41-320.jpg)
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Figure 3. Species density curves from a simulation of the spatial version of coevolution
of strategies for the iterated PD discussed in the text. The first 10,000 generations of
the simulation are shown.
Neumann neighborhood consisting of the site itself and its four nearest neighbors), and the highest scoring strategy in N2 is
adopted at the site at the next time step. Ties are broken at random. In an evolutionary model, mutations can occur in the
reproduction.
Because the scores of the nearest neighbors in turn depend on the strategies of their neighbors, the strategy at a certain site is
updated depending on the strategies in a neighborhood of radius 2. If the set of allowed strategies is finite, the model is a
cellular automaton.
Cellular automaton models of this kind (with a fixed set of strategies and without evolution) were introduced by Axelrod [5].
He found that the ranking of the strategies submitted to his second tournament changed completely in the spatial case.
Complicated patterns of coexisting AllD and TfT players were also observed. In Nowak and May [72, 73] the dynamics of
the memoryless strategies AllC and AIID on a lattice was studied in more detail; in particular spatiotemporal chaos was
observed. A model closely related to a lattice PD was also studied in Wilson, Pollack, and Dugatkin [105].
A different approach to spatial games is to let all players on the lattice make simultaneous moves and to let strategies depend
on the actions in a neighborhood on the lattice, which gives a genuine n-person game. This approach has been investigated
by Matsuo and coworkers [58,1].
We [51] studied a spatial evolutionary model where the spatiotemporal dynamics was introduced as described earlier. The
representation of strategies and adaptive moves were identical to those of Lindgren [49] (see previous section).
Figure 3 shows an example of a simulation of this model. The payoff matrix is given by the standard parameter values
(R, S, T, P) = (3, 0, 5, 1), the error rate is Perr = 0.01, and the mutation rates are Pmut = 0.002, and Pdupl = Psplit = 0.001. In the
initial state, the four memory 1 strategies appear with equal probability. The lattice size is 128 x 128.
This simulation shows several important differences between the spatial model and the differential equation model discussed
above (see Figure 2), which from a physicist's perspective could be viewed as a mean-field approximation to the spatial
model. At memory 1, a frozen state of AIIC and AllD is found, where TfT is maintained at significant levels by spreading
waves of activity generated by mutations from AllD to TfT (see Figure 4d). At memory 2, the strategy 1001 (Simpleton)
takes over most of the lattice. The noncooperative strategies 00 and 0001 can coexist with 1001 at low](https://image.slidesharecdn.com/28194266-250517172049-c19ec913/85/Artificial-Life-An-Overview-Christopher-G-Langton-42-320.jpg)
![Page 25
levels by forming a network of mostly diagonal lines. In the mean-field model, the noncooperative strategy 0001 dominates
at memory 2; on the lattice this strategy can only exploit its nearest neighbors, and the cooperative strategy 1001 has an
advantage.
No analog of the symbiotic pair of strategies seen at memory 3 in Figure 2 is found in the spatial model. Memory 4 strategies
of type sl often appear on the lattice as well; in the simulation shown in Figure 3, we see two closely related memory 4
strategies of this type (sl and s2) appear, and then a similar memory 5 strategy s3. In many simulations, the strategy s3 takes
over the entire lattice and forms a homogenous state. In Figure 3, however, we find another strategy tl = 1001000000001111
and some closely related strategies that are able to coexist with s3. This coexistence is not observed in the mean field model.
An accidental defection in a game between two strategies of type t1 results in the sequence (..., CC, CD*, CC, DD, CC,
CC,...). The advantage of this pattern is that it reduces the score less than the error-correcting mechanism of, for example, s2
or s3. The strategy t1 is at the same time more resistant than 1001 to exploitation by defectors.
This example illustrates how the introduction of spatial degrees of freedom allows coexistence of strategies through the
formation of stable spatial domains.
For other values for the payoff matrix, a rich variety of dynamical behavior is observed. (See Lindgren and Nordahl [51] for
a detailed description.) Even if we restrict ourselves to the space of memory 1 strategies, a number of different regions of
qualitatively different spatiotemporal dynamics are found (typically with discontinuous transitions at the boundaries between
them). Some examples of fixed-time configurations from simulations with memory 1 are shown in Figure 4. The payoff
matrix can always be transformed to the normal form (R, S, T, P) = (1, 0, p, q); the standard parameter values correspond to
(p, q) = (5/3, 1/3). The behavior in this case is similar to Figure 4d.
Figure 4a has (p, q) = (1.4, 0.05). In this region we find spatiotemporal chaos involving AllD, TfT, and AllC. In Figure 4c we
have (p, q) = (1.9,0.8). Here we find rather irregular wave activity and expanding patches with all four memory 1 strategies
present. By decreasing q, we move into a region dominated by spiral waves (which break into smaller fragments because of
mutations) (see Figure 4b).
Varying the payoff matrix also affects the nature of the evolutionary dynamics. A tendency toward constancy of the
qualitative nature of the spatiotemporal dynamics during the evolutionary process is seen, so that one may, for example, have
strategies that evolve toward longer memory while the dynamics constantly is spatiotemporally chaotic [51].
One of the more important properties of the spatial model is its capacity to support a larger diversity of species than the
ordinary coevolution model. In particular, one can find very complex frozen states where a large number of different frozen
patches coexist.
These are somewhat reminiscent of plant communities. There are around 3 × 105 known plant species on earth, which all
depend on a quite small number of resources. This number is much larger than allowed by results based on ordinary
population dynamics, which limit the number of species in terms of the number of resources [48, 55]. Static explanations in
terms of varying equilibria in a heterogenous environment have been suggested (e.g., [96]). One may speculate that
dynamical processes could generate diversity even in a homogenous spatial system.
Another option for modeling the spatiotemporal dynamics is to keep the discrete spatial lattice and discrete time, but to
consider continuous population densities at each site. The sites could be coupled by diffusion. In this way one obtains a
coupled map lattice (CML) (e.g., [43]), possibly with a variable number of degrees of freedom at each site if some
mechanism for adding and deleting species is included. We have](https://image.slidesharecdn.com/28194266-250517172049-c19ec913/85/Artificial-Life-An-Overview-Christopher-G-Langton-43-320.jpg)
![Page 26
Figure 4. Examples of typical configurations from simulations with memory I strategies
and a payoff matrix given by (a) (p, q) = (1.4, 0.05), (b) (p, q) = (1.9,0.2),(c) (p, q) = (1.9,0.8),
(d) (p, q) = (1.4, 0.5). The coding of strategies is such that from light to dark we have the
order AllD, TfT, ATfT, and AllC.
studied a one-dimensional model with a copy of the model of Lindgren [49] at each site [50]. For the standard payoff matrix,
the dynamics of this system is rather similar to the mean-field model—successful new strategies typically propagate and take
over the entire lattice as soon as they are discovered at one site.
The third option for modeling spatiotemporal dynamics is in terms of partial differential equations (PDE). For a finite
number of strategies, one could consider the reaction-diffusion-like system obtained by adding a diffusion term to equation
1:
(3)](https://image.slidesharecdn.com/28194266-250517172049-c19ec913/85/Artificial-Life-An-Overview-Christopher-G-Langton-44-320.jpg)
![Page 27
Finally, we have the case of moving or diffusing individuals in continuous space. (A case suitable for a Swarm
simulation—studies of systems with strategies for motion as well as the game, e.g, avoidance behavior, would be particularly
interesting.) We are not aware of any simulation of a spatial game of this kind.
Some recent work in the biology literature, however, is closely related—Enquist and Leimar [27] discussed a system where
individuals form temporary associations while playing the game. Defectors are rejected after a short time compared to the
average duration of a game between two cooperators and then search for a new partner to exploit. As expected, increased
mobility favors defectors, which then more easily can find a new victim. Data from sphecid wasps, where in some species
females cooperate by sharing nests, show that cooperation is less likely in species that form large population aggregations,
which lowers the search time for defectors.
Unfortunately these authors only consider a mean-field approximation, not the actual spatial system, and only discuss the
relative stability of a few chosen strategies instead of performing an evolutionary simulation. If an actual spatial system with
local reproductive dynamics was studied, it is conceivable that domain formation could occur, so that mean field theory
would not be a good approximation. This would favor cooperation.
3 Artificial Community Structure
Are ecological communities structured entities or just random collections of species that respond independently to the
environment? Questions of this kind can be addressed through field studies of real ecosystems, through laboratory
experiments that assemble artificial ecologies of real organisms and by making mathematical models.
In our opinion, there is also a niche for artificial life in the study of community structure. By creating artificial ecologies out
of artificial rather than real organisms, many constraints on real experiments and field studies can be circumvented. Real
ecological studies are severely limited in space and time. (See Pimm [82] for a discussion of time and length scales
accessible and nonaccessible in ecological, biogeographical, and paleontological studies.) Given enough computer resources,
artificial ecologies could be studied on a much wider range of scales. Artificial ecosystems can also be manipulated in many
ways that are impossible for real communities.
On the other hand, compared with simple mathematical models, which may summarize the interaction between two species
in terms of two real numbers as in the Lotka-Volterra approach, artificial ecologies could capture much more of the
complexity of interactions in real biological systems. Individual variability can enter in a natural way; learning and
individual adaptation can also be included.
As an example of the complexity of interactions, think of herbivores interacting with a plant community [41]. Not only do
plants and trees provide food for the herbivore, they also provide shelter from sun and wind, escape routes and places to hide
from predators, and branches and twigs to make nests and squats from. The grazing of herbivores also affects the plant
community: Defoliation can stimulate grasses and trees to produce more leaves; dispersal of fruits, nuts, and seeds by
herbivores may affect the spatial structure of the plant community. Apart from direct interactions, herbivores may interact
indirectly with other herbivores through their effects on the vegetation, both by reducing resources for other species and by
providing access to them (e.g., when elephants fell whole trees). Other indirect interactions may involve changing the risk of
predation for other species. Larger species avoid predators by detecting them at a distance and benefit from reduced cover.
On the other hand, smaller species that avoid predators by hiding would benefit from increased cover.](https://image.slidesharecdn.com/28194266-250517172049-c19ec913/85/Artificial-Life-An-Overview-Christopher-G-Langton-45-320.jpg)
![Page 28
A crude classification of the interactions between species would label interactions depending on the signs of the couplings in
an imagined set of Lotka-Volterra equations: predation, competition, and mutualism (if one assumes that all couplings are
nonzero). In many cases, studies of community structure take only who-eats-whom into account for a number of exceptions
(see Kawanabe et al. [45]). Our own approach has been rather different: Starting out from models of the evolution of
cooperation, which provide complex interactions between individuals, we then attempt to extend the model to describe
predation and resource flow.
In the next two sections, we discuss food webs and simple models of community structure. However, our own goal is not to
make models of food webs. Instead, we attempt to build simple artificial ecologies with some degree of biological
plausibility, and food webs are only one example of observables that could be measured (although a rather useful example,
because a reasonable amount of experimental data exist, and a number of statistical regularities in the data have been
suggested; see section 3.1).
Another issue that needs to be considered if artificial life models are going to make contributions to biology is that of
physical realism. Real ecosystems are subject to constraints such as conservation of energy and matter. Many biological
scaling laws that involve the body size of organisms (see, e.g., Johnson [42] for an overview) have a physical basis, even if
they are not directly derivable from physical scaling.
In the coevolving strategy models of the previous section, there are no obvious conserved quantities, and who-eats-whom to
some extent becomes a matter of interpretation. In principle, these models could be equally relevant to ecology, but
observables related to energy flow are not easily studied. In section 3.3, we describe a model where resources are derived
from an external environment, and the result of a game determines their distribution. We also discuss other artificial life
models where resources have been explicitly included.
3.1 Food Webs
A food web is a graphical representation of who-eats-whom in an ecological community. In most cases food webs are
compiled in a qualitative way by ecologists, so that a (directed) link from A to B is present if and only if species B eats
species A. Quantitative data showing the relative importance of different links can sometimes also be found in the literature.
An example of an experimental food web from the literature is shown in Figure 5 (redrawn from Niering [70]), which shows
the most significant feeding relationships among the species on the Kapingamarangi Atoll in Micronesia. This web has some
features in common with many reported webs. Many species with similar feeding habits have been clustered into groups
(e.g., insects), and there is a cutoff so that rare trophic links are not included (as an example, the fact that Polynesian rats
occasionally feed on newly hatched sea turtles is not included).
A food web is obviously not a complete description of the community or even of the resource flow in the system. But food
webs may still be useful observables to consider, both for real and artificial ecologies. A number of statistical regularities
have been claimed to exist in the structure of food webs (e.g., [16, 81]):
• The average number of trophic links L is approximately proportional to the number of species , where is
small.
• The fractions of top predators, intermediate species, and basal species are approximately constant across webs.
• The fractions of trophic linkages of different types: top-intermediate, top-bottom,](https://image.slidesharecdn.com/28194266-250517172049-c19ec913/85/Artificial-Life-An-Overview-Christopher-G-Langton-46-320.jpg)
![Page 29
Figure 5. Food web from the Kapingamarangi atoll in Micronesia,
drawn using the data of Niering [70].
intermediate-intermediate, and intermediate-bottom are also approximatively constant across webs.
• Averages of maximal food chain length are typically fairly low (approximately 3-4) and do not appear to depend on the
productivity of the environment [80]. On the other hand, they do depend on the dimensionality of the environment; three-
dimensional environments, such as pelagic water columns and forest canopies, appear to have longer food chains than do two-
dimensional environments, such as grasslands and intertidal zones.
• Cycles are rare. Food webs in the literature typically do not include cycles due to cannibalism or cycles due to the
presence of decomposers.
• Food webs can often be represented as interval graphs, that is, graphs that represent how a set of subintervals of the real
line overlap each other.
Critiques of food web theory can be found, for example, in Paine [77] and Polis [83]. Most published food webs contain a
fairly limited number of species, and trophically similar species are often considered as groups. Experimental studies that
reflect more of the complexity of real ecosystems (e.g., [83, 106]) are likely to change some of these conclusions.
An example of a recent experimental study that disagrees with the link-species scaling law is the work by Havens [36],
where power law scaling with was found in a study of communities in small lakes and ponds. In this case the
webs were resolved down to genus and species, but the interactions were not measured. Instead, diet information from other
sources was used, which makes comparisons with other studies difficult. Multivariable scaling that also involves resolution
should be investigated in this context.
The study of artificial ecologies might be useful in sorting out which regularities are real and which are artifacts of
experimental procedures, because data are more easily available, and the artificial ecosystems can be freely manipulated.](https://image.slidesharecdn.com/28194266-250517172049-c19ec913/85/Artificial-Life-An-Overview-Christopher-G-Langton-47-320.jpg)
![Page 30
In these cases, quantitative comparisons between real and artificial communities can be made via scaling laws. There are
other types of statistical regularities in ecological systems where similar comparisons can be made. One of the most well
known is the area-species law (e.g., [56]), a power law for the number of species on an island as a function of its area, S ~ c
× Az, with an exponent z » 0.3. (The exponent does not appear to be universal.) Under certain assumptions, this power law
can be related to a log-normal distribution of population abundances [61, 86]. Regularities in the patterns of resource flows
have also been suggested [65].
3.2 Community Models
In this section we briefly discuss some food web and community assembly models that have been studied in the literature.
These models fall into two classes: One could consider only static patterns (e.g., food webs), or one could attempt to model
the dynamic process that creates these patterns.
An example of a model of the first kind is the cascade model of Cohen et al. [15,16]. This model essentially assumes that
food webs are random feed-forward networks. This allows many of their statistical properties to be calculated analytically.
No dynamics is involved, just assumptions about the probability measure on the space of webs (although extensions
involving population dynamics have been studied [17]).
The work by Gardner and Ashby [33], May [59, 60], and others on the relation between complexity and stability led to some
work on the dynamics of communities. If large systems with randomly generated interactions between species typically are
unstable (as claimed by May), is it possible that communities generated by more realistic assembly processes would be more
stable?
A number of authors (e.g., [84, 89, 90, 97, 108]) studied models where species were removed from and/or added to the
system according to various principles (which unfortunately did not include integration of the population dynamics).
Increased stability was typically found. Only more recently has integration of the Lotka-Volterra equations been used in this
context [95]. Comparisons between communities structured by invasion and by coevolution were also attempted [91, 92].
More recent work (both theoretical and experimental) by Drake and others [20-23, 74, 82] has focused more on the dynamics
of the assembly process. Are there multiple attractors for the assembly dynamics depending on the order in which species are
introduced? What is the distribution of local extinction events caused by invasion, and is there a connection to self-organized
criticality?
The interactions between species in these models are in many cases obtained by choosing invading species at random from a
large, predefined food web. In artificial life models, one would in most cases design a reasonable interaction between species
in a simple artificial world; a food web then emerges in a natural way from the underlying interaction (if one assumes that it
includes some type of predation). Such models could also enable us to study the interplay between coevolution and spatial
dispersal of species without making too many oversimplifying assumptions.
3.3 Artificial Ecologies
Models such as the coevolving strategy model described earlier can be interpreted as very simple artificial ecologies, where
the result of the game directly determines the interaction between species. However, as we have pointed out before, the
notions of resources and conservation laws are missing in these models (as well as in various coevolutionary landscape
models [9, 44, 71]).
Explicit resource flows do appear in a number of artificial life models. Some of these may still not have any immediate
ecological interpretation, for example, in the case of more ambitious models where the notion of individuality is intended to
be an emergent](https://image.slidesharecdn.com/28194266-250517172049-c19ec913/85/Artificial-Life-An-Overview-Christopher-G-Langton-48-320.jpg)
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Figure 6. The food web and energy flow matrix after 33,600 generations in a simulation of model I
of Lindgren and Nordahl [52]. The first part of the histogram represents energy inflows from the environment
(always positive); the second energy flows between species (signs depend on the directions of the flows).
The open bars show the energy dissipation for each species. The magnitude of the flow is shown relative
to the total energy flow for the species in question.
property rather than being imposed from the outside (as in the models of Rasmussen and coworkers [87]). Examples of
models with a more direct ecological interpretation include the models of Lindgren and Nordahl [52], Holland's Echo
[38,39], the model studied by Johnson [42], and many more.
The interactions between individuals in the first model of Lindgren and Nordahl [52] (Model 1) are still based on the iterated
Prisoner's Dilemma, but the result of the game now determines the distribution of a resource e (''energy"). Each strategy
stores a certain amount of energy; the energy transfered in the interaction between two strategies is proportional to the score
difference in the game between them (up to cutoff terms).
The system lives in an external environment consisting of a number of fixed strategies; energy can flow into the system as a
result of playing the game against the environment strategies.
The conservation of energy in the interaction turns the game into a zero-sum game. The cooperative effects of the PD are
reintroduced by letting the dissipation of energy for each species depend on the score in the game, so that high-scoring
strategies utilize their resources more efficiently.
Figure 6 shows an example of a food web and matrix of energy flow between species generated in a simulation of this
model. The species seen in the web are trophic species, that is, equivalence classes of genomes that interact in approximately
the same way with all other genomes. Some of the proposed statistical features of real food webs, such as the approximately
linear link-species scaling, are nicely reproduced by the model (see Lindgren & Nordahl [52]).](https://image.slidesharecdn.com/28194266-250517172049-c19ec913/85/Artificial-Life-An-Overview-Christopher-G-Langton-49-320.jpg)
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In te second model of Lindgren and Nordahl [52], the genomes consist of three parts: a strategy gene, a gene that indicates
preferences for whom to play, and a tag gene on which other organisms base their choice. In this way a more distinct
difference between genotype and phenotype is introduced—the tag gene can be regarded as the "visual appearance" of an
organism. This model allows species to develop a higher degree of specificity in their dietary preferences. It also allows the
evolution of phenomena such as camouflaged predators that hide among the environment strategies, and mimicry.
Introducing spatial degrees of freedom is at least as important in these models as in the ordinary model for coevolution of
strategies. With a model that allows interactions with an external environment, phenomena that depend on having a
heterogenous environment can be modeled. Extensions to cases with several different resources would also be interesting.
These models are rather similar in spirit to Holland's Echo [38, 39]—we use a more complex interaction between individuals
(the IPD instead of simple pattern matching); Echo, on the other hand, has more emphasized multiple resources.
Another simpler model where hierarchical food webs are observed is that of Johnson [42]. This model incorporates some
physical constraints by assigning a body size to each organism. The movement rate and metabolic costs scale as (externally
imposed) power laws as function of body size. Organisms have genetically determined food preferences among the species
smaller than the organism itself. The dynamics of the system is a Monte Carlo simulation, where individuals interact and
move by diffusion on a lattice. This model could be viewed as a natural way of extending the cascade model of Cohen et al.
to a dynamical system with discrete individuals.
4 Discussion
The problem of understanding the evolution of cooperation (at least when covered by the IPD) is a case where methods that
could be classified as artificial life, in particular coevolutionary simulations, already have yielded significant results. We
believe that in the future, an understanding of the underlying evolutionary dynamics will be reached for many biological
problems. All problems that today are analyzed in terms of game theory and ESS are obvious candidates, but also many
other problems where this approach is less suitable. The evolution of flocking behavior in birds is one example. In the case
of understanding community structure, the ability to perform a large number of simulations and to sort out statistical patterns
will be important.
Acknowledgments
This work was supported by the Swedish Natural Science Research Council.
References
1. Adachi, N., & Matsuo, K. (1992). Ecological dynamics of strategic species in Game World. FUJITSU Scientific and
Technica lJournal, 28, 543-558.
2. Andersson, M. (1984). The evolution of eusociality. Annual Review of Ecology and Systematics, 15, 165-189.
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6. Axelrod, R. (1987). The evolution of strategies in the iterated Prisoner's Dilemma. In: L. Davis (Ed.); Genetic algorithms
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7. Axelrod, R. (1986). Evolutionary approach to norms. The American Political Science Review, 80, 1095.
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11. Boerlijst, M. C., & Hogeweg, P. (1991). Self-structuring and selection: spiral waves as a substrate for prebiotic evolution.
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18. Creel, S. (1993). Why cooperate? Game theory and kin selection. Trends in Ecology and Evolution, 8, 71-72.
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![eseguite ne' tempi favorevolissimi giungono più presto a caricare un
quadro di ampia superficie, od una batteria, per la ragione che il
fuoco vi cola incessantemente: laddove nel nuovo apparecchio
spiccando le scintille con quella interruzione, che porta l'abbassare, e
rialzar lo scudo, più tardi ci si perviene. Ho detto ne' tempi
favorevolissimi: perchè poi sono gli effetti dell'Elettroforo sì vivi
anche ne' tempi men propizj, che vuolsi bene spesso preferire un
simile apparato che sia grande, per l'oggetto pure di caricare quadri,
e batterie, alla macchina di vetro ordinaria, da cui le molte volte si
pena a cavar partito. Oltre di che io credo non sarà difficile col
tempo immaginare de' mezzi per ottenere cotesto necessario
accostamento, e discostamento dello scudo più speditamente, e con
un moto uniforme, e con minor incomodo. Dirò anche che sto per
metter mano ad un meccanismo assai semplice onde venirne a capo.
Una molla, che al premere della mano, od al girar d'una cordicella o
staffa, alzi, ed abbassi lo scudo, promette di dispensarmi da molta
parte d'incomodo. Oppure in altra forma lo scudo portato da un
pendolo, cui dia moto una ruota, e un peso, e che vada a baciare a
destra, e a sinistra due piatti, ossia faccie di mastice elettriche, e così
andando, e venendo incontri nel mezzo da salutare con le scintille un
conduttore, o la caraffa, mi rappresenta un doppio apparato, che per
la ragione della celerità de' movimenti potrà darmi effetti molto più
che duplicati.
Ma infine io dichiaro col miglior cuore che non ho l'abilità di riuscir
bene in simili costruzioni meccaniche; che d'altra parte non è questo
il mio scopo principale; e che per quanto io tenga conto, e lo
tengano tutti quelli, innanzi a cui ho mostrate in esteso l'esperienze,
dei comodi che ne offre l'Elettroforo, io valuto assai più i lumi che mi
si vanno svolgendo su diversi punti della teoria elettrica: intorno a
che pubblicherò fra non molto le mie osservazioni già in parte
comunicate al Signor Dottor Priestley[35].](https://image.slidesharecdn.com/28194266-250517172049-c19ec913/85/Artificial-Life-An-Overview-Christopher-G-Langton-58-320.jpg)
![ARTICOLI DI TRE LETTERE[36]
Scritte al Sig. Canonico Fromond.
Como 26 Ottobre 1775.
Aspetto con impazienza le osservazioni vostre sulla migliore struttura
dell'Elettroforo. Intanto vi darò io nuova della riuscita di quello che
ho ultimamente terminato di legno del diametro poco meno di due
piedi. In questi due ultimi giorni che spira una forte tramontana ho
ottenuto scintille a dieci, dodici, ed anche quattordici diti trasversi:
v'immaginate com'erano guizzanti. Per averle di questa forma
presento non più la nocca, ma la punta del dito. Sovente in luogo
della scintilla esce dal dito un grandissimo fiocco, collo scoppiettar in
seguito di più scintille succedentisi. È tale la forza, e la copia del
fuoco, che le punte metalliche affatto ottuse, come d'una chiave,
anzi l'anello di essa, e fin le palle, se non sono affatto grosse, fanno
appunto l'officio di punte, e gettano il fiocco. Che più? Tre sole
scintille dello scudo caricano una mezzana caraffa a dare una scossa
penosa; e dieci in dodici la sopraccaricano a segno di scaricarsi
spontaneamente.
Como 14 Novembre 1775.
Vi ho detto già come pensava d'or in avanti di costruire l'apparato
portatile, per avere in un egual volume assai maggiore capacità. In
luogo di stendere il mastice sopra un piatto, lo stendo nella cavità
d'un emisfero, dando poi allo scudo la stessa conveniente figura.
Trovo anche meglio dell'emisfero divisato un cono troncato, che può
essere lungo benissimo d'un palmo, e largo quanto porta l'apertura
della tasca: un'altro cono ch'entri nella cavità del primo mi fa l'ufficio](https://image.slidesharecdn.com/28194266-250517172049-c19ec913/85/Artificial-Life-An-Overview-Christopher-G-Langton-59-320.jpg)
![LETTERA
Al Sig. Giuseppe Klinkosch.
R. Consigliere, Pubblico e Primario Professore di Anatomia
nell'Università di Praga, e Membro della Reale Società delle Scienze
di Gottinga.
Maggio 1776.
Ho ricevuto alcune settimane sono sotto coperta a me diretta, e
marcata dell'officio di Praga uno scritto tedesco, che tratta in parte
del mio Elettroforo perpetuo. Siccome ho fermo nell'opinione, essere
l'autor medesimo, che abbia voluto obbligarmi coll'inviare a me
questa operetta; così mi credo permesso di trasmettergli io pure
alcuni fogli italiani da me pubblicati l'anno scorso in un'Opera
periodica concernenti il medesimo Elettroforo. Non senza difficoltà
ho io potuto intendere, Signore, cotesto vostro tedesco, attesa la
poca cognizione, che ho di cotal lingua; di che mi duole pur assai. Se
voi trovaste mai la medesima difficoltà rispetto al mio italiano,
starebbero tra di noi le cose pari. Se non che io voglio pur procurare
di rendermi, o più scusabile, o ben anche più benemerito di voi,
accompagnando i fogli impressi con alcuna cosa scritta di mia mano,
e alla meglio che mi verrà fatto in una lingua, che non è la vostra nè
la mia, ma che saravvi senza dubbio più famigliare che l'italiana[37].
Non mi sorprende punto, Signore, che voi stimiate dover diffalcar
molto da quel merito, e vanto dell'Elettroforo, che il volgo de' Fisici,
siccome voi dite, troppo precipitosamente gli ha accordato.
L'ammirazione, che molti ne presero ha oltrepassato, e quello ch'io
poteva a buon dritto pretendere, e ciò che avrei mai potuto sperare.](https://image.slidesharecdn.com/28194266-250517172049-c19ec913/85/Artificial-Life-An-Overview-Christopher-G-Langton-69-320.jpg)
![non già di tutte, e nullamente delle sue Teorie, cui ho avuto sempre
in mira di oppugnare rispetto ad uno de' precipui capi (ciò che anche
mi provai di fare nella lettera latina menzionata), e cui mi applico
presentemente più di proposito a riformare, come già accennai.
Ritornando ora al mio apparato, mi pare aver lasciato abbastanza
intendere, che io ne riduco tutta la novità, per quanto è della sua
costruzione, alla miglior foggia d'armatura, ed allo strato resinoso
sostituito alla lastra di vetro: quanto poi sia degli effetti, all'intensità
costante dei segni elettrici, e vera perennità di essi: ciò che vale ad
esprimere per se solo il nome di Elettroforo perpetuo. Non deggio
però dissimulare le opposizioni, che intorno a ciò sò essermi state
fatte; e sono: che la disposizione propria dei corpi resinosi ben più
che del vetro a ritenere l'elettricità, è stata osservata, e conosciuta
gran tempo prima di me da Grey, Du-fay, Epino ec.: che quest'ultimo
inoltre in compagnia di Wilke ci avea dato l'esempio di un vero
Elettroforo con quel bellissimo esperimento dello zolfo fuso in una
coppa di metallo, ond'egli traeva i segni elettrici sì dal recipiente,
come dal corpo di zolfo, ogni volta che ne li disgiungeva: e ciò anche
dopo settimane, e mesi.
Nulla io ho a ridire riguardo a questa anteriorità di tempo; ciò che
posso assicurare si è, che non son già io partito dalle sperienze di
Wilke o d'Epino (delle quali non era nemmanco informato) per
giugnere alla costruzione del mio apparato; bensì partii da quelle,
che si faceano comunemente per la Vindice Elettricità servendosi di
lamine di vetro: quì veramente io seguiva le sperienze di Beccaria ad
oggetto di confutare, come ho sopra indicato, un fondamento della
sua teoria; e così dietro ai miei principj fui condotto primieramente a
dar una forma più convenevole all'armatura, onde ottenere valida, e
intiera forza d'elettricità[38]; e ben tosto a sostituire le resine al vetro
acciò mi si mantenessero più durevoli i segni; richiamandomi allora
come io mi era già assicurato della disposizione singolare, che hanno
questi corpi di conservare tenacemente l'elettricità impressa; e
rivolgendo pure in mente le idee, onde io mi era argomentato di
spiegare questa tenacità medesima in una lettera al Dr. Priestley fino
dal Maggio del 1772[39].](https://image.slidesharecdn.com/28194266-250517172049-c19ec913/85/Artificial-Life-An-Overview-Christopher-G-Langton-72-320.jpg)
![Iacquet[40], nella quale niente trovo detto di questa importante
operazione della boccetta, sia ad oggetto di rianimare per se stessa
l'elettricità indebolita, ed innalzarla al più alto grado d'intensità, sia
per renderla realmente perpetua. Egli però nulla verisimilmente
veduto avea di quanto erasi da me scritto, e pubblicato, e non
conosceva l'Elettroforo, che sul rumore pervenutogliene, e dietro
alcune poche sperienze di fresco da lui fatte. Non so attribuire ad
altra cagione che questa, da una parte la confidenza, con cui parla di
qualche fenomeno come fosse da lui scoperto, dall'altra il silenzio
tenuto riguardo a tante altre sperienze, di cui io avea dato il
dettaglio. Non vi si parla punto della maniera di animare un con
l'altro una serie di Elettrofori; nè della facilità di cambiare a talento,
ossia rovesciare l'elettricità sullo strato resinoso: niuna parola della
sua mirabile tenacità, che regge non che a dispetto d'un'aria
vaporosa, ma all'insulto dell'alito della bocca; nulla del mezzo
singolare di spegnerla cotesta ostinata elettricità ec. Torno a dire,
non son punto soddisfatto del ragguaglio, che il Sig. Ab. Iacquet si è
accinto a dare del mio Elettroforo, comechè egli ne abbia molto
innalzato il pregio, dichiarandolo un nuovo apparecchio, che
stordisce i più abili Elettrizzanti. Riconosco che questa espressione è
alquanto esagerata: e apprendo da voi, Sig., che lo stordimento non
fu, nè è di tutti, conciossiachè abbiate saputo tenervene voi così in
guardia, che preso non ne rimaneste. Avete fatto ancor più: sorto
siete colla vostra lettera stampata a fare svenir cotesto abbagliante
stupore dagli occhi pure dei prevenuti; e io non dubito punto, che la
riputazion grande di cui godete, non abbia prodotto l'effetto preteso,
e forse, chi sa? oltre il giusto. Non intendo quì parlare della scoperta
dell'Elettricità vindice: ho abbastanza palesato sopra ciò i miei
sentimenti, cioè, che ben lungi di dolermi con voi d'alcun torto, ho
occasione anzi d'esservi tenuto. Mi lagno soltanto di ciò, che questo
vostro scritto tende di più a diminuire il pregio dell'Elettroforo, preso
anche in qualità di semplice apparecchio, o stromento, giacchè ne lo
fa comparire senza il corredo de' suoi più singolari vantaggi: mi
lagno, dico, unicamente dello scritto, non già di voi, Signore, cui fo la
giustizia di credere, che non avete voi cercato di celare questi](https://image.slidesharecdn.com/28194266-250517172049-c19ec913/85/Artificial-Life-An-Overview-Christopher-G-Langton-75-320.jpg)
![DEI CONDUTTORI ELETTRICI[41]
Da molto tempo io mi era proposto di lavorare a un'Opera
sull'Elettricità, in cui avrei ridotto la massima parte de' fenomeni
all'azione, e giuoco delle atmosfere elettriche. Molte altre
occupazioni, e ricerche di genere diverso me ne hanno distolto: non
ne ho però deposto il pensiero. Ma perchè io vedo che la cosa potrà
andare in lungo, e Voi già mostraste desiderio, o Signore, che io vi
facessi parte delle mie idee, ed osservazioni, ho pensato intanto di
soddisfarvi in qualche maniera, staccando dal resto questa particella
che può in certo modo stare da se; le altre cose tutte essendo così
legate, che non potrebbero una senza l'altra, e senza l'intiero
complesso, essere, nè spiegate a dovere, nè abbastanza intese.
§. 1. Della capacità dei Conduttori Elettrici.
È stato dimostrato, e niuno più de' Fisici Elettrizzanti dubita, essere
la capacità de' Conduttori in ragione non già della massa, ma del
volume, e superficie di essi. Tralle altre la bella, e originale sperienza
di Franklin della catena ammucchiata, e accolta in un catino
elettrizzato, la quale quando esce fuori, e si dispiega nell'aria
accresce capacità al Conduttore, e come vi ricada ne lo riduce
all'angusta capacità di prima[42] ma singolarmente, e soprattutto le
sperienze fatte intorno al così detto pozzo elettrico di cui Voi foste il
primo, o Signore, a darci una bella analisi[43], ci fan vedere, e toccar
con mano come l'elettricità sull'esterna faccia solamente de'
Conduttori si dispieghi[44]. Quindi è che nelle nostre macchine per
uso de' Conduttori comodi a un tempo, e capaci soglionsi in oggi
adoperare grossi cilindri, e sfere vuote d'ottone (giacchè il fargli](https://image.slidesharecdn.com/28194266-250517172049-c19ec913/85/Artificial-Life-An-Overview-Christopher-G-Langton-79-320.jpg)
Artificial Life An Overview Christopher G Langton
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- 5. Page i Artificial Life Page ii Complex Adaptive Systems John H. Holland, Christopher Langton, and Stewart W. Wilson, advisors Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence John H. Holland Toward a Practice of Autonomous Systems: Proceedings of the First European Conference on Artificial Life edited by Francisco J. Varela and Paul Bourgine Genetic Programming: On the Programming of Computers by Means of Natural Selection John R. Koza
- 6. From Animals to Animats 2: Proceedings of the Second International Conference on Simulation of Adaptive Behavior edited by Jean-Arcady Meyer, Herbert L. Roitblat, and Stewart W. Wilson Intelligent Behavior in Animals and Robots David McFarland and Thomas Bösser Advances in Genetic Programming edited by Kenneth E. Kinnear, Jr. Genetic Programming II: Automatic Discovery of Reusable Programs John R. Koza Turtles, Termites, and Traffic Jams: Explorations in Massively Parallel Microworlds Mitchel Resnick From Animals to Animats 3: Proceedings of the Third International Conference on Simulation of Adaptive Behavior edited by Dave Cliff, Philip Husbands, Jean-Arcady Meyer, and Stewart W. Wilson Artificial Life IV Proceedings of the Fourth International Workshop on the Synthesis and Simulation of Living Systems edited by Rodney A. Brooks and Pattie Maes Comparative Approaches to Cognitive Science edited by Herbert L. Roitblat and Jean-Arcady Meyer Artificial Life: An Overview edited by Christopher G. Langton
- 7. Page iii Artificial Life An Overview edited by Christopher G. Langton A Bradford Book The MIT Press Cambridge, Massachusetts London, England Page iv Fourth printing, 1998 First MIT Press paperback edition, 1997 © 1995 Massachusetts Institute of Technology All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher. Printed and bound in the United States of America. Library of Congress Cataloging-in-Publication Data Artificial Life: an overview / edited by Christopher G. Langton. p. cm.—(Complex adaptive systems) "A Bradford Book." Includes bibliographical references (p. ) and index. ISBN 0-262-12189—1 (HB), 0-262-62112-6 (PB) 1. Biological systems—Computer simulation. 2. Biological systems—Simulation methods. 3. Artificial Intelligence. I. Langton, Christopher G. II. Series. QH324.2.A74 1995 574'.01'13—dc20 94-46217 CIP
- 8. Page v Contents Foreword vii Editor's Introduction ix Artificial Life as a Tool for Biological Inquiry Charles Taylor and David Jefferson 1 Cooperation and Community Structure in Artificial Ecosystems Kristian Lindgren and Mats G. Nordahl 15 Extended Molecular Evolutionary Biology: Artificial Life Bridging the Gap Between Chemistry and Biology P. Schuster 39 Visual Models of Morphogenesis Przemyslaw Prusinkiewicz 61 The Artificial Life Roots of Artificial Intelligence Luc Steels 75 Toward Synthesizing Artificial Neural Networks that Exhibit Cooperative Intelligent Behavior: Some Open Issues in Artificial Life Michael G. Dyer 111 Modeling Adaptive Autonomous Agents Pattie Maes 135 Chaos as a Source of Complexity and Diversity in Evolution Kunihiko Kaneko 163 An Evolutionary Approach to Synthetic Biology: Zen and the Art of Creating Life Thomas S. Ray 179
- 9. Beyond Digital Naturalism Walter Fontana, Günter Wagner, and Leo W. Buss 211 Learning About Life Mitchel Resnick 229 Books on Artificial Life and Related Topics David G. Stork 243 Computer Viruses as Artificial Life Eugene H. Spafford 249 Page vi Genetic Algorithms and Artificial Life Melanie Mitchell and Stephanie Forrest 267 Artificial Life as Philosophy Daniel Dennett 291 Levels of Functional Equivalence in Reverse Bioengineering Stevan Hamad 293 Why Do We Need Artificial Life? Eric W. Bonabeau and Guy Theraulaz 303 Index 327
- 10. Page vii Foreword Christopher G. Langton Editor-in-Chief Santa Fe Institute This book is intended as a high-level index to the Artificial Life enterprise. It provides a point of entry to the field for both the newcomer and the seasoned researcher alike. The essays in this book introduce the many subdisciplines of Artificial Life and organize a large body of citations to the literature in the field. I would recommend this book as an excellent text for a graduate seminar on Artificial Life, accompanied by readings drawn from the citations tailored to the professor's or the student's interests. As Artificial Life is a highly interdisciplinary field, drawing researchers from across the academic and scientific spectrum, the authors have made an extra effort to make their essays comprehensible to readers from outside their own particular disciplines. They have defined technical terms where needed and provided background motivation for techniques and approaches that might otherwise require in- depth knowledge of some highly specialized body of theory. Thus, this book should prove accessible to anyone with a moderate background in the sciences. I have made a special effort to include not only scientific and engineering papers, but also reviews of some of the philosophical and social issues, as it is just as important to understand how a field fits into the web of science and society as it is to understand the internal details of the field. CHRISTOPHER G. LANGTON
- 11. Page ix Editor's Introduction Christopher G. Langton Editor-in-Chief Santa Fe Institute This book consists of the first three issues of Artificial Life. These initial issues contain a special set of overview articles contributed by members of the editorial board of the journal. In these articles, each editor has attempted to review his or her own thread of special interest within the broad and diverse tapestry of research efforts that have come to be associated with the term "Artificial Life." In general, each article contains a bit of history on a particular research topic, a review of some of the more important problems, a description of the most promising techniques and methods for addressing these problems, and a view toward the future, with suggestions of the impact that Artificial Life techniques will have on our understanding of the biological phenomena under study. The primary purpose of this initial set of overview articles is to "prime the pump" for future research in the field of Artificial Life, thereby stimulating future contributions to the journal itself. They are also intended to help define and delineate the field of Artificial Life more thoroughly than has been done until now. The term Artificial Life literally means "life made by humans rather than by nature." As you will see in these articles, Artificial Life is many things to many people, and I will not attempt to give a concise definition of it here. In fact, Artificial Life is not yet ready to be constrained by quick and short definitions—the field is still in the process of defining itself, as is proper for any new discipline. The articles in this volume carefully stake out claims to certain areas of study, but there is far more intellectual territory out there waiting to be discovered and laid claim to. Among all of the things that Artificial Life is or will come to be, however, it is probably safe to say that the field as a whole represents an attempt to increase vastly the role of synthesis in the study of biological phenomena. Synthesis has played a vital role in the grounding of many scientific disciplines, because it extends the empirical database upon which the theory of the discipline is built beyond the often highly accidental set of entities that nature happened to leave around for us to study.
- 12. Take the field of chemistry as an example: In the earliest stages of research into the constitution of matter, people took stock of the kinds of chemical compounds that nature had provided them with, catalogued and classified them, analyzed them by taking them apart into their constituent pieces, and then analyzed the pieces. This was fine as far as it went, but there was a great deal of accident and historical process involved in the determination of the kinds of chemical compounds that nature happened to leave around for study, and it would have been very difficult to observe the law-regularities in the highly irregular and unique set of compounds that early researchers happened to have available for study. It was only through the process of synthesis—putting the constituent pieces of matter together in new and different ways—that researchers were able to extend the set of chemical compounds available for study far beyond the irregular set provided to them by nature. It was only within the context of this much larger set of "possible" chemical compounds that researchers were able to see beyond the accidental nature of the "natural" chemical compounds, and glimpse the regularities in Page x the constitution of matter. To have a theory of the actual, it is necessary to understand the possible. The situation is much the same in biology. The set of biological entities provided to us by nature, broad and diverse as it is, is dominated by accident and historical contingency. We trust implicitly that there were lawful regularities at work in the determination of this set, but it is unlikely that we will discover many of these regularities by restricting ourselves only to the set of biological entities that nature actually provided us with. Rather, such regularities will be found only by exploring the much larger set of possible biological entities. Many biologists have speculated wistfully about "rewinding the tape" of evolution, starting the process over again from slightly different initial conditions. What would emerge? What would be the same? What would be different? We sense that the evolutionary trajectory that did in fact occur on earth is just one out of a vast ensemble of possible evolutionary trajectories—each leading to a biology that could have happened in principle, but didn't in fact solely for reasons of accident combined with common genetic descent. We sense that the regularities we seek would be revealed to us if we could just get a glimpse of that space of possible biologies. Just as chemistry did not become lawful until the set of compounds under study was extended beyond the set originally provided by nature, so it is likely that biology will not become lawful until the set of biological entities under study is vastly extended beyond the set originally provided to us by nature. This is the role of synthesis, and this is the primary motivation for the field of Artificial Life: to give us a glimpse of that wider space of possible biologies.
- 13. Not only did the synthetic method in chemistry lead to a more solid theoretical grounding of the field itself, but the very nature of synthesis led to novel chemical compounds with many practical industrial and engineering applications, such as synthetic rubber, plastics, medicinal compounds, and so forth. Likewise, a major motivation for the field of Artificial Life, besides the desire for a firmer theoretical grounding for biology, is the promise it holds for the synthesis of biological phenomena in forms that will be of great practical use in our industrial and engineering endeavors. Nature has discovered ingenious solutions to many hard engineering problems, problems that we have not been able to solve by our traditional engineering methods. The synthetic process of attempting to recreate these biological solutions in other materials will be of great practical use. Furthermore, we may even borrow the engineering method nature used to come up with these ingenious solutions in the first place: the process of evolution. By synthesizing the mechanisms underlying the evolutionary process in computers and in other "nonbiological" media, we can discover solutions to engineering problems that have long resisted our traditional approaches. However, as was the case with synthetic chemistry, we need not restrict ourselves to attempting merely to recreate biological phenomena that originally occurred naturally. We have the entire space of possible biological structures and processes to explore, including those that never did evolve here on earth. Thus, Artificial Life need not merely attempt to recreate nature as it is, but is free to explore nature as it could have been—as it could still be if we realize artificially what did not occur naturally. Of course, we must constantly be aware of which of our endeavors are relevant to biology, and which break ground that is ultimately outside of the domain of biological relevancy. However, much of the latter will be of interest on its own right, regardless of whether or not it teaches us anything about biology as it is understood today. Artificial Life will teach us much about biology—much that we could not have learned by studying the natural products of biology alone—but Artificial Life will ultimately reach beyond biology, into a realm that we do not yet have a name for, but which must include culture and our technology in an extended view of nature. Page xi I don't want merely to paint a rosy picture of the future of Artificial Life. It will not solve all of our problems. Indeed, it may well add to them. The potential that Artificial Life holds for unlocking the secrets of life is great, but in unlocking those secrets we run the risk of unlocking a Pandora's box. As has been the case with our mastery of any new technology in the past, the mastery of the technology of life holds tremendous potential for beneficial use, but it also holds tremendous potential for abuse, whether accidental or intentional. Perhaps the simplest way to emphasize this point is by merely pointing out that Mary Shelley's prophetic story of Dr. Frankenstein can no longer be considered to be merely science fiction. We are on the verge of duplicating Dr. Frankenstein's feat and, therefore, of duplicating the consequences that lead to his ultimate ruin. Mary Shelley's genius was to paint the scientist Frankenstein as the real monster of the story, by his refusal to accept responsibility for the potential consequences of his pursuit of knowledge for its own sake. There is a lesson here for all science, not just Artificial Life, but it is especially poignant when one considers what it is that Artificial Life is attempting to accomplish.
- 14. Artificial Life will have a tremendous impact on the future of life on earth as well as on our view of ourselves and the "role" of human beings in the greater overall scheme of the universe. In addition to scientific and technical issues, Artificial Life raises many questions more appropriately treated by the disciplines of philosophy and ethics. What is the ontological status of artificially created "living" entities? What rights do they have? What is the nature of the relationship between ourselves as creators and our artifacts as living creations? How will Artificial Life impact society? How, if at all, can we guarantee peaceful coexistence with autonomously evolving synthetic life forms sharing our physical environment? What is the future of life, natural and artificial? Obviously, the domain of discourse concerning Artificial Life is potentially very large, involving virtually all of the academic disciplines. This is quite a diverse area for a single field to cover, including research in wetware, hardware, software, and more. It is expected that the "bread and butter" of the field will consist in computational approaches to open problems in biological theory and in the application of biological principles to engineering domains. However, we cannot ignore the impact that our studies will have on life itself, on us as living things, or on our understanding of ourselves and our place in the universe. This volume should serve as an initial orientation to the diverse territory of Artificial Life research, but it is only a crude map pieced together through the efforts of these early explorers. There is much more to be discovered, and there is much more to be learned even about the territories reviewed here. My hope is that this early map will inspire others to further explorations.
- 15. Page 1 Artificial Life as a Tool for Biological Inquiry Charles Taylor Department of Biology University of California at Los Angeles Los Angeles, CA 90024 taylor@cs.ucla.edu David Jefferson Department of Computer Science University of California at Los Angeles Los Angeles, CA 90024 jefferson@cs.ucla.edu Keywords artificial life, evolution, natural selection, origin of life, development, wetware, emergent properties Abstract Artificial life embraces those human-made systems that possess some of the key properties of natural life. We are specifically interested in artificial systems that serve as models of living systems for the investigation of open questions in biology. First we review some of the artificial life models that have been constructed with biological problems in mind, and classify them by medium (hardware, software, or ''wetware") and by level of organization (molecular, cellular, organismal, or population). We then describe several "grand challenge" open problems in biology that seem especially good candidates to benefit from artificial life studies, including the origin of life and self-organi- zation, cultural evolution, origin and maintenance of sex, shifting balance in evolution, the relation between fitness and adaptedness, the structure of ecosystems, and the nature of mind. The question of what the major current problems of Biology are cannot be answered, for I do not know of a single biological discipline that does not have major unresolved problems.... Still, the most burning and as yet most intractable problems are those that involve complex systems. Ernst Mayr [42] 1 Introduction Natural life on earth is organized into at least four fundamental levels of structure: the molecular level, the cellular level, the organism level, and the population-ecosystem level. A living thing at any of these levels is a complex adaptive system exhibiting behavior that emerges from the interaction of a large number of elements from the levels below. Understanding life in any depth requires knowledge at all these levels.
- 16. To deal with this multilevel complexity, a broad methodological shift is in progress in the biological sciences today as a new collection of Artificial Life models of natural biological systems become available for the first time. These modeling tools, some expressed as software, some as hardware, and some as wet-bench lab techniques (wetware), are powerful enough to capture much of the complexity of living systems, yet in a form that is more easily manipulable, repeatable, and subject to precisely controlled experiment than are the corresponding natural systems. In Artificial Life there is a major intellectual divide, similar to the one in the field of Artificial Intelligence, between "engineered" systems designed to accomplish some complex task by any means the designer can devise, even if only distantly related to the way natural systems accomplish it, and systems meant to accurately model biological Page 2 systems and intended for testing biological hypotheses. For example, most of the literature on genetic algorithms [26] has centered on function optimization, and the technical concerns have been about which algorithm variations are most efficient for which class of optimization problems. While these issues are important for many purposes, they are not central to the behavior of living systems. We are specifically interested in those Artificial Life systems that tell us something about natural life. In this review, we will describe some of the modeling techniques under development for biological problems in order to survey the breadth of research in those areas. Then we will describe a number of open problems in biology that seem especially good candidates to benefit from the tools that Artificial Life is beginning to offer. 2 Brief Survey of Artificial Life Models Applied to Problems in Biology Researchers have produced Artificial Life models at each of the levels of organization recognized in natural life, from the molecular to the population level, sometimes covering two or three levels in a single model. At present there is a tendency to study the molecular level through wetware experiments, the cellular and population levels with software experiments, and the organismic level with hardware (robotic) studies, although that may change in the future. We will classify the Artificial Life systems we discuss by medium: wetware, hardware, or software. 2.1 The Molecular Level: Wetware Systems
- 17. Wetware Artificial Life systems are the most similar to natural life and indeed are actually derived from natural life, today at least. Most of the experiments are attempts to direct an artificial evolutionary process toward the production of ribonucleic acid (RNA) molecules with specific catalytic properties. Experiments typically begin with a pool of 1013 to 1015 variant RNA molecules, placed in a solution of substrates for a specific reaction that the experimenter wishes to catalyze. Because initially the sequences are almost all distinct, and there are trillions of them, some will presumably "accidentally" catalyze the reaction at least weakly. The more "successful" RNA molecules, those that promote the target reaction more strongly than others, are then selected and separated from the "unsuccessful" and replicated many times, with mutations inserted, by using a variant of the polymerase chain reaction (PCR)—a relatively new technique for creating vast numbers of copies of nucleic acid sequences. These new daughter sequences are then tested and selected again, and the whole cycle is repeated for a number of generations until RNA sequences with sufficiently strong catalytic properties are evolved. Examples of wetware research along these lines include work by (a) Beaudry and Joyce, where RNA ribozymes that normally cleave specific RNA sites were evolved to cleave DNA as well; by (b) Bartel and Szostak [2], who evolved catalytic RNAs from a pool of random-sequence RNAs; and by (c) Lehman and Joyce [36], who evolved RNA sequences to work with different metal ions than they normally would. So far the RNA sequences produced artificially have been similar to natural sequences; however, they have enzymatic functions not possessed by any preexisting natural RNA, so far as we know, indicating an obvious potential for evolving chemically useful RNA molecules. And someday, perhaps, if the RNA molecules are selected not on the basis of their own catalytic behavior but on that of the proteins they code for, then we can look forward to evolving artificial genes for medically useful protein molecules. If we view the direct goal of these experiments as producing some particular catalytic properties in RNA, the experiments are not biological modeling as we have defined it. But taken collectively, they do have a biological significance well beyond their potential economic and medical value. They help us calibrate the degree to which RNA can catalyze biochemical reactions, a job normally done by proteins, and they lend strong
- 18. Page 3 credibility to the hypothesis of the "RNA world" [30], one of the most important theories about the origin of life. This RNA world hypothesis asserts that there was a time early in the earth's history when there were few if any deoxyribonucleic acid (DNA) or protein molecules, and the primordial soup was instead dominated by RNA molecules that were able to accomplish both replication and catalysis. By demonstrating that pure replicating RNA systems are capable of evolving specific catalytic behaviors, these Artificial Life studies are providing evidence for the plausibility of the RNA world that is more direct than any other line of research so far. 2.2 The Cellular Level: Software Systems It is customary to distinguish between chemical evolution, which refers to evolutionary history from the stage of self-replicating molecules to the stage of encapsulated cells, and organic evolution, which refers to evolution since life became organized almost exclusively into cells that, either alone or in assemblages, behave and reproduce as clearly defined units. Much research in Artificial Life is directed at understanding just how a differentiated multicellular assemblage can replicate itself, and how such replication might have evolved. John von Neumann was the first to characterize conditions for self-replication in cellular automata systems [6, 58]. He constructed self-replicating systems that possess the full computational power of universal Turing machines using a very large number of cells, each with 29 possible states. Langton [33] dropped the requirement of universality (after all, natural cells do not seem to have that) and found very much simpler systems that are capable of self-replication, nicely displayed in Langton [34]. Reggia, Armentrout, Chou, and Peng [53] have identified a number of even simpler self-replication patterns in cellular automata. Whatever the first self-replicating molecules may have been, their organization into cells must have required the evolution of mechanisms for spatial segregation in a chemical environment. How this occurred has been an open question in chemical evolution since Oparin posited a role for coacervates in the 1920s (see Chang, DeMarais, Mack, Miller, & Strathern [8]). Recently Boerlijst and Hogeweg [4] have studied cellular automata that generate hypercycles and seem to generate spatial diversity spontaneously. While it is still too early to know just how directly this corresponds to the actual evolution of cells, these studies serve to enlarge the set of possible explanations.
- 19. It took only 1 billion years or so for the first cells to form on earth but about 3 billion more years for these to evolve into metazoans (multicellular organisms) shortly before the Cambrian period. There are many questions about how this might have been accomplished, and it appears that several major steps were involved. One step was the formation of endosymbiotic associations, where distinct types of cells associate, with one inside the cell membrane of the other (as apparently happened in the formation of chloroplasts and mitochondria within eucaryotic cells). Another step was the association of genetically related cells to form multicellular organisms, in which only some of the cells reproduce. These issues are only partly understood. While there have been a number of fine studies on symbiotic associations generally (e.g., [28,59]), there has been much less work directed at endosymbiosis, although there has been some [56]. And while there have been several studies of how individual cells might reproduce to form the next higher level of organization [37,44,51], these have been clearly exploratory. The cellular level of life is an area where it would seem that artificial life research has only begun. 2.3 The Organism Level: Hardware Systems To model the behavior of living things at the organism level, for example, of insects, one must model the organism's sensory and nervous system, its body, and its envi- Page 4 ronment. Although we are quite used to thinking of nervous systems as fantastically complex, we tend to ignore the fact that animals' bodies are highly complex as well, with extremely complicated geometries, mechanical, dynamical and thermal properties, energy constraints, growth and developmental programs, etc. In principle all of the components of an animal—nervous system, body, environment—can be simulated in software. In practice, however, the amount of computation required to reasonably model the properties of sound or light in a complicated environment, or the mechanical properties of an organism with 100 coupled elastic parts, is vast and effectively beyond the capacity of computational technology for some time to come. However, it is now becoming possible to let the real physical environment model itself, and to represent the bodies of animals and their interactions with the environment by using small, computer-controlled, autonomous mobile robots (mobots). With this technology, we can now model how organisms accomplish the integration of various perceptual modalities, how they navigate in space, how they control their senses and muscles to accomplish precisely coordinated movements, and how they do all these things in real time.
- 20. One research project of this kind involved the mobot Genghis, developed by Angle [1] and programmed by Maes and Brooks [41] to learn to walk. Genghis is a six-legged robot, approximately 1 foot long and 1 food wide, designed to traverse rugged terrain. Each leg is powered by two motors and there are two sensors, one in front and one in back, to detect whether the body is touching the ground, and another sensor to measure the distance Genghis has traveled. In most such systems, coordination for tasks such as walking is statically programmed; Genghis, however, has to learn to walk. The leg modules are coordinated by a network of finite automata that receives feedback from the sensors about stability and forward movement, and produces output to the motors. Starting from a random neural network, Genghis learns how to achieve a reliable tripod gait in just few minutes. Several features of the Genghis experiments and others like it are worth noting: (a) Emergent functionality of control: Control of Genghis' gait is an emergent property, in that no individual part of the neural net "knows" how to walk. (b) Task-level decomposition: The agents that govern behavior are essentially autonomous. At the lowest level, one simple task is accomplished (e.g., standing up), upon which is superimposed the next layer (e.g., moving), upon which is superimposed another (e.g., obstacle avoidance), and so on. This layering of behaviors, each one making use of others that preexist, is analogous to the way that task proficiency might be accomplished by evolution in natural life. (c) Low- level processing: Because there is no global model, much of the reasoning is accomplished at a low level, close to the perception level, in much the same way that visual information seems to be processed in the mammalian retina. These points are discussed in Maes [40] and Brooks [5]. Adherents to this approach make the narrow claim that it is a good way to control mobile robots for complex tasks, and the broader claim that it is a good way to engineer intelligent systems generally. If so, then using mobots to model animals will aid in extracting some of the principles of intelligent behavior generally, whether natural or artificial. 2.4 Software Life at the Population Level: Equational Models versus Artificial Life Models Models of population behavior for the study of ecosystem organization, population genetics, macroevolution, geographic dispersal, etc. have traditionally been expressed formally as systems of algebraic or differential equations. Unfortunately, equational models are subject to many limitations. For example, in many models it is common to refer to the derivative of a variable with respect to population size N. This in turn
- 21. Page 5 implies the assumption of very large populations in order for such a derivative to make sense, which has the effect of washing out small population effects, such as genetic drift, or extinction. Another difficulty is that it would take tens to hundreds of lines of equations to express even a simple model of an organism's behavior as a function of the many genetic, memory, and environmental variables that affect its behavior, and there are simply no mathematical tools for dealing with equational systems of that complexity. Furthermore, equational models are generally poor at dealing with highly nonlinear effects such as thresholding or if-then-else conditionals, which arise very frequently in the description of animal behavior. One of the most fundamental and successful insights of the field of Artificial Life has been the development of an alternative population modeling paradigm that dispenses with equations entirely, and represents a population procedurally, that is, as a set of coexecuting computer programs, one for each cell or one for each organism. We consider this feature, the representation of organisms by programs, to be the defining feature of "artificial life" models of population behavior, the property that distinguishes them from other mathematical or computational models of populations. Artificial Life models offer the advantage of coding an organism's behavior explicitly as a program, rather than implicitly as the solution to equations that must be integrated. This directness of encoding typically makes Artificial Life systems much easier to use and modify, as new information is obtained or new hypotheses are entertained, than is possible with equational models. Today most Artificial Life models represent each organism as a Lisp program, a finite automaton, or a neural net. The genes of the organism are represented variously as bit strings, character strings, or list structures, either contained within the organism or stored as a separate data object that serves to encode the structure or behavior of the organism. Software organisms can reproduce either asexually, with point mutations altering the genetic data passed from parent to child, or sexually, with the child's genome derived by combining information from two parent genomes. An early example of the artificial life modeling approach is the RAM system [55], developed by Taylor, Jefferson, Turner, and Goldman, in which animal-like processes (parameterized Lisp programs) and environment-like processes could execute concurrently and synchronously. A RAM animal's program is a Lisp routine whose parameters serve as genes. RAM animals reproduce asexually but live in a common environment in which they interact and compete ecologically. The RAM system was relatively limited in two ways: (a) The "genes" defined a relatively small parameter space within which variation could occur, leaving limited scope for innovation and evolution; and (b) because at the time it was built only a few hundred individuals could be simulated for a few tens of generations per hour of workstation time, so the process of natural selection was subject to drift unless the selection forces were exceptionally strong.
- 22. Jefferson et al. [291 drastically extended and scaled up the idea of representing organisms as programs with such systems as Genesys. In that system, executed on a Connection Machine, animals were represented as neural nets in some cases or as finite automata in others. The genes of each organism were represented as bit strings that encoded either the weights of a neural net, or the transition table of a finite automaton. With a population of 64K individuals evolving at the rate of one generation per minute, and starting from a population of random bit strings, Genesys was able to evolve the ability to follow a broken rectilinear trail in a grid environment in 100-200 generations. Since RAM and Genesys, many other systems representing organisms as programs have been developed to explore problems in biology. We can illustrate the diversity of this approach by classifying these systems according to the general purposes for which they were developed—the study of evolution, behavior, ecology, developmental biology, or teaching. Page 6 Evolution. Artificial Life models are especially well suited for studying the dynamics of natural evolution and were originally invented for this purpose. Imagine a genetic algorithm in which each genome encodes a computer program, and the programs in the population are selected and bred on the basis of their ability to survive and prosper in some environment. One would expect that the future generations of programs will perform better than their progenitors, and, indeed, in practice this is typically the case—although it depends on how the programs are represented, as Collins and Jefferson [10] have argued. For a number of reasons, artificial neural networks, encoded in various ways into bit strings, seem to be especially good representations for evolution. Sexual selection is an evolutionary phenomenon recognized by Darwin and emphasized by Fisher [19] in the 1930s. If a female produces sons who are extreme for some trait (e.g., wattle color) and also daughters who have a preference for that extreme— through linkage, pleiotropy, or some other mechanism—then that trait will be selected to a high frequency in the population even if it has very disadvantageous side effects. It has been suggested that chance differences in traits subject to such runaway selection might underlie the tremendous diversity of secondary sexual characters in many tropical birds. The mathematical analysis of this phenomenon, however, requires a system of several nonlinear differential equations, so it is very complex and has been successful for only a few special cases. Collins and Jefferson [11] constructed an Artificial Life model of sexual selection, endowing the organisms with the relevant heritable traits and preferences. They explored this system in some generality, identifying where such explanations are plausible and where they are not. In particular, they were able to show that certain propositions that had been demonstrated analytically under very restrictive assumptions were actually true under a much broader set of circumstances than was provable by mathematical analysis. There are many other problems in sexual selection (see, e.g., Williams [60]) where similar methods would appear to be useful.
- 23. Behavior. Even Darwin was impressed by how exquisitely adapted animals seem to be to their environments. Indeed, when it has been possible to develop models of optimal behavior from theoretical principles and then compare these to the way animals actually behave, the fit is often striking. How is that accomplished? Do animals figure out the relevant formulae, differentiate them, and solve for zero? Koza, Rice, and Roughgarden [32] have recently examined the feeding behavior of Anolis lizards, a small, well studied group that inhabits the Caribbean region, and compared their actual foraging behavior to optimal foraging behavior as determined by a theoretical analysis, noting that the fit was quite close. They then compared that to the foraging behavior of simulated lizards that they evolved via genetic algorithms, and found that it was not difficult for the evolution to endow the lizard with behavioral strategies that closely approximate the optimal. In a similar vein, Gibson, Taylor, and Jefferson [22] used the RAM system described earlier to model the peculiar mating behavior of sage grouse in which the females choose from among male suitors. Dozens of males will gather to form leks (local mating markets) in which they display and attract the attention of females. Gibson et al. were trying to discover what influenced the females in selecting males. By searching a space of parameterized Artificial Life models, they found that if females, when choosing a mating lek, considered the distance from their nest, the number of males there, and the expected waiting time for the top male, most of the variance in their observed behavior was explainable. Similar work by Denoubourg, Theraulaz, and Beckers [15] on "swarm intelligence" has identified plausible sets of rules that are sufficient to explain much of the complex behavior used by ants and other social insects. In a more theoretical direction, Lindgren and Nordahl [39] examined how the outcomes of iterative games of the Prisoner's Dilemma, a widely used model for the evo- Page 7 lution of cooperation, might differ when there is misinformation among the players. Their analysis is remarkable because it lends credence to the position that social behavior will by itself lead to increased complexity in participant behavior. This approach is described more fully in Lindgren [38]. Ecology. Behavioral and ecological phenomena are often closely related, and both are rich with examples of collective action and emergent phenomena. At an abstract level, Ray [52] has shown how several trophic levels might emerge as a general property of ecological systems. Similarly, Ikegami [27] used variations of the Prisoner's Dilemma analogous to symbiosis and host/predator or predator/prey interactions to examine this evolution of interspecies associations. Toquenaga, Ichinose, Hoshino, and Fuji [57] and Fry, Taylor, and Devgan [21] have used Artificial Life models to examine complex modes of behavior and population growth. By programming empirically- derived rules of behavior into the artificial animals, they observed the consequences of the collective behavior that was exhibited by ensembles of animals and the environments with which they interacted.
- 24. Developmental biology. Emergent phenomena are nowhere more evident than in developmental biology, where large numbers of cells, following presumably simple rules of behavior, collectively generate complex and interesting patterns. Prusinkiewicz [50] has explored the use of algebraic formulae for cell division and differentiation. These generate some stunning visual representations as well as realistic botanical patterns. Recently, Fleischer and Barr [20] have developed a system where cells change state and/or produce fields that mimic diffusion of growth regulators. Because there is such a large amount of new information accumulating, consistent with simple collective behavior both within and between cells, it seems likely to us that Artificial Life systems will prove invaluable in the future for precisely formulating and testing hypotheses about development. Teaching. It is sobering to reflect that 40% of Americans do not believe in Darwinian evolution and that this is true for 25% of all college-educated Americans as well. Religious convictions seem to be only part of the problem. Rather, it appears that the major obstacle is failure to understand the theory of evolution itself, aggravated by the fact that even many secondary school biology teachers have serious misunderstandings. It is well established that students are less likely to understand and absorb when they are passively presented with facts than when they are actively involved in construction and experimentation. Artificial Life, however, offers a student the possibility of watching evolution in action, actively intervening with it and creating his or her own microworld. The Blind Watchmaker program by Dawkins [14] is especially noteworthy in this regard, as are the efforts of Resnick [54] to explore how children learn about collective behavior, and of the Apple Vivarium group (A. Kay [personal communication]), who are exploring Artificial Life systems to provide better ways of teaching ecology, evolution, and biology in general, in a classroom setting. Papert [47], whose earlier Mindstorms was so influential for introducing computers to the K-12 classrooms, has recently advocated [48] a cybernetic approach to teaching science in the early grades. The argument he makes is compelling, and if generally adopted, then we may see a major influence of Artificial Life on the next generation of scientists. 3 Open Problems in Biology that Are Amenable to Study by Artificial Life Modeling The opening quotation by Ernst Mayr concerns the need for understanding biological systems as complex adaptive systems. In the past, despite several brave attempts,
- 25. Page 8 disussion of holistic properties and emergence in biology typically devolved into mysticism or obfuscation. The study of Artificial Life, if it accomplishes nothing else, is providing a platform for more informed discussion of those issues. We believe that several of the major outstanding problems in biology, especially in the study of evolution, are likely to benefit from the study of Artificial Life. In this section a few such problems are described. We will focus on evolution simply because it is the foundation upon which so much of biology is based, because it is permeated with problems of emergence, and because we are more familiar with this area. 3.1 Origin of Life and Self-Organization Questions abound when one attempts to understand how life originated on earth and possibly elsewhere in the universe as well. If we restrict our attention to the origin of life on earth, those problems involve reconstructing the physical, chemical, geologic, and competitive forces that shaped the peculiar history of life on earth, the sequence of chemical reactions that may have occurred, the manner in which they became packaged and encapsulated so that organic evolution could supplant that which occurred previously, etc. Work along theoretical lines, such as that by Langton [35]; Farmer, Kauffman, and Packard [18,31]; or Eigen and Schuster [17] will be required, as well as experimental work [30]. As yet there has been little research in Artificial Life directed toward the actual constraints that operate on the other planets in our solar system and prevented (or at least constrained) the origin of life there. Most is directed at learning the minimal chemical requirements for replication to get started. 3.2 Cultural Evolution Ideas and other atomic particles of human culture often seem to have a life of their own—origination, mutation, reproduction, spreading, and dying. In spite of several bold attempts to construct theories of cultural evolution (e.g., [7,13]), an adequate theory remains elusive. The financial incentive to understand any patterns governing fads and fashion is enormous, and because cultural evolution has contributed so much to the uniqueness of human nature, the scientific motivation is equally great. Much of the problem with cultural evolution is similar to that for prebiotic evolution— the difficulty of identifying just what evolves (the "units of evolution"), how these units maintain their identity, and how they interact with one another. This area would seem to benefit from the same sorts of considerations that govern the origin of life. 3.3 Origin and Maintenance of Sex
- 26. Few problems in contemporary evolutionary theory are attracting as much attention as is the evolution of sex, sometimes referred to as "the cost of meiosis" [43]. All else being equal, a female who reproduces asexually will leave twice as many genes in her offspring as will a female who reproduces with a male. This would seem to impose a tremendous hurdle for sexuality to overcome, yet it persists, and sex is widespread in the natural world. Why? The answer almost certainly involves complex interactions among linkage, pleiotropy, epistasis, parasitism, and nonlinear relations between genotype and fitness. There are many qualitative theories but little in the way of testable quantitative research. The ability to construct and examine large, but finite, populations with a variety of arbitrary constraints makes Artificial Life systems an excellent platform from which to study the theoretical side of this problem. We have observed, for example, that the ability of sexual systems to rid themselves of maladaptive mutations (Muller's ratchet) can be significant in populations of bit strings that evolve by genetic algorithm [12]. The genetic algorithm literature also has many examples where these issues are addressed in the context of optimization problems [23]. Page 9 3.4 Shifting Balance Paradigm Wright, in his four-volume treatise on population genetics [61], argued that the key issues in evolution today had their roots in the disagreements of the 1930s-1950s among Fisher, Haldane, and himself. This related particularly to how populations of organisms traversed their adaptive landscape—through gradual fine-tuning by natural selection on large populations, or alternatively in fits and starts with a good bit of chance to "jump" adaptive valleys in order to find more favorable epistatic combinations. The traditional mathematical models of population genetics and evolution require extensive linearization and so are not very good for exploring the nonlinear interactions that this problem requires. On the other hand, Artificial Life models are ideal for studying this problem, and several studies have begun on the importance of population size for evolving solutions with arbitrary degrees of epistasis. It may be that the rules that govern adaptation in artificial systems are different from those for natural systems, but these studies will certainly highlight which issues are most important, and there will certainly be some generalizations that pertain to both worlds. 3.5 Fitness and Adaptedness
- 27. Even before Darwin, it was recognized that there is some degree of direction or progress toward more complex forms over geologic time—the "chain of being," although how much direction there might be and how that effect is produced by natural selection remain murky. This concern can be compressed essentially into one question, What is the relation between adaptedness and fitness, that is, between adaptation and what is selected for? This question has occupied some of the greatest evolutionists of this century [16] and remains quite open [60]. It is now well understood that natural selection does not necessarily maximize adaptedness, even in theory [45]. Yet field biologists are constantly impressed by just how good the fit seems to be, and optimization arguments abound in population ecology (see Koza et al. [32]). In a classic essay, Gould and Lewontin [24] assailed the widespread use of optimization, pointing out that chance, structural necessity, pleiotropy, historical accident, and a host of other contributors will detract from making this "the best of all possible worlds." The analysis of artificially living systems is beginning to shed needed light on this issue. Miglino, Nolfi, and Parisi [44] studied the evolution of generating functions that produced neural nets, which then determined the behavior of organisms, which in turn determined the fitness of artificial organisms in their environments. They found that a variety of genotypes coded for identical neural nets, that a variety of neural nets coded for the same behavior, and that a variety of behaviors achieved the same fitness in their system. However, the opportunities these various solutions offered for future evolution differed significantly. Similar observations were made by Hinton and Nowlan [25] in their study of the Baldwin effect in evolved learning by neural networks. As research in Artificial Life acquires greater ability to capture development of organisms and intervening levels of organization between molecules and populations, the field is likely to contribute to the analysis of this problem that Dobzhansky characterized as "the most important theoretical problem in the study of evolution" (personal communication). 3.6 Structure of Ecosystems In natural ecosystems there are a number of patterns that seem fairly general. For example, in their study of many food webs, Pimm, Lawton, and Cohen [49] observed a number of patterns, among them (a) the average proportion of top predators, intermediate species, and basal species remained roughly constant; (b) linkage density is approximately constant; and (c) the modal number of trophic levels is three to four.
- 28. Page 10 There are others that also point to emergent properties of natural ecosystems. The reasons underlying these regularities are seldom understood. As Artificial Life develops and ecosystems are evolved, perhaps along the lines of Ray [52] or Holland [26], it will be interesting to see if the same patterns evolve. Perhaps others will emerge, such as the intermediate connectedness of complex adaptive systems and their posture near the edge of chaos [31,35]. 3.7 Mind in Nature No problems in science are more venerable or profound than those surrounding the nature of mind. Will it be possible to design or evolve robots that experience the same sensations that we do? Do radically different life forms experience equally different forms of consciousness? Or is consciousness a universal property that organisms experience to various degrees but fundamentally alike in kind (and how can we tell)? How could mind and consciousness be produced by Darwinian evolution? Two recent and lucid accounts of these problems are those by Nagel [46] and Churchland [9]. Like most people, we have our own views on these problems. But unless these views are subject to rigorous definition, testing, and verification, they cannot be considered scientific. As the ability to construct Artificial Life systems improves, it may well become possible to construct systems that exhibit behavior that is typically ascribed to "mind." Such systems will, in a sense, play a role analogous to that played by Escherechia coli or Drosophila melanogaster that have permitted manipulation and dissection of mechanisms in natural living systems. If that happens, and we believe it will, then the field of Artificial Life will have contributed to what is surely one of the scientific grand challenges of all time. References 1. Angle, C. M. (1989). Genghis, a six-legged autonomous walking robot. Bachelor's thesis, Department of EECS, Massachusetts Institute of Technology, Cambridge, MA. 2. Bartel, D. P., & Szostak, J. W. (1993). Isolation of new ribozymes from a large pool of random sequences. Science, 261, 1411-1418. 3. Beaudry, A. A., & Joyce, G. F. (1992). Directed evolution of an RNA enzyme. Science, 257, 635-641. 4. Boerlijst, M., & Hogeweg, P. (1992). Self-structuring and selection: Spiral waves as a substrate for prebiotic evolution. In C. Langton, C. E. Taylor, J. D. Farmer, & S. Rasmussen (Eds.), Artificial life II, 255-276. Reading, MA: Addison-Wesley. 5. Brooks, R. A. (1991). New approaches to robotics. Science, 253, 1227-1232. 6. Burks, A. (1970). Essays on cellular automata. Urbana, IL: University of Illinois Press.
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- 33. Page 15 Cooperation and Community Structure in Artificial Ecosystems Kristian Lindgren Institute of Physical Resource Theory Chalmers University of Technology S-412 96 Göteborg, Sweden Mats G. Nordahl* Santa Fe Institute 1660 Old Pecos Trail, Suite A Santa Fe, NM 87501 USA Keywords evolution, Prisoner's Dilemma, cooperation, community structure, food webs, lattice games Abstract We review results on the evolution of cooperation based on the iterated Prisoner's Dilemma. Coevolution of strategies is discussed both in situations where everyone plays against everyone, and for spatial games. Simple artificial ecologies are constructed by incorporating an explicit resource flow and predatory interactions into models of coevolving strategies. Properties of food webs are reviewed, and we discuss what artificial ecologies can teach us about community structure. 1 Introduction Artificial ecologies consisting of artificial organisms are likely to become useful tools for understanding general principles for how ecological communities are organized. In particular they could be used to study phenomena on scales in time and space that cannot be accessed in ordinary experiments and field studies. Many of the artificial ecologies discussed in this paper are based on the iterated Prisoner's Dilemma (IPD). This game simultaneously provides an abstract model for the evolution of cooperation and a very complex coevolutionary landscape. The path followed in this review starts out with a discussion of different mechanisms for the evolution of cooperation and altruistic behavior. We then discuss the IPD in detail. Models of coevolution of strategies are reviewed, both in situations where everyone plays against everyone and in spatial settings where interactions are localized. Populations of coevolving strategies can be viewed as simple artificial ecological communities. An important aspect of community structure is who is eaten by whom. We review some basic facts about the structure of food webs and briefly discuss mathematical models of community structure and assembly. Finally we discuss how explicit resource flows can be combined with coevolution of strategies, which allows us to include predatory as well as cooperative interactions. This route is different from that followed in most investigations of community structure, where predation often is the only interaction considered. 2 The Evolution of Cooperation Altruistic behavior, that is, behavior that benefits another individual or organism (not necessarily a relative), while being apparently detrimental to the organism itself, is an important phenomenon both in nature and human society. Cooperative behavior often depends on a certain amount of altruism, in that the participants need to refrain from * present address: Institute of Theoretical Physics, Chalmers University of Technology, S-41296 Göteborg, Sweden.
- 34. Page 16 taking advantage of others by acting according to short-term self-interest. In other cases, cooperation could be profitable enough that it is dictated even by shortsighted selfishness. In the early history of evolutionary theory, the emphasis appears to have been mostly on the struggle for existence. (See Cronin [19] for a discussion.) Some early writers, such as the anarchist Kropotkin [47], did, however, stress the importance of cooperative interactions both in a biological context and in society. A number of scenarios for how altruistic and cooperative behavior could be established have later been suggested. The main difficulty in the evolution of altruistic behavior and cooperation is explaining how this behavior could be stable against cheaters who enjoy the benefits without giving something in return. One case, which will not be discussed further in this article, is when the altruistic behavior is directed toward relatives (e.g., [34]). From the viewpoint of reproduction of genes, an individual is equivalent to two of his brothers or eight of his cousins. In the terminology of biologists, this is called kin selection. A number of cases of altruistic behavior in biology, such as eusociality among ants, bees, and wasps (e.g., [2]), have been claimed to at least in part depend on kin selection. Another important mechanism is reciprocal altruism (e.g., [98]). In this case favors are given, and favors are expected back in return. In many cases, this could be viewed as enlightened self-interest that takes the shadow of the future into account. The game theoretic models discussed later mostly fall under this heading. A third mechanism could be group selection, where selection can be viewed as operating at higher levels. A simple mathematical example where clearly defined higher units of selection (different kinds of spiral waves) appear is the spatial hypercycle model studied by Boerlijst and Hogeweg [10,11]. Another case where cooperative behavior can occur is when cooperation follows from immediate self-interest. This was called by-product mutualism in Dugatkin, Mesterton-Gibbs, and Houston [24]; in a game theoretic framework, parameters have changed so that the game is no longer a Prisoner's Dilemma (PD) (see section 2.1), but the trivial game where both players prefer cooperation. For example, this could be the case if the profit of a group grows faster than linearly with the number of participants. Cooperative hunting of larger prey among lions has been suggested as one example [24] (but see also [18]). Finally, explanations of cooperation in human society could take cultural as well as genetic transmission into account, and could involve, for example, explicit modeling of societal norms (e.g., [5,14,93]). This list of scenarios is undoubtedly incomplete, and many examples may be hard to classify as one scenario or the other. Consider, for example, the case of cleaning symbiosis discussed in Trivers [98], where certain small fish (cleaners) clean larger fish (e.g., a grouper, which serves as host) of ectoparasites. The large fish appears to have very strong barriers against feeding on the cleaners— the cleaner, which is comparable in size to the ordinary prey of the larger fish, even works in the mouth of its customer. Cleaners are identified, for example, by their swimming pattern. Species that mimic cleaners but instead bite off pieces of the fins of the large fish also exist. This is certainly a reciprocal relationship—both species obviously benefit from it. But whether the benefit (e.g., of having parasites removed) is large enough that this is a case of an interaction in both players' short-term interest is not immediately obvious. An IPD model would have the property that a single defection by the large fish ends the game; it also fails to include evolution of signals that are clearly important. (An example of a model of mutualism where recognition is included is given by Weisbuch and Duchateau [102]).
- 35. Page 17 Table 1. Payoff Matrix M for the Prisoner's Dilemma. In the rest of this section, we concentrate on models of the evolution of cooperation based on the IPD. The previous examples should, however, serve as a reminder that the PD by no means covers all aspects of the evolution of cooperation. 2.1 The Prisoner's Dilemma The Prisoner's Dilemma (PD) provides a useful framework for studying how cooperation can become established in a situation where short-range maximization of individual utility leads to a collective utility (welfare) minimum. This is a two- person game where the players simultaneously choose between the two actions ''cooperate" and "defect," which we denote by C and D (or equivalently 1 and 0). The game was first studied by Flood and Dresher at Rand Corporation in 1950 [30]. (An account of the first iterated Prisoner's Dilemma-like game played can also be found in Poundstone [85].) The name is derived from an anecdote by Tucker, which goes more or less as follows: Two persons have been caught, suspected of having committed a crime together. Unless one of them confesses, there is no evidence to sentence them. The prosecutor offers a reward to the one that confesses; the other will in this case get a severe sentence. If both confess, they will be imprisoned, but for a shorter time. If they stay quiet, they will be released in the absence of evidence. The results of the players' choices are quantified by the payoff matrix of Figure 1. Here R is the reward for mutual cooperation (i.e., keeping quiet), and T is the temptation to defect against a cooperating opponent, who then gets the sucker's payoff S. In the case of mutual defection, both get the penalty P. The PD is defined by the inequalities T > R > P > S and 2R > T + S. R = 3, T = 5, S= 0, and P= 1 is a common choice in the literature. The PD is a non-zero-sum game, that is, the total score distributed among the players depends on the actions chosen. If the game is only played once, a player maximizes her score by defecting, regardless of the move of the opponent. Thus, two rational players share the lowest total payoff for mutual defection. This is the Nash equilibrium of economic theory—none of the players is willing to change to cooperation. If, on the other hand, the game is played more than once, that is, there is a high probability that a player encounters the same opponent again, cooperating strategies may be more successful. (We assume that the objective is maximizing the score, rather than beating the opponent.) This is the iterated Prisoner's Dilemma (IPD). A computer tournament arranged by Axelrod [3-5,8] showed that a very good strategy is given by cooperating unless your opponent defected in the previous round. This strategy that mimics the opponent's last action is called Tit-for-Tat (TfT). For a game consisting of a known fixed number of rounds, the cooperative behavior is destabilized [87]. In the last round, the single-round dilemma appears, and both players should defect—but then the same reasoning applies to the next to last round, and so on. In this particular situation, defection is the unique Nash equilibrium. This
- 36. Page 18 somewhat pathological behavior can be avoided by considering an infinitely iterated game or by choosing the number of rounds stochastically. One complicating factor in a repeated game is the possibility of mistakes by the players (noise). These could be either mistakes where the action performed by a player is different from the intended one, or misinterpretations of the opponent's action (which leads to the players seeing different histories). Noise in the iterated game destroys the cooperative pattern between two TfT players. An accidental defection causes a sequence of alternating revenges; another mistake can then result in either mutual cooperation or defection. In the infinitely iterated game, the score for TfT playing against itself drops from R to (R + S + T + P)/4 for any non-zero noise level. A strategy that defects only if the opponent defects twice in a row (Tit-for-two-Tats, Tf2T) is stable against a low noise rate but can be exploited by a strategy that cooperates only every second round. Another possibility is the strategy called Simpleton by Rapoport and Chammah [87]: change action if the score received in the previous round was less than R, that is, cooperate when the actions of the previous round are identical. For an accidental defection D* during a period of mutual cooperation, the players return to cooperation after a single round of mutual defection, that is, (. . ., CC, CC, CD*, DD, CC, CC,. . .). Whether this strategy can be exploited or not depends on the payoff matrix. When T + P < 2R (to 0th order in the mistake probability Perr), defection scores less than cooperation against Simpleton; for the standard parameter values, equality holds, and Simpleton can be exploited by uncooperative strategies. The strategies discussed so far depend only on a finite portion of the history of the game. TfT, Simpleton, and Tf2T can be classified in terms of the maximal number of history bits used by the strategy as memory 1, 2, and 3, respectively. They are also deterministic, which means that the history determines the action uniquely. Some successful deterministic strategies of higher memory will be discussed below. A strategy that makes a stochastic choice of action with probabilities depending on the history is called probabilistic. A TfT- like strategy that forgives defections with a suitably tuned probability can both resist exploitation and cooperate with its own kind in a manner stable against accidental defections [69,75]. Probabilistic strategies with tunable random number generators appear to be rare in nature, however. The PD has been applied to explain the emergence of altruistic behavior in a number of situations, both in biology and in human society. Axelrod [5] discusses cooperative behavior between British/French and German soldiers in the trench warfare of World War I. During the first years of the war, the same units faced each other for long periods, which placed them in a situation reminiscent of an IPD, and a TfT behavior was established (quotation from Hay [37]): "It would be child's play to shell the road behind the enemy's trenches, crowded as it must be with ration wagons and water carts, into a bloodstained wilderness . . . but on the whole there is silence. After all, if you prevent your enemy from drawing his rations, his remedy is simple; he will prevent you from drawing yours." In many other applications to human society, it is natural to consider a similar game with a larger number of players—an n- person PD. One situation where this occurs is in the sharing of a common resource (the tragedy of the commons), such as air and water in an environmental context. Another situation, where cooperation is a less desirable outcome, is an oligopoly consisting of a small number of firms that sell almost identical products (such as coffee, gasoline, or airline tickets), and compete by adjusting prices (e.g., [57]). Two strategy tournaments for this situation modeled by a three-person generalized PD with continuous actions were organized at MIT by Fader and Hauser; see [28] for details.
- 37. Page 19 Game theory [100, 101] has found a number of applications in biology [62]. Some cases where interpretations of altruistic behavior in terms of the PD have been attempted are food (blood) sharing among vampire bats [103,104], interactions between breeding adults and nonbreeders in tree swallows [53], and cooperative inspection of approaching predators in small fish such as sticklebacks [66]. The identification of the game and strategy followed (e.g., [67,76]) is often somewhat uncertain in these examples. In biological applications of game theory, the analysis has often focused on finding evolutionarily stable strategies. An evolutionarily stable strategy (ESS) [62] is a strategy that cannot be invaded by any other strategy present in arbitrarily small amounts. (Other, less intuitive definitions involving invasion by a group of strategies also appear in the literature [13].) A distinction is often made between the case where strategies exist that achieve equal scores to the strategy in question, and can invade through genetic drift, and the case where a strategy dominates strictly. In the PD, a number of results about ESSs are known: In the error-free case, no deterministic strategy or finite mixture of such can be an ESS in the infinitely iterated game [13,29]; for general probabilistic strategies, the same result has been shown except in the still open case of no discounting of the future [54]. When mistakes occur, ESSs can exist ([12]; see also later). An analysis of a system in terms of evolutionary stability should not be viewed as complete. Knowledge of the fixed points of a dynamical system and their stability is not the same as a complete understanding of the system. The artificial life perspective could contribute to a greater understanding of the evolutionary dynamics of many different systems. Let us finally remark that in some of the evolutionary models discussed later, the PD provides not only a model of the evolution of cooperation, but it also generates an interesting example of a complex coevolutionary landscape [44, 71], which can serve as a simple prototype model for the study of coevolutionary phenomena. 2.2 Evolutionary Dynamics Evolutionary dynamics can be imposed on the space of strategies by viewing strategies as interacting individuals in a population. All pairwise interactions in the population could be included, or individuals could interact only with some subset of the population, such as their neighbors in space. Through these interactions, each individual receives a score that represents the success in the game. We can introduce population dynamics by letting successful strategies produce more offspring in the next generation. If strategies are represented as individuals, births and deaths could be given by a stochastic process. Species could also be represented by their population size; in this case the dynamics is given by a set of differential equations. An evolutionary process requires a mechanism for generating variation as well as a mechanism for selection. This can be arranged by including mutations in the step where strategies are reproduced. The exact nature of these will depend on the representation scheme used. A number of evolutionary simulations of this type have been performed for the IPD: Axelrod [6] applied a genetic algorithm (e.g., [38]) to evolve PD strategies of fixed memory length 6. The strategies played games of 151 rounds against eight selected strategies from his tournament [5]. A coevolutionary simulation, in which the strategies played against each other, was also discussed. In another experiment, Miller [68] represented strategies as 15-state finite automata with 148-bit genotypes. Here a coevolutionary model, where each generation was evaluated by playing all pairwise games, was studied more extensively. A population of 30 individuals was followed for 50 generations; games consisted of 150 rounds. Three cases were studied: perfect information, and a probability for misunderstanding
- 38. Page 20 of 0.01 or 0.05. No successful error-correcting strategies were discovered, possibly because of the very short evolutionary time scale of the simulations. Several other experiments of this kind have been performed. (We are probably not aware of them all; we also do not attempt to discuss models of dynamics in strategy spaces containing only a small number of strategies.) Interesting examples are, for example, the work by Fujiki and Dickinson [32], who used a representation in terms of Lisp programs (a representation later used by Koza in his genetic programming approach [46]), the work by Marks [57] where strategies for the three-person generalized PD discussed earlier also were considered, and work by Fogel [31] which suggested that the initial moves in the game may become a tag that allows strategies to recognize each other. A model introduced by one of us [49] uses the infinitely IPD with noise as an interaction between individuals and considers the evolution of deterministic finite memory strategies with an initial population containing only memory 1 strategies. The memory length is allowed to change through neutral gene duplications and split mutations. The genomes in the model represent strategies in the game, which determine the next move of a player given the history h = ((x0, y0), . . ., (xt, yt)) of the game. Here (xt, yt) are the moves of the player and the opponent at time t. We consider deterministic strategies of finite memory m > 0. For m even, the strategy depends on the last m/2 moves of both players; for m odd on the last moves of the opponent and the last moves of the player herself. If we let 1 denote the action C, and 0 the action D, a strategy of memory m can be represented as a binary string s of length 2m (see Figure 1). In the reproduction of a strategy, three types of mutations can occur: point mutations, gene duplications, and split mutations. Point mutations flip single bits in the genome with frequency Pmut. Gene duplications increase the memory from m to m + 1 (with frequency Pdupl) while leaving the actual strategy unchanged. This corresponds to duplicating the genome, for example, 1011 → 10111011. Gene duplication is a neutral mutation, which increases the size of the evolutionary search space without affecting the phenotype. Additional point mutations can then give rise to new strategies without shorter memory equivalents. Finally, the split mutation keeps only a randomly chosen half of the genome with frequency Psplit. Each strategy i has a real-valued population size xi. The population densities evolve in time according to (1) where the term (identical to the average score of the population) (2) ensures that the total population stays constant. The interaction coefficient gij is the score obtained when strategy i plays the noisy infinitely iterated PD against strategy j. The infinite game can be viewed as a Markov chain of finite memory, which means that the result of the game can be calculated analytically. (See Lindgren [49] for details.) At each time step, mutations act in the way described previously. In this way new species can be introduced. Species are removed from the system if their population falls below a threshold value.
- 39. Page 21 Figure 1. The representation of strategies in the model of Lindgren [49] is illustrated for the memory 3 strategy 0001 1001. Figure 2. A typical simulation of the coevolving strategy model of Lindgren [49]; 30,000 generations of the simulation are shown. A typical example of a simulation of the model is shown in Figure 2. In general, a succession of stable periods separated by periods of rapid evolution are seen (reminiscent of punctuated equilibria [26]).
- 40. Page 22 Cooperation can be observed at several levels in the model. The elementary actions C and D represent cooperation at the lowest level. In an application of the PD, they would be an abstraction of behavior with a more interesting substructure. The average score tends to increase in the time evolution (although not monotonically), which indicates an increasing degree of cooperation at the level of elementary actions. But we also observe cooperative behavior at the level of strategies. Consider, for example, the first period of stasis, where TfT (01) and ATfT (10) coexist. This coexistence is possible because TfT suppresses invasion attempts by AllD (00), which otherwise would outcompete ATfT, and similarly ATfT suppresses invasion attempts by AllC (11), which could outcompete TfT. In other words, the strategies cooperate through indirect effects where one suppresses the predators of the other, and vice versa. However, TfT and ATfT do not manage to get very high scores in the game. The stable period at memory 3 is dominated by a symbiotic pair of strategies. This is an example of mutualism where the strategies achieve a fairly high score by cooperating to correct errors [49], something they cannot do when interacting with themselves. The evolution of error correcting mechanisms is an interesting example of emergent higher level behavior in the model. The first error-correcting strategy that appears in the simulations is 1001 or Simpleton, which was discussed earlier. In case of an accidental defection, two strategies of this type return to cooperation after a single round of mutual defection. For the standard payoff matrix, this behavior is too forgiving, and defectors can invade. A strategy that defects twice before returning to cooperation, however, is sufficiently punishing to avoid exploitation. This type of strategy requires memory 4 (a history of two rounds) and often appears as a very stable final state for the standard parameter values (see Figure 2). We denote this strategy type sl; it is defined by fixing seven of the positions in the genome to lxx10xxx0xxxx001, where the symbol x stands for undetermined actions that occur infrequently (order ) when sl plays itself. Several strategies that fit this template can in fact be shown to be ESSs (under reasonable assumptions about the allowed class of invading strategies for the infinite game). The choices of representation and adaptive moves in this model, of course, are not unique. Another choice was made in the model studied by Ikegami [40], where strategies were represented as trees of unequal depth representing all contexts where the strategy defects. Mutations included genetic fusion [43], where a tree is attached to a leaf of another. This choice of representation favors the evolution of noncooperative strategies. Probabilistic strategies could also be considered. Nowak and Sigmund [75,76] have studied the coevolution of probabilistic strategies in the memory 1 and memory 2 subspaces, respectively. Extensions of the simple PD model are also possible, for example, in the form of tags and signals, communication, and control over whom to play. Stanley, Ashlock, and Tesfatsion [94] have studied evolution of strategies for the noise-free IPD, where strategies have the option of choosing and refusing partners depending on the results of the games between them. Models of the evolution of cooperation that go beyond the standard framework of the IPD, both by extending it and by focusing more in detail on actual mechanisms of interaction and cooperation so that a PD appears implicitly, are certainly worth pursuing. 2.3 Spatial Games The fact that the physical world has three spatial dimensions did not enter into the evolutionary models discussed in the previous section. In some cases, this may be a reasonable approximation—we could consider organisms mobile enough that in a generation, all individuals in the population have time to interact with each other.
- 41. Page 23 Table 2. Different Paradigms for Spatial Dynamics. individuals discrete continuous space-time discrete CA CML continuous Gas/Swarm PDE But in general the environment may provide barriers so that different evolutionary paths can be explored in different regions of the world, and it is essential to take spatial effects into account. In the context of explaining speciation, Mayr [63, 64] has argued for the importance of spatial separation (see also [26]). A typical case would involve a small founder population capable of rapid evolution separated off from the region inhabited by the majority of its species, for example, on an island. The spatiotemporal dynamics of the system can also be important. Even in a homogenous environment, the dynamics of the system could generate spatial structure, which could influence evolutionary processes. As an example, Boerlijst and Hogeweg [10,11] studied a cellular automaton model of the hypercycle model of Eigen and Schuster [25] and found spiral wave dynamics that increased the stability against parasites. Selection for certain altruistic properties (catalytic support and faster decay rates) was observed—the introduction of spatial degrees of freedom allows localized structures to form, and selection can take place at the level of these structures as well. The spatial dynamics could also affect the stability of ecological systems and in that way influence evolutionary processes. As an example, space-time chaos can allow locally unstable systems to persist with essentially constant global population levels (e.g., [35]). Several different ways of introducing spatial degrees of freedom can be imagined. In Figure 2.3 we have classified these into four groups, depending on whether space and time are treated as continuous or discrete, and whether we consider separate individuals or a continuous local population density. Let us first consider the case with discrete individuals and discrete space and time. In this case we obtain models that are essentially cellular automata (CA) (e.g., [107]) or lattice Monte Carlo simulations, depending on whether sites are updated simultaneously or asynchronously in random order. One class of lattice games is obtained in the following way: Let each lattice site be occupied by a single strategy; empty lattice sites are not allowed. All lattice sites are updated simultaneously in the following manner: First, the score of a site is calculated as the sum of the average scores obtained when the strategy at the site plays the infinitely iterated game against the strategies in the neighborhood N1 (e.g., the four nearest neighbors on a square lattice). The score of a site is then compared to the scores in a neighborhood N2 (e.g., the von
- 42. Page 24 Figure 3. Species density curves from a simulation of the spatial version of coevolution of strategies for the iterated PD discussed in the text. The first 10,000 generations of the simulation are shown. Neumann neighborhood consisting of the site itself and its four nearest neighbors), and the highest scoring strategy in N2 is adopted at the site at the next time step. Ties are broken at random. In an evolutionary model, mutations can occur in the reproduction. Because the scores of the nearest neighbors in turn depend on the strategies of their neighbors, the strategy at a certain site is updated depending on the strategies in a neighborhood of radius 2. If the set of allowed strategies is finite, the model is a cellular automaton. Cellular automaton models of this kind (with a fixed set of strategies and without evolution) were introduced by Axelrod [5]. He found that the ranking of the strategies submitted to his second tournament changed completely in the spatial case. Complicated patterns of coexisting AllD and TfT players were also observed. In Nowak and May [72, 73] the dynamics of the memoryless strategies AllC and AIID on a lattice was studied in more detail; in particular spatiotemporal chaos was observed. A model closely related to a lattice PD was also studied in Wilson, Pollack, and Dugatkin [105]. A different approach to spatial games is to let all players on the lattice make simultaneous moves and to let strategies depend on the actions in a neighborhood on the lattice, which gives a genuine n-person game. This approach has been investigated by Matsuo and coworkers [58,1]. We [51] studied a spatial evolutionary model where the spatiotemporal dynamics was introduced as described earlier. The representation of strategies and adaptive moves were identical to those of Lindgren [49] (see previous section). Figure 3 shows an example of a simulation of this model. The payoff matrix is given by the standard parameter values (R, S, T, P) = (3, 0, 5, 1), the error rate is Perr = 0.01, and the mutation rates are Pmut = 0.002, and Pdupl = Psplit = 0.001. In the initial state, the four memory 1 strategies appear with equal probability. The lattice size is 128 x 128. This simulation shows several important differences between the spatial model and the differential equation model discussed above (see Figure 2), which from a physicist's perspective could be viewed as a mean-field approximation to the spatial model. At memory 1, a frozen state of AIIC and AllD is found, where TfT is maintained at significant levels by spreading waves of activity generated by mutations from AllD to TfT (see Figure 4d). At memory 2, the strategy 1001 (Simpleton) takes over most of the lattice. The noncooperative strategies 00 and 0001 can coexist with 1001 at low
- 43. Page 25 levels by forming a network of mostly diagonal lines. In the mean-field model, the noncooperative strategy 0001 dominates at memory 2; on the lattice this strategy can only exploit its nearest neighbors, and the cooperative strategy 1001 has an advantage. No analog of the symbiotic pair of strategies seen at memory 3 in Figure 2 is found in the spatial model. Memory 4 strategies of type sl often appear on the lattice as well; in the simulation shown in Figure 3, we see two closely related memory 4 strategies of this type (sl and s2) appear, and then a similar memory 5 strategy s3. In many simulations, the strategy s3 takes over the entire lattice and forms a homogenous state. In Figure 3, however, we find another strategy tl = 1001000000001111 and some closely related strategies that are able to coexist with s3. This coexistence is not observed in the mean field model. An accidental defection in a game between two strategies of type t1 results in the sequence (..., CC, CD*, CC, DD, CC, CC,...). The advantage of this pattern is that it reduces the score less than the error-correcting mechanism of, for example, s2 or s3. The strategy t1 is at the same time more resistant than 1001 to exploitation by defectors. This example illustrates how the introduction of spatial degrees of freedom allows coexistence of strategies through the formation of stable spatial domains. For other values for the payoff matrix, a rich variety of dynamical behavior is observed. (See Lindgren and Nordahl [51] for a detailed description.) Even if we restrict ourselves to the space of memory 1 strategies, a number of different regions of qualitatively different spatiotemporal dynamics are found (typically with discontinuous transitions at the boundaries between them). Some examples of fixed-time configurations from simulations with memory 1 are shown in Figure 4. The payoff matrix can always be transformed to the normal form (R, S, T, P) = (1, 0, p, q); the standard parameter values correspond to (p, q) = (5/3, 1/3). The behavior in this case is similar to Figure 4d. Figure 4a has (p, q) = (1.4, 0.05). In this region we find spatiotemporal chaos involving AllD, TfT, and AllC. In Figure 4c we have (p, q) = (1.9,0.8). Here we find rather irregular wave activity and expanding patches with all four memory 1 strategies present. By decreasing q, we move into a region dominated by spiral waves (which break into smaller fragments because of mutations) (see Figure 4b). Varying the payoff matrix also affects the nature of the evolutionary dynamics. A tendency toward constancy of the qualitative nature of the spatiotemporal dynamics during the evolutionary process is seen, so that one may, for example, have strategies that evolve toward longer memory while the dynamics constantly is spatiotemporally chaotic [51]. One of the more important properties of the spatial model is its capacity to support a larger diversity of species than the ordinary coevolution model. In particular, one can find very complex frozen states where a large number of different frozen patches coexist. These are somewhat reminiscent of plant communities. There are around 3 × 105 known plant species on earth, which all depend on a quite small number of resources. This number is much larger than allowed by results based on ordinary population dynamics, which limit the number of species in terms of the number of resources [48, 55]. Static explanations in terms of varying equilibria in a heterogenous environment have been suggested (e.g., [96]). One may speculate that dynamical processes could generate diversity even in a homogenous spatial system. Another option for modeling the spatiotemporal dynamics is to keep the discrete spatial lattice and discrete time, but to consider continuous population densities at each site. The sites could be coupled by diffusion. In this way one obtains a coupled map lattice (CML) (e.g., [43]), possibly with a variable number of degrees of freedom at each site if some mechanism for adding and deleting species is included. We have
- 44. Page 26 Figure 4. Examples of typical configurations from simulations with memory I strategies and a payoff matrix given by (a) (p, q) = (1.4, 0.05), (b) (p, q) = (1.9,0.2),(c) (p, q) = (1.9,0.8), (d) (p, q) = (1.4, 0.5). The coding of strategies is such that from light to dark we have the order AllD, TfT, ATfT, and AllC. studied a one-dimensional model with a copy of the model of Lindgren [49] at each site [50]. For the standard payoff matrix, the dynamics of this system is rather similar to the mean-field model—successful new strategies typically propagate and take over the entire lattice as soon as they are discovered at one site. The third option for modeling spatiotemporal dynamics is in terms of partial differential equations (PDE). For a finite number of strategies, one could consider the reaction-diffusion-like system obtained by adding a diffusion term to equation 1: (3)
- 45. Page 27 Finally, we have the case of moving or diffusing individuals in continuous space. (A case suitable for a Swarm simulation—studies of systems with strategies for motion as well as the game, e.g, avoidance behavior, would be particularly interesting.) We are not aware of any simulation of a spatial game of this kind. Some recent work in the biology literature, however, is closely related—Enquist and Leimar [27] discussed a system where individuals form temporary associations while playing the game. Defectors are rejected after a short time compared to the average duration of a game between two cooperators and then search for a new partner to exploit. As expected, increased mobility favors defectors, which then more easily can find a new victim. Data from sphecid wasps, where in some species females cooperate by sharing nests, show that cooperation is less likely in species that form large population aggregations, which lowers the search time for defectors. Unfortunately these authors only consider a mean-field approximation, not the actual spatial system, and only discuss the relative stability of a few chosen strategies instead of performing an evolutionary simulation. If an actual spatial system with local reproductive dynamics was studied, it is conceivable that domain formation could occur, so that mean field theory would not be a good approximation. This would favor cooperation. 3 Artificial Community Structure Are ecological communities structured entities or just random collections of species that respond independently to the environment? Questions of this kind can be addressed through field studies of real ecosystems, through laboratory experiments that assemble artificial ecologies of real organisms and by making mathematical models. In our opinion, there is also a niche for artificial life in the study of community structure. By creating artificial ecologies out of artificial rather than real organisms, many constraints on real experiments and field studies can be circumvented. Real ecological studies are severely limited in space and time. (See Pimm [82] for a discussion of time and length scales accessible and nonaccessible in ecological, biogeographical, and paleontological studies.) Given enough computer resources, artificial ecologies could be studied on a much wider range of scales. Artificial ecosystems can also be manipulated in many ways that are impossible for real communities. On the other hand, compared with simple mathematical models, which may summarize the interaction between two species in terms of two real numbers as in the Lotka-Volterra approach, artificial ecologies could capture much more of the complexity of interactions in real biological systems. Individual variability can enter in a natural way; learning and individual adaptation can also be included. As an example of the complexity of interactions, think of herbivores interacting with a plant community [41]. Not only do plants and trees provide food for the herbivore, they also provide shelter from sun and wind, escape routes and places to hide from predators, and branches and twigs to make nests and squats from. The grazing of herbivores also affects the plant community: Defoliation can stimulate grasses and trees to produce more leaves; dispersal of fruits, nuts, and seeds by herbivores may affect the spatial structure of the plant community. Apart from direct interactions, herbivores may interact indirectly with other herbivores through their effects on the vegetation, both by reducing resources for other species and by providing access to them (e.g., when elephants fell whole trees). Other indirect interactions may involve changing the risk of predation for other species. Larger species avoid predators by detecting them at a distance and benefit from reduced cover. On the other hand, smaller species that avoid predators by hiding would benefit from increased cover.
- 46. Page 28 A crude classification of the interactions between species would label interactions depending on the signs of the couplings in an imagined set of Lotka-Volterra equations: predation, competition, and mutualism (if one assumes that all couplings are nonzero). In many cases, studies of community structure take only who-eats-whom into account for a number of exceptions (see Kawanabe et al. [45]). Our own approach has been rather different: Starting out from models of the evolution of cooperation, which provide complex interactions between individuals, we then attempt to extend the model to describe predation and resource flow. In the next two sections, we discuss food webs and simple models of community structure. However, our own goal is not to make models of food webs. Instead, we attempt to build simple artificial ecologies with some degree of biological plausibility, and food webs are only one example of observables that could be measured (although a rather useful example, because a reasonable amount of experimental data exist, and a number of statistical regularities in the data have been suggested; see section 3.1). Another issue that needs to be considered if artificial life models are going to make contributions to biology is that of physical realism. Real ecosystems are subject to constraints such as conservation of energy and matter. Many biological scaling laws that involve the body size of organisms (see, e.g., Johnson [42] for an overview) have a physical basis, even if they are not directly derivable from physical scaling. In the coevolving strategy models of the previous section, there are no obvious conserved quantities, and who-eats-whom to some extent becomes a matter of interpretation. In principle, these models could be equally relevant to ecology, but observables related to energy flow are not easily studied. In section 3.3, we describe a model where resources are derived from an external environment, and the result of a game determines their distribution. We also discuss other artificial life models where resources have been explicitly included. 3.1 Food Webs A food web is a graphical representation of who-eats-whom in an ecological community. In most cases food webs are compiled in a qualitative way by ecologists, so that a (directed) link from A to B is present if and only if species B eats species A. Quantitative data showing the relative importance of different links can sometimes also be found in the literature. An example of an experimental food web from the literature is shown in Figure 5 (redrawn from Niering [70]), which shows the most significant feeding relationships among the species on the Kapingamarangi Atoll in Micronesia. This web has some features in common with many reported webs. Many species with similar feeding habits have been clustered into groups (e.g., insects), and there is a cutoff so that rare trophic links are not included (as an example, the fact that Polynesian rats occasionally feed on newly hatched sea turtles is not included). A food web is obviously not a complete description of the community or even of the resource flow in the system. But food webs may still be useful observables to consider, both for real and artificial ecologies. A number of statistical regularities have been claimed to exist in the structure of food webs (e.g., [16, 81]): • The average number of trophic links L is approximately proportional to the number of species , where is small. • The fractions of top predators, intermediate species, and basal species are approximately constant across webs. • The fractions of trophic linkages of different types: top-intermediate, top-bottom,
- 47. Page 29 Figure 5. Food web from the Kapingamarangi atoll in Micronesia, drawn using the data of Niering [70]. intermediate-intermediate, and intermediate-bottom are also approximatively constant across webs. • Averages of maximal food chain length are typically fairly low (approximately 3-4) and do not appear to depend on the productivity of the environment [80]. On the other hand, they do depend on the dimensionality of the environment; three- dimensional environments, such as pelagic water columns and forest canopies, appear to have longer food chains than do two- dimensional environments, such as grasslands and intertidal zones. • Cycles are rare. Food webs in the literature typically do not include cycles due to cannibalism or cycles due to the presence of decomposers. • Food webs can often be represented as interval graphs, that is, graphs that represent how a set of subintervals of the real line overlap each other. Critiques of food web theory can be found, for example, in Paine [77] and Polis [83]. Most published food webs contain a fairly limited number of species, and trophically similar species are often considered as groups. Experimental studies that reflect more of the complexity of real ecosystems (e.g., [83, 106]) are likely to change some of these conclusions. An example of a recent experimental study that disagrees with the link-species scaling law is the work by Havens [36], where power law scaling with was found in a study of communities in small lakes and ponds. In this case the webs were resolved down to genus and species, but the interactions were not measured. Instead, diet information from other sources was used, which makes comparisons with other studies difficult. Multivariable scaling that also involves resolution should be investigated in this context. The study of artificial ecologies might be useful in sorting out which regularities are real and which are artifacts of experimental procedures, because data are more easily available, and the artificial ecosystems can be freely manipulated.
- 48. Page 30 In these cases, quantitative comparisons between real and artificial communities can be made via scaling laws. There are other types of statistical regularities in ecological systems where similar comparisons can be made. One of the most well known is the area-species law (e.g., [56]), a power law for the number of species on an island as a function of its area, S ~ c × Az, with an exponent z » 0.3. (The exponent does not appear to be universal.) Under certain assumptions, this power law can be related to a log-normal distribution of population abundances [61, 86]. Regularities in the patterns of resource flows have also been suggested [65]. 3.2 Community Models In this section we briefly discuss some food web and community assembly models that have been studied in the literature. These models fall into two classes: One could consider only static patterns (e.g., food webs), or one could attempt to model the dynamic process that creates these patterns. An example of a model of the first kind is the cascade model of Cohen et al. [15,16]. This model essentially assumes that food webs are random feed-forward networks. This allows many of their statistical properties to be calculated analytically. No dynamics is involved, just assumptions about the probability measure on the space of webs (although extensions involving population dynamics have been studied [17]). The work by Gardner and Ashby [33], May [59, 60], and others on the relation between complexity and stability led to some work on the dynamics of communities. If large systems with randomly generated interactions between species typically are unstable (as claimed by May), is it possible that communities generated by more realistic assembly processes would be more stable? A number of authors (e.g., [84, 89, 90, 97, 108]) studied models where species were removed from and/or added to the system according to various principles (which unfortunately did not include integration of the population dynamics). Increased stability was typically found. Only more recently has integration of the Lotka-Volterra equations been used in this context [95]. Comparisons between communities structured by invasion and by coevolution were also attempted [91, 92]. More recent work (both theoretical and experimental) by Drake and others [20-23, 74, 82] has focused more on the dynamics of the assembly process. Are there multiple attractors for the assembly dynamics depending on the order in which species are introduced? What is the distribution of local extinction events caused by invasion, and is there a connection to self-organized criticality? The interactions between species in these models are in many cases obtained by choosing invading species at random from a large, predefined food web. In artificial life models, one would in most cases design a reasonable interaction between species in a simple artificial world; a food web then emerges in a natural way from the underlying interaction (if one assumes that it includes some type of predation). Such models could also enable us to study the interplay between coevolution and spatial dispersal of species without making too many oversimplifying assumptions. 3.3 Artificial Ecologies Models such as the coevolving strategy model described earlier can be interpreted as very simple artificial ecologies, where the result of the game directly determines the interaction between species. However, as we have pointed out before, the notions of resources and conservation laws are missing in these models (as well as in various coevolutionary landscape models [9, 44, 71]). Explicit resource flows do appear in a number of artificial life models. Some of these may still not have any immediate ecological interpretation, for example, in the case of more ambitious models where the notion of individuality is intended to be an emergent
- 49. Page 31 Figure 6. The food web and energy flow matrix after 33,600 generations in a simulation of model I of Lindgren and Nordahl [52]. The first part of the histogram represents energy inflows from the environment (always positive); the second energy flows between species (signs depend on the directions of the flows). The open bars show the energy dissipation for each species. The magnitude of the flow is shown relative to the total energy flow for the species in question. property rather than being imposed from the outside (as in the models of Rasmussen and coworkers [87]). Examples of models with a more direct ecological interpretation include the models of Lindgren and Nordahl [52], Holland's Echo [38,39], the model studied by Johnson [42], and many more. The interactions between individuals in the first model of Lindgren and Nordahl [52] (Model 1) are still based on the iterated Prisoner's Dilemma, but the result of the game now determines the distribution of a resource e (''energy"). Each strategy stores a certain amount of energy; the energy transfered in the interaction between two strategies is proportional to the score difference in the game between them (up to cutoff terms). The system lives in an external environment consisting of a number of fixed strategies; energy can flow into the system as a result of playing the game against the environment strategies. The conservation of energy in the interaction turns the game into a zero-sum game. The cooperative effects of the PD are reintroduced by letting the dissipation of energy for each species depend on the score in the game, so that high-scoring strategies utilize their resources more efficiently. Figure 6 shows an example of a food web and matrix of energy flow between species generated in a simulation of this model. The species seen in the web are trophic species, that is, equivalence classes of genomes that interact in approximately the same way with all other genomes. Some of the proposed statistical features of real food webs, such as the approximately linear link-species scaling, are nicely reproduced by the model (see Lindgren & Nordahl [52]).
- 50. Page 32 In te second model of Lindgren and Nordahl [52], the genomes consist of three parts: a strategy gene, a gene that indicates preferences for whom to play, and a tag gene on which other organisms base their choice. In this way a more distinct difference between genotype and phenotype is introduced—the tag gene can be regarded as the "visual appearance" of an organism. This model allows species to develop a higher degree of specificity in their dietary preferences. It also allows the evolution of phenomena such as camouflaged predators that hide among the environment strategies, and mimicry. Introducing spatial degrees of freedom is at least as important in these models as in the ordinary model for coevolution of strategies. With a model that allows interactions with an external environment, phenomena that depend on having a heterogenous environment can be modeled. Extensions to cases with several different resources would also be interesting. These models are rather similar in spirit to Holland's Echo [38, 39]—we use a more complex interaction between individuals (the IPD instead of simple pattern matching); Echo, on the other hand, has more emphasized multiple resources. Another simpler model where hierarchical food webs are observed is that of Johnson [42]. This model incorporates some physical constraints by assigning a body size to each organism. The movement rate and metabolic costs scale as (externally imposed) power laws as function of body size. Organisms have genetically determined food preferences among the species smaller than the organism itself. The dynamics of the system is a Monte Carlo simulation, where individuals interact and move by diffusion on a lattice. This model could be viewed as a natural way of extending the cascade model of Cohen et al. to a dynamical system with discrete individuals. 4 Discussion The problem of understanding the evolution of cooperation (at least when covered by the IPD) is a case where methods that could be classified as artificial life, in particular coevolutionary simulations, already have yielded significant results. We believe that in the future, an understanding of the underlying evolutionary dynamics will be reached for many biological problems. All problems that today are analyzed in terms of game theory and ESS are obvious candidates, but also many other problems where this approach is less suitable. The evolution of flocking behavior in birds is one example. In the case of understanding community structure, the ability to perform a large number of simulations and to sort out statistical patterns will be important. Acknowledgments This work was supported by the Swedish Natural Science Research Council. References 1. Adachi, N., & Matsuo, K. (1992). Ecological dynamics of strategic species in Game World. FUJITSU Scientific and Technica lJournal, 28, 543-558. 2. Andersson, M. (1984). The evolution of eusociality. Annual Review of Ecology and Systematics, 15, 165-189. 3. Axelrod, R. (1980). Effective choice in the Prisoner's Dilemma. Journal of Conflict Resolution, 24, 3-25. 4. Axelrod, R. (1980). More effective choice in the Prisoner's Dilemma. Journal of Conflict Resolution, 24, 379-403. 5. Axelrod, R. (1984). The evolution of cooperation. New York: Basic Books.
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- 56. non accade di dover fare co' primi, che non abbisognano d'altro maneggio per giorni, e settimane. Diciamo or qualche cosa della superiorità riguardo alla grandezza, o forza de' segni: e così diremo anche della facilità d'ottenerli mercè di alcune cautele. In generale le scintille da un apparato di mediocre capacità s'ottengono ben vive: e sono stato modesto anzichè nò nel dire che emulavano quelle d'una competente macchina ordinaria. Adunque un Elettroforo da tasca, qual è il descritto nelle figure, che porta lo scudo del diametro di pollici cinque inglesi, mi dà scintille alla distanza di due buoni diti, e talor più. Con un'altro, che fu il primo da me costrutto di pollici otto, e tre quarti le ottengo all'intervallo di più di tre diti; e da uno di pollici diciassette vengono sì scuotenti, e fragorose, che son quasi insoffribili. Io mi aspetto da uno che sto facendo costruire di più di due piedi di diametro, effetti sovragrandi, e strepitosi, superiori a quelli della miglior macchina ch'io mi abbia visto: giacchè mi s'ingrandiscono smodatamente i segni in ragione che cresce la superficie. Eppure con una superficie sì poco estesa, com'è quella di due pollici nel piccolo Elettroforo che ho chiamato esploratore i segni sono bastantemente forti per manifestarsi con scintilluzze, e dare una carica sensibile ad una piccola boccetta. Ma ecco le attenzioni necessarie per averne sì grandiosi effetti: e primamente riguardo alla costruzione. Egli è di troppo essenziale che lo strato del mastice sia sottile; e il meglio è sempre che lo sia il più che far si possa, salvo che la troppa sottigliezza non provochi la scarica attraverso l'istesso mastice: perciò è da curar bene che alcuna screpolatura non dia luogo ad una spontanea esplosione; e l'orlo pure del piatto deve restare convenientemente distante dallo scudo od essere coperto dal mastice, ad oggetto di permettere la più forte carica, senza che se ne ecciti l'esplosione spontanea. La faccia poi del mastice vuol essere sì piana, che benissimo vi s'adatti lo scudo, piano esso pure nell'inferior faccia, però senz'ombra quasi d'angolo, e ben ritondato nel contorno. Dico piano il mastice, sebbene con la superficie alquanto scabra riesca con eguale, o forse miglior esito; ma intendo che non v'abbiano ridossi, e grandi
- 57. ineguaglianze, onde lo scudo sia tenuto discosto da molti tratti di superficie. È egli necessario l'avvertire, che se il mastice pel lungo uso si trova insudiciato convien ripulirlo? Non si crederebbe quanto contribuisca l'essere esso mondo, e scevro d'ogni lordura. Però giova assaissimo tenerlo sempre ben custodito: e quando pur si vegga imbrattato (di che anche s'accorge per un certo viscidume, se si stropiccia) raschiandolo con una lama di coltello, e col far iscorrere per brevissima ora la faccia di questo mastice sopra le brage, o entro la fiamma stessa, gli vien tosto ridonata colla sua nitidezza l'ottima disposizione ad agire. Ho trovato che passandolo sopra la fiamma di una candela, quella sottil patina di che è lordo s'imbianca, e s'annebbia come fa l'alito sulla faccia di uno specchio, e tosto come questa sparisce, lasciandovi la maggior lucentezza. Ecco dunque un mezzo facilissimo di raccomodare il mastice guasto o imbrattato, senza fonderlo tutto di bel nuovo. Riguardo al maneggio dell'apparato, se la giornata non è del tutto favorevole bisogna asciugar bene al fuoco, o al sole non già tanto il mastice, che, come s'è detto da principio, poco o nulla teme l'umido, ma la boccetta, e il manico isolante: ed è più spediente ancora in luogo di regger lo scudo per il bastoncino di ceralacca, alzarlo con cordicelle di seta asciutte, e monde, e piuttosto lunghe. Come abbiam già toccata l'importanza di tener lungi dalla faccia del mastice la polvere, e i peli, si vuol aggiungere che importa finanche di nascondere i manichetti perchè essi pure a poca distanza rubano molto; il tener discoste le vesti ec. Quando poi occorre d'indurre primamente l'elettricità sul mastice collo stropiccío della mano, è più necessaria la cautela di far rientrare i manichetti (fig. 5); e necessarissimo è che essa mano sia ben asciutta: altrimenti varrà meglio lo strofinare con carta, panno, e singolarmente con velluto bianco; ma trovandosi quella asciutta, io prometto che il solo scorrere velocemente sulla faccia del mastice colla palma due, o tre volte senza premerla con forza, basterà perchè abbiate tosto dallo scudo la scintilla quasi d'un dito. Dopo tutto questo che ho detto de' vantaggi del mio Elettroforo, non ho pena a confessare, che le macchine ordinarie ben grandi, e ben
- 58. eseguite ne' tempi favorevolissimi giungono più presto a caricare un quadro di ampia superficie, od una batteria, per la ragione che il fuoco vi cola incessantemente: laddove nel nuovo apparecchio spiccando le scintille con quella interruzione, che porta l'abbassare, e rialzar lo scudo, più tardi ci si perviene. Ho detto ne' tempi favorevolissimi: perchè poi sono gli effetti dell'Elettroforo sì vivi anche ne' tempi men propizj, che vuolsi bene spesso preferire un simile apparato che sia grande, per l'oggetto pure di caricare quadri, e batterie, alla macchina di vetro ordinaria, da cui le molte volte si pena a cavar partito. Oltre di che io credo non sarà difficile col tempo immaginare de' mezzi per ottenere cotesto necessario accostamento, e discostamento dello scudo più speditamente, e con un moto uniforme, e con minor incomodo. Dirò anche che sto per metter mano ad un meccanismo assai semplice onde venirne a capo. Una molla, che al premere della mano, od al girar d'una cordicella o staffa, alzi, ed abbassi lo scudo, promette di dispensarmi da molta parte d'incomodo. Oppure in altra forma lo scudo portato da un pendolo, cui dia moto una ruota, e un peso, e che vada a baciare a destra, e a sinistra due piatti, ossia faccie di mastice elettriche, e così andando, e venendo incontri nel mezzo da salutare con le scintille un conduttore, o la caraffa, mi rappresenta un doppio apparato, che per la ragione della celerità de' movimenti potrà darmi effetti molto più che duplicati. Ma infine io dichiaro col miglior cuore che non ho l'abilità di riuscir bene in simili costruzioni meccaniche; che d'altra parte non è questo il mio scopo principale; e che per quanto io tenga conto, e lo tengano tutti quelli, innanzi a cui ho mostrate in esteso l'esperienze, dei comodi che ne offre l'Elettroforo, io valuto assai più i lumi che mi si vanno svolgendo su diversi punti della teoria elettrica: intorno a che pubblicherò fra non molto le mie osservazioni già in parte comunicate al Signor Dottor Priestley[35].
- 59. ARTICOLI DI TRE LETTERE[36] Scritte al Sig. Canonico Fromond. Como 26 Ottobre 1775. Aspetto con impazienza le osservazioni vostre sulla migliore struttura dell'Elettroforo. Intanto vi darò io nuova della riuscita di quello che ho ultimamente terminato di legno del diametro poco meno di due piedi. In questi due ultimi giorni che spira una forte tramontana ho ottenuto scintille a dieci, dodici, ed anche quattordici diti trasversi: v'immaginate com'erano guizzanti. Per averle di questa forma presento non più la nocca, ma la punta del dito. Sovente in luogo della scintilla esce dal dito un grandissimo fiocco, collo scoppiettar in seguito di più scintille succedentisi. È tale la forza, e la copia del fuoco, che le punte metalliche affatto ottuse, come d'una chiave, anzi l'anello di essa, e fin le palle, se non sono affatto grosse, fanno appunto l'officio di punte, e gettano il fiocco. Che più? Tre sole scintille dello scudo caricano una mezzana caraffa a dare una scossa penosa; e dieci in dodici la sopraccaricano a segno di scaricarsi spontaneamente. Como 14 Novembre 1775. Vi ho detto già come pensava d'or in avanti di costruire l'apparato portatile, per avere in un egual volume assai maggiore capacità. In luogo di stendere il mastice sopra un piatto, lo stendo nella cavità d'un emisfero, dando poi allo scudo la stessa conveniente figura. Trovo anche meglio dell'emisfero divisato un cono troncato, che può essere lungo benissimo d'un palmo, e largo quanto porta l'apertura della tasca: un'altro cono ch'entri nella cavità del primo mi fa l'ufficio
- 60. di scudo, e può chiudere in seno una boccia di discreta capacità, e l'uno, e l'altro facendoli di latta, oppur lastra di rame, ottone ec., e tutto insieme porta poco peso, e men imbarazzo. Ma io non voglio curarmi tanto di questi apparati portatili, nè dell'eleganza, quanto della grandiosità degli effetti, di cui fan pompa i grandi: sicchè mi tratterrò a parlare dell'apparato mio massimo. Ho dunque tralle mani il grande Elettroforo del diametro di quasi due piedi che ho fatto terminare tosto che ripatriai. L'attività di questo è veramente sorprendente. Basta dire che ottengo non di rado scintille a dieci, dodici, e più diti trasversi: scintille che appajono in vaghissima forma guizzanti emulatrici appunto del telo di Giove. Per averle tali elettrizzo il mastice per eccesso, e presento allo scudo alzato la punta del dito, ovver facendomi ribrezzo, l'anello d'una chiave, da cui ora balza la scintilla lunga come dissi, e guizzante, or una serie di scintillette crepitanti succedonsi, or ne spiccia con leggier sibilo un lunghissimo fiocco. Una canna spaccata della lunghezza di due braccia vestita nella parte convessa di carta dorata raschiata con pelle di pesce rappresenta ancor meglio, e nella maggior estensione il balenar vivissimo della folgore su tra le nubi, mentre è percossa tutta, o per gran tratto almeno, ad ogni scintilla che riceva dallo scudo, da una, o più striscie di luce verde-lucenti. Finalmente una caraffa di mediocre capacità in quattro, o sei volte che io faccia giuocar lo scudo, riceve una carica, che mi scuote validamente. Nè crediate già che effetti cotanto strepitosi abbian luogo solamente ne' tempi all'elettricità molto propizj: gli ho ottenuti di poco minori in questi ultimi giorni di nebbia, e pioggia incessante, mercè la sola attenzione di asciugare le lunghe cordicelle di seta, con cui alzo lo scudo. Nè pur temiate che lasciando l'apparato in riposo, e senza ravvivarlo per molte ore, o per alcun giorno, vada a cader di molto la forza: dopo due, o tre dì io ricavo ancora scintille tali, che il dito non può soffrirle che con pena, e con dieci, o dodici di esse porto una discreta carica alla boccetta: così poi volendola metter a profitto col bel giuoco di rifonderla sul mastice, ottengo tosto la massima intensione. A finirla, non v'è più da dubitare, che col mio apparato
- 61. non si possano creare, ed avere ad ogni ora, e ne' tempi singolarmente men propizj, effetti di gran lunga superiori a quelli della miglior macchina a globo, o a disco. A buon conto io posso fare il mio piatto di metallo, o di legno magnitudine quantalibet ad effectus quantoslibet, come diceva il P. Beccaria, vantando il suo tavolino fulminante. Due sono solamente gl'inconvenienti che s'incontrano, volendosi far l'apparato di una smisurata grandezza: uno intrinseco, e sostanziale, l'altro estrinseco, e accidentale. Il primo è che crescendo in ragione dell'ampiezza della superficie la forza della carica, della scarica, e quella pure della scintilla, che tende a balzar dallo scudo mentre s'alza, il mastice ne vien tosto in alcun sito spezzato, o fuso, salvo che non sia di una comoda spessezza; ma che? la spessezza maggiore toglie molto della capacità della carica, e quindi anche della forza dell'elettricità permanente (dico elettricità permanente non più vindice, perchè l'idea che ci porta il termine vindice è meno al fatto, ed alla teoria confacente per non dire assolutamente erroneo, come avrò luogo di provare in altro tempo). Il secondo inconveniente riguarda l'incomodo nell'usare di un apparato assai grande. Per nulla dire, che convien tenersi col braccio allungato, e col corpo, e vesti discoste nell'alzar lo scudo, pur troppo devo sentire, che il peso di questo, sebben sia di legno inargentato, stanca potentemente, e che m'impedisce di alzarlo, ed abbassarlo, come vorrei, con celerità. Quanto però all'incomodo nel far agire cotesto scudo, penso di potervi agevolmente portar riparo: tra gli altri presidj quello mi propongo di un vette, o che verrà più opportuno, di alcune carrucole. Questo ingegno mi porrà in istato di vincere il peso con poca forza, e di far giuocar lo scudo standomi ad una comoda distanza, e con tutto agio della persona. Esso scudo poi ho già pensato a farlo dieci volte più leggiero che quel di legno: e vuol essere di tela stesa a foggia de' nostri quadri sopra una cornice, ma questa ritonda (meglio anche della cornice di legno s'impiegherebbe un larghissimo collare di vimini che riuscirebbe, e più leggiero, e men soggetto a gettarsi) di tela dissi, in tal maniera stesa, e poscia inargentata. Avrà
- 62. questa, oltre la leggierezza, un altro considerabilissimo vantaggio di adattarsi bene, e sempre a combaciamento colla faccia del mastice assoggettata, e per la propria pieghevolezza, e per virtù dell'adesione elettrica. Con tali espedientissimi sussidj io potrò costruire, e render maneggevole anche ad un uomo solo un apparato grande di sette, otto, e più piedi. Immaginatevi una tavola grande come quella per il giuoco del Bigliardo, ma rotonda, foderata convenientemente di latta, o di rame con sopra steso bene in piano un mastice nero, e lucente siccome specchio: vedetevi indosso posato un bel coperchio a plat-fond inargentato, o dorato, pendente da quattro capi di corda di seta che terminano poi uniti in un solo a un congegno di carrucole, e guidato nel salire, e scendere da due altre corde di seta fisse verticalmente, che giuocano in altre due girelle annesse a due parti estreme, ed opposte di esso coperchio, o scudo: ecco l'uomo a qualche passo dalla tavola, che col tirar una fune pendente, quasi in atto di suonar le campane, fa che suonino invece scintille fragorosissime, e fischino fiammelle, e getti di luce a tutti i lati a distanza di più palmi contro i varj conduttori ad arte, o a caso d'intorno disposti: dite, non è quel coperchio l'idea d'una nuvola fulminante? Non vi fa terrore l'accostarvi? Eppur io, dato bando ad ogni spavento, amo anzi pronosticare utili cose, e vantaggiose, e mi compiaccio raffigurar ivi quella camera per la Medicina elettrica che vorrebbe il Sig. Priestley istituita. Ne vaneggio io già decantando così grandi, e strepitosi gli effetti d'un così vasto apparato: oso predirli tali, incoraggito, e quasi rassicurato dall'azione di quello, sopra cui sto attualmente sperimentando, il quale sebben non giunga ancora a due piedi di diametro, è mirabile il vedere di quanto lungo tratto si lascia addietro tutti gli altri apparati di circa un piede, o minori. Ma la spessezza del mastice per tanta estensione di superficie richiesta, che notai per primo, e intrinseco inconveniente mi dà ancor molto a pensare. Se non che ho fondamento di credere che una linea, e mezza, o poco più sia per essere sufficiente per qualunque ampiezza, e il fondamento riposa sopra delle prove che ho fatte a quest'oggetto. Altronde per prove similmente fatte mi risulta che tale
- 63. spessezza di una linea, e mezza (sebbene si diminuisca di molto la virtù della mezza linea in sù) porta ancora una carica abbastanza forte. Ho detto che io estimo poter bastare per qualunque grande apparato l'altezza nel mastice d'una linea, e mezza: intendo però che questo sia dappertutto unito, e sodo sopra un piano similmente eguale, e liscio, che non abbia screpolature, nè vi si coprano sotto dei vacui, o bolle d'aria. Ma come emendar quelle, e purgarlo affatto di queste? Non è difficil cosa il venirne a capo. Steso bene, e rassodato nella vostra tavola il mastice, scorretevi sopra dappertutto, senza però toccarlo, con un largo, e grosso ferro rovente. In un subito vi si apriranno sulla superficie innumerabili buchi, i quali per forza dell'istesso calore di lì a poco si riempiranno, e spariranno. Non basta, avviene spesso che adoperando l'apparato, e tormentandolo, salti fuori quà, e là una magagna, per cui avete ad ogni tratto una esplosione spontanea. Allora conviene andar in cerca colla lanterna del sito, ove s'asconde il vizio: e la lanterna è una boccia ben carica con cui scorrendo sopra, una scintilla che scappi furtivamente vi avverte a pelo di ciò che dovete correggere col vostro ferro rovente. Como 21 Dicembre 1775. Ho provato a far lo scudo, giusta quanto avea divisato, con una tela stesa su d'una cornice. Ho scelto la tela incerata, e senza punto inargentarne la faccia stessa incerata che guarda, e bacia il mastice, mi sono contentato di vestire di foglia d'argento la faccia che resta scoperta, e il contorno della cornice. Trovo che questo scudo giuoca ottimamente, e corrisponde a tutta l'aspettazione mia. Dapprima avendo pensato che l'argentatura alla faccia che tocca il mastice era per lo manco inutile, credei il meglio non vestire di foglia metallica che il contorno della cornice da cui si cavano le scintille ec. Ma poi m'avvidi ben presto che essendo la tela incerata conduttore pochissimo, buono, a stento, e lentamente dismetteva ella il suo nativo fuoco in ragione che l'eccesso del mastice lo esigeva, o viceversa: ciò era chiaro da vedere che toccando col dito, con
- 64. catenella lo scudo posato, toccandone dico l'orlo inargentato, una piccola scintilla si estraeva: indi a qualche momento tornando a toccare, un'altra piccola scintilla; e così successivamente per alcuni minuti. Da ciò ne risultava, che alzando lo scudo dopo consumata dirò così la scarica, cioè dopo estratta tutta quella serie di scintillette, vibravasi scintilla fragorosissima guizzante ec. ma alzando esso scudo dopo un sol toccamento, la scintilla non ne sortiva che men forte di molto. Allora fu dunque che mi volsi al ripiego di vestir di foglia metallica la faccia tutta esterna della tela: così la scarica si fa sensibilmente tutta in un sol toccamento, non impedendola guari la poca spessezza della tela che prima l'impediva coll'estension sua. Del resto torno a dire, il dare una superficie metallica alla faccia che guarda il mastice, è inutile senz'altro, anzi può essere per alcun riguardo di nocumento. In prima l'estrema mobilità del fluido elettrico ne' corpi metallici, e qualche picciola prominenza che si trovi in detta faccia inferiore, dà facilmente luogo a qualche disperdimento: si provoca più fortemente l'elettricità inerente nel mastice a tradursi per quella: non così però una superficie quasi coercente, qual è quella dell'incerata nuda. D'altra parte poi un simile scudo, che non affaccia metallo alla superficie del mastice, nè minaccia di romperlo, o fonderlo colla scintilla nel venir alzato, nè sopra posandovi, e ricevendo la carica, provoca sì facilmente per qualche sopraggiunta screpolatura al mastice medesimo l'esplosione spontanea, come d'ordinario addiviene cogli scudi sin quì usati, per poco che s'incalzi la carica. Giacchè siamo sul punto di sopprimere la superficie metallica ad oggetto di toglier massimamente il luogo all'esplosioni spontanee, non debbo lasciare di farvi parte d'alcune altre mie osservazioni, e avanzamenti circa la pratica, e la teoria dell'Elettroforo. Ho dunque sospettato che non fosse necessario, che il mastice steso venisse sopra un metallo: e basterà bene, io mi dicea, che sia steso sopra un corpo non isolante. Ho provato dunque a versare il mastice sopra un disco di legno nudo, e sopra uno di cartone: ed ho veduto difatti che si hanno i segni quasi egualmente forti di quando adoperasi un piatto di metallo. Noto solamente che facendo un Elettroforo di legno
- 65. grande non può farsi la scarica che lentamente (presso a poco come ho osservato nel caso dello scudo non vestito di metallo in ambe le facce) mercecchè il fuoco che si dismette dalla faccia superiore ossia dallo scudo non può tostamente restituirsi per entro al legno non molto permeabile, e condursi alla faccia inferiore del mastice, o viceversa. Del resto dando tempo che ciò effettuar si possa, veggo che il legno si presta ottimamente a tutti gli effetti. Si potrebbe anche rimediare al difetto che nasce da questa lentezza, versando sì il mastice sopra tavole di legno nudo, ma coprendo poi di metallo il di sotto delle tavole medesime, le quali vorrebber essere grosse sol di poche linee. Ma la fermezza di esse? Mi pare che queste sottili tavole così guernite si potrebbero indi assoggettare a un gran tavolo fermo, e sodo. Ma a che però, mi dite; un tale macchinamento? Per istendere il mastice sul legno nudo, anzichè sul metallo? Appunto: giacchè per questo modo verremo (ciò che mi era proposto a principio) a dare niun luogo più alle esplosioni spontanee: e sì potremo stendere senza timore di questo il nostro mastice molto più sottile; che importa pur tanto per la miglior riuscita. Eccovi, Amico, un nuovo indirizzo per la costruzione di quel tremendo Elettroforo che vorrei pur veder eseguito: ecco le correzioni che ho potuto immaginare tanto riguardo allo scudo, quanto riguardo al piatto, o disco. Saranno queste le ultime? Non so. Ma non le chiamate perciò inutili: sono sempre passi che portano all'ingrandimento, e i dati fin quì non furono mai senza alcun progresso. Non termino senza darvi un ragguaglio delle considerazioni mie sul raro fenomeno di elettrizzarsi costantemente in più, il mastice di quel mio grande Elettroforo. Io sono ben persuaso che voi non sarete riuscito ad osservare il medesimo in qualunque maniera vi ci siate preso. L'essere l'apparato grande, o piccolo punto non rileva; nè io ho voluto insinuare che la grandezza mettesse quella differenza: indicai solo che il mastice il quale mi presentava tale singolarità era quello dell'apparato grande, sebbene ne fosse la composizione simile agli altri mastici che adoperava. Era difatto così la cosa riguardo agl'ingredienti, e manipolazione, ma io non poneva mente a un accidente sopravvenuto durante la cottura del mastice, che ha
- 66. dovuto alterarlo: l'accidente fu che vi si appiccò la fiamma, e ne venne in molta parte consumato: il residuo contrasse dell'abbruciato, o del carbone di maniera che lascia sempre tinta la mano, o la carta quando si stropiccia, e facilissimamente si sfregola. Dunque ho concluso che da questa alterazione dipenda l'indole mutata nel mastice di elettrizzarsi, cioè positivamente. Portando poi più addentro la considerazione, ho preso a sospettare che codesta mutazione d'indole derivi dal deterioramento della virtù di elettricità originaria, o almen vi vada di paro: osservando che infatti cotesto mastice mezzo bruciato aveva pochissima virtù di elettrizzarsi per istropicciamento: laddove l'altro che costantemente contraeva per la via medesima elettricità in meno, e fino stropicciato con lamine metalliche, godeva di un'elettricità generosa. L'induzione per me felicemente si estendeva ad altri corpi, i quali non meno che la resina affettano l'elettricità difettiva, e sono i legni abbrustoliti. In questi aveva osservato già, e scritto nel 3 Cap. della mia dissertazione latina 1771, che i legni abbrustoliti di fresco, e a dovere, danno a qualsivoglia corpo anche metallico con cui si strofinano, finchè dura in quelli la massima virtù; ma che a misura che questa decade, degradano anche dall'indole sua, e ricevono prima da alcuni metalli solamente, poi da più, poi da tutti, e fin talvolta dal panno nero ec. Or nella resina mi si spiega più largo il campo di questo passaggio. Occupa un estremo il mastice, che ho veramente ottimo, il quale con leggierissimo, e breve stropicciamento conseguisce una elettricità affatto generosa; tien l'altro estremo quel mastice mezzo bruciato, dal quale, sebbene stropicciato per una sì vasta estensione, qual è quella di due piedi nell'apparato grande, appena ottengo una scintilluzza (dico semplicemente stropicciato ch'eccita nello scudo una debolissima scintilla, perchè poi infondendovi maggior forza d'elettricità con altra macchina, o colla caraffa acquista non meno che il mastice migliore; tutti i gradi di forza). Di mezzo a questi tengo altri mastici, i quali convenientemente si elettrizzano per istropicciamento. Parallelamente dunque a questa originaria virtù il primo affetta sì fortemente l'elettricità in meno, che non consente di elettrizzarsi in più nemmeno dalla carta dorata, od altre foglie metalliche:
- 67. solamente coll'amalgama di mercurio ve lo costringo. Il secondo, o per dir meglio l'ultimo in ordine alla virtù, è passato a mutar affatto indole, e non che elettrizzarsi in più per l'affritto di corpi metallici, lo stesso fa con qualsivoglia corpo. I mezzani finalmente danno alla mano, carta nuda, panno, cuojo ec., e ricevono dalla carta dorata, foglie di stagno ec. L'induzione dunque, e l'analisi vengono in conferma di quel mio sospetto circa il decadimento della virtù, cagione del rovesciarsi l'indole nei corpi resinosi. Ma credete voi che di queste osservazioni possa contentarmi? L'induzione è ancor troppo poco estesa: d'altra parte io la vorrei confermata colla sintesi; e voglio dire che niente ho per istabilito finchè non giunga a comporre a mia posta de' mastici che abbian l'un'indole, e di que' che abbiano l'altra, col solo mezzo di differenziarne la qualità, ossia virtù. Dirovvi per ora che mi ci sono provato, e in qualche parte con esito. Ho preso lo spediente per deteriorare la qualità del mastice, di meschiarvi del carbone messo in polvere. Il carbone, come si sa, è un corpo conduttore poco meno che i metalli: per questo lo scelsi, e dirollo pure, per veder d'accostarmi all'alterazione che dovette ricevere quel mio mastice, che fu in preda qualche tempo alle fiamme. Il resultato fu che una certa dose di carbone meschiata all'altro mio mastice d'ottima condizione lo deteriorò d'assai, e lo ridusse difatti a ricevere dalle foglie metalliche a cui prima dava. Non potei però giammai ottenere che ricevesse dalla mano, carta nuda, panno ec., e in somma che mutasse affatto indole come il mastice mezzo bruciato. Provai dunque ad appiccarvi la fiamma, e lasciarlo in buona parte consumare; ma nemmeno con questo mi riuscì. Accrebbi la dose del carbone; ma allora non si elettrizzò più nè per eccesso, nè per difetto. I tentativi fatti adunque non finiscono di appagarmi: non depongono però contro la concepita idea. Anzi mi resta ancor luogo a credere che il mastice alterato a segno di non vestir più sensibile elettricità per lo stropicciamento, abbia di poco oltrepassato il segno che cercava: può anche non averlo oltrepassato, ed essersi elettrizzato realmente in più, ma così debolmente che non ne abbia
- 68. avuti segni sensibili: i quali segni sono forse sensibili soltanto nel grande apparato per esser tanta la superficie stropicciata.
- 69. LETTERA Al Sig. Giuseppe Klinkosch. R. Consigliere, Pubblico e Primario Professore di Anatomia nell'Università di Praga, e Membro della Reale Società delle Scienze di Gottinga. Maggio 1776. Ho ricevuto alcune settimane sono sotto coperta a me diretta, e marcata dell'officio di Praga uno scritto tedesco, che tratta in parte del mio Elettroforo perpetuo. Siccome ho fermo nell'opinione, essere l'autor medesimo, che abbia voluto obbligarmi coll'inviare a me questa operetta; così mi credo permesso di trasmettergli io pure alcuni fogli italiani da me pubblicati l'anno scorso in un'Opera periodica concernenti il medesimo Elettroforo. Non senza difficoltà ho io potuto intendere, Signore, cotesto vostro tedesco, attesa la poca cognizione, che ho di cotal lingua; di che mi duole pur assai. Se voi trovaste mai la medesima difficoltà rispetto al mio italiano, starebbero tra di noi le cose pari. Se non che io voglio pur procurare di rendermi, o più scusabile, o ben anche più benemerito di voi, accompagnando i fogli impressi con alcuna cosa scritta di mia mano, e alla meglio che mi verrà fatto in una lingua, che non è la vostra nè la mia, ma che saravvi senza dubbio più famigliare che l'italiana[37]. Non mi sorprende punto, Signore, che voi stimiate dover diffalcar molto da quel merito, e vanto dell'Elettroforo, che il volgo de' Fisici, siccome voi dite, troppo precipitosamente gli ha accordato. L'ammirazione, che molti ne presero ha oltrepassato, e quello ch'io poteva a buon dritto pretendere, e ciò che avrei mai potuto sperare.
- 70. Si è tenuto in conto di una scoperta mia propria quello, ch'io fui ben lontano dall'attribuirmi, val a dire un nuovo genere di Elettricità, ossia una nuova maniera di eccitarla. Si può vedere per altro, ch'io faceva intendere assai chiaro col primo annunzio che uscì del mio nuovo apparecchio nella Scelta d'Opuscoli di Milano per il mese d'Agosto, e più apertamente ancora colla lettera al D. Priestley in data de' 10 Giugno, pubblicata in appresso nella medesima Scelta, ch'io non avea fatto altro più, che tener dietro, e dar risalto a un ramo di Elettricità, che già era noto sotto il nome di Elettricità Vindice. Tanto non vien egli indicato dai termini stessi, onde ho cognominata l'elettricità del mio apparato Vindice indeficiente? Ma poi anche in termini più formali mi esprimeva nella succennata lettera a Priestley: basta vederne il secondo paragrafo, ove, dopo avergli detto, che i fatti ch'io era per riferire appartengono all'Elettricità Vindice; e che egli da ciò immaginerebbe tosto, che si tratta d'una lastra isolante vestita, e snudata a vicenda della sua armatura, vengo a spiegare in qual maniera sono riuscito coll'ajuto d'un'armatura più conveniente, e col surrogare alle consuete lastre di cristallo altre di resinosa materia a rendere cotesta elettricità di una forza stupenda, e di una durevolezza ancor più maravigliosa. Ma non solamente ho io fatta menzione dell'Elettricità Vindice nel modo che si è veduto: ho parlato eziandio della teoria di essa, e fatto caso delle sue leggi come di già stabilite. Ho detto in un luogo: siccome richiede la teoria dell'Elettricità Vindice: sul fine poi della lettera mi trattengo a parlare d'una contrarietà di sentimenti tra me, e il Padre Beccaria sul conto dell'elettricità dell'armatura in virtù della scarica, e per l'atto dello snudamento; e mi argomento di comprovare con nuovi fatti quella mia opinione avanzata già in una lettera latina al medesimo Padre Beccaria impressa fin dall'anno 1769, nella quale molto mi occupava a sviluppare cotesto principio dell'Elettricità Vindice. Egli è dunque fuor d'ogni dubbio e contrasto, ch'io era ben lungi dal pretendere alla scoperta della sovente menzionata Elettricità Vindice, od a quelle sue leggi già conosciute, e stabilite; comechè io volgessi in mente già da gran tempo, ed or più di proposito mi studj di
- 71. riformarne alcuna, anzi pure un de' precipui capi della teoria. Che se poi alcuni, come voi dite, mi hanno gratuitamente attribuito un merito, e una lode, che per nulla ragione mi si devono, e contro cui io protesto, a chi dovrassene far carico? a me non già. D'uopo è però convenire, che molte persone dovettero formare appunto quel giudizio, che ne formarono, attesochè le sperienze dell'Elettricità Vindice lungi ben erano dall'essere famigliari: infatti il numero di coloro, che aveanle viste non è già grande, e assai più scarso si troverà di chi le avesse da se stesso eseguite compitamente sopra le consuete lastre di vetro; non essendo il riuscir di questa maniera sì agevole, bensì frutto di somma diligenza, e destrezza, concesso soltanto alla mano de' più esperimentati. Ora tostochè comparve il mio apparato, i di lui effetti tanto più grandi, e sorprendenti, quanto facili ad ottenersi, dovettero colpire, e fermar gli occhi di tutti: il nome imponente di Elettroforo Perpetuo concorse pur anche a far crescere quella specie di stordimento; infine l'amore del nuovo, e del maraviglioso indusse a credere, che tutto lo fosse, di sorte che accoppiando all'invenzione del nome, e dell'apparato quella puranco del genere di elettricità, venne così indistintamente attribuita ogni cosa al medesimo autore. Giusto è bene, che per rivendicare il merito a chi è dovuto, io venga spogliato di quello che mal mi conviene; ed io con pieno animo acconsento a questo, e mi fo sollecito ancora di contribuirvi. Guardimi per tanto il Cielo, ch'io muova lamento contro di voi, Signore, perchè impreso abbiate di farlo; debbo e voglio anzi sapervene grado: solo mi credo permesso di porvi sott'occhio che non si son fatte da voi le parti in tutto giuste, perciocchè attribuito avete al Padre Beccaria ben più di quello, che non gli si compete, ponendo l'Elettricità Vindice in vista di scoperta tutta sua. Epino dietro il celebre sperimento de' Gesuiti di Pekino, Symmer con le sue calze di seta, Cigna con una serie di sperienze analoghe prodigiosamente combinate, e variate, e in gran parte nuove hanno aperta questa bella carriera, nella quale entrato il Padre Beccaria vi ha fatto di vero i più gran progressi, giugnendo a stabilire delle leggi semplici, e luminose. Parlo di alcune di queste leggi ossia canoni,
- 72. non già di tutte, e nullamente delle sue Teorie, cui ho avuto sempre in mira di oppugnare rispetto ad uno de' precipui capi (ciò che anche mi provai di fare nella lettera latina menzionata), e cui mi applico presentemente più di proposito a riformare, come già accennai. Ritornando ora al mio apparato, mi pare aver lasciato abbastanza intendere, che io ne riduco tutta la novità, per quanto è della sua costruzione, alla miglior foggia d'armatura, ed allo strato resinoso sostituito alla lastra di vetro: quanto poi sia degli effetti, all'intensità costante dei segni elettrici, e vera perennità di essi: ciò che vale ad esprimere per se solo il nome di Elettroforo perpetuo. Non deggio però dissimulare le opposizioni, che intorno a ciò sò essermi state fatte; e sono: che la disposizione propria dei corpi resinosi ben più che del vetro a ritenere l'elettricità, è stata osservata, e conosciuta gran tempo prima di me da Grey, Du-fay, Epino ec.: che quest'ultimo inoltre in compagnia di Wilke ci avea dato l'esempio di un vero Elettroforo con quel bellissimo esperimento dello zolfo fuso in una coppa di metallo, ond'egli traeva i segni elettrici sì dal recipiente, come dal corpo di zolfo, ogni volta che ne li disgiungeva: e ciò anche dopo settimane, e mesi. Nulla io ho a ridire riguardo a questa anteriorità di tempo; ciò che posso assicurare si è, che non son già io partito dalle sperienze di Wilke o d'Epino (delle quali non era nemmanco informato) per giugnere alla costruzione del mio apparato; bensì partii da quelle, che si faceano comunemente per la Vindice Elettricità servendosi di lamine di vetro: quì veramente io seguiva le sperienze di Beccaria ad oggetto di confutare, come ho sopra indicato, un fondamento della sua teoria; e così dietro ai miei principj fui condotto primieramente a dar una forma più convenevole all'armatura, onde ottenere valida, e intiera forza d'elettricità[38]; e ben tosto a sostituire le resine al vetro acciò mi si mantenessero più durevoli i segni; richiamandomi allora come io mi era già assicurato della disposizione singolare, che hanno questi corpi di conservare tenacemente l'elettricità impressa; e rivolgendo pure in mente le idee, onde io mi era argomentato di spiegare questa tenacità medesima in una lettera al Dr. Priestley fino dal Maggio del 1772[39].
- 73. Del rimanente pare non si possano metter in confronto i piccoli saggi di Epino, e di Wilke sopra lo zolfo, e altre resine fuse, col mio Elettroforo per conto della grandezza degli effetti. E forse che gli si vorranno paragonare le sperienze di Beccaria colle sue lastre di cristallo vestite di sottili lamine metalliche? Ognuno, io credo, ha dovuto riconoscere la superiorità a questo riguardo del mio apparato: voi, Signore, sì, voi medesimo la riconoscete, e mi fate l'onor di dire, che gli amatori me ne deggiono saper grado. Grado dunque mi sapranno (tal'è la mia lusinga) della costruzione d'un apparecchio così semplice, che tien luogo d'una buona macchina per tutte le sperienze ordinarie, col quale anzi si possono diversificare di più maniere, e facilissimamente; apparecchio, che può farsi tanto piccolo da esser portatile in tasca, oppur grande a qual si voglia segno, onde averne effetti superiori a quelli di qualunque altra macchina, di cui l'attività malgrado i tempi, e l'aria men propizia poco, o punto vien a perdere; che infine (e questo è il massimo suo pregio) può conservar per sempre l'elettricità, una volta impressavi, cioè a dire senza che faccia mestieri ricorrere ad un novello stropicciamento, o ad elettricità straniera. Ecco dunque ove mette capo tutta la mia pretesa alla novità: egli è d'aver inventato, o (se questo ancora sembra troppo forte) perfezionato cotal apparato al segno di riunire tutti gli accennati vantaggi, e ridotto a grandissimo comodo per tutti. Infatti quanti di questi apparati veduti non si sono sparsi, e moltiplicati in poco tempo? Tanto già non succedette cogli apparecchi di Epino, di Cigna, di Beccaria, che pur qualcuno, invidioso forse della considerazione, e grido, che si acquistò il mio Elettroforo, non cessa per anco di porgli incontro. Ho nominato Cigna, perchè se v'ha persona, che si sia portata più vicina alle sperienze mie sull'Elettroforo, e, dirò così, vi abbia preluso, egli è desso Sig. Cigna. È certo almeno, ch'ei pervenne avanti di me a caricare la caraffa per mezzo dell'elettricità vindice, o simmeriana, com'egli amò appellarla: e ciò ricevendo nel pomo della caraffa la scintilla di una lamina di piombo tenuta con fili di seta isolata, allorchè dopo avervi applicato, ed accostato ben davvicino un
- 74. nastro fortemente elettrizzato, e dopo aver toccata col dito essa lamina, ne ritirava bruscamente il nastro, replicando poi tante volte questo giuoco, quante bastassero scintille ad una tal carica. Ma non è meno certo, che con un simile apparecchio non si può sperare di caricare una boccia che debolmente, e ciò anche con molta pena, ed imbarazzo, laddove nulla v'ha di più facile che il caricarla convenientemente, e ad ogn'ora coll'Elettroforo, e sì anche con uno da tasca. Mi cade ora a proposito di domandare, se un tal nome, che conviene tanto propriamente al mio apparecchio, e che è stato comunemente addottato, converrebbe di pari a quello di Cigna, o a quel d'Epino, o alle lastre del P. Beccaria. Accordiamolo loro pure: sicuramente però, che quest'altro termine di perpetuo, il qual compete a tutto rigore al mio Elettroforo, niuno pensa tampoco di appropriarlo a qualsisia degli altri. Sfido tutti gli elettrizzanti, se alcun d'essi con lastre di cristallo, o con calze di seta applicate a laminette sottili di metallo può perpetuare l'elettricità, anzi solo mantenerla, senza nuovo strofinamento, o senza prenderne altronde in imprestito, a molti giorni. Vi si giugnerebbe, ne son ben d'accordo, colla coppa, e massa di zolfo d'Epino, mercè il giuoco di caricar la boccetta, e portarne indi il fondo a scorrere sulla faccia stessa dello zolfo: al qual giuoco però nè esso, nè alcun altro ha giammai pensato, avendolo io, per confessione degli stessi miei oppositori, e ritrovato, ed insegnato il primo. Non è già poco per me, che essi faccian caso di questo giuoco della boccetta, intantochè ne apporta la perpetuità dei segni elettrici: s'eglino ristringono a ciò tutto il merito della mia scoperta, e i pregi dell'Elettroforo, non me ne chiamerò scontento, quantunque vi sia apparenza almeno, che io potessi pretendere a qualche cosa di più. Ella è finalmente questa perennità dei segni, e cotesto giuoco singolare della boccetta, che ho fatto tanto valere, e su cui ho più di tutto appoggiato ne' miei primi scritti. A questo luogo non posso lasciar di manifestare, che non fui già soddisfatto del conto, che rende dell'Elettroforo la lettera dell'Ab.
- 75. Iacquet[40], nella quale niente trovo detto di questa importante operazione della boccetta, sia ad oggetto di rianimare per se stessa l'elettricità indebolita, ed innalzarla al più alto grado d'intensità, sia per renderla realmente perpetua. Egli però nulla verisimilmente veduto avea di quanto erasi da me scritto, e pubblicato, e non conosceva l'Elettroforo, che sul rumore pervenutogliene, e dietro alcune poche sperienze di fresco da lui fatte. Non so attribuire ad altra cagione che questa, da una parte la confidenza, con cui parla di qualche fenomeno come fosse da lui scoperto, dall'altra il silenzio tenuto riguardo a tante altre sperienze, di cui io avea dato il dettaglio. Non vi si parla punto della maniera di animare un con l'altro una serie di Elettrofori; nè della facilità di cambiare a talento, ossia rovesciare l'elettricità sullo strato resinoso: niuna parola della sua mirabile tenacità, che regge non che a dispetto d'un'aria vaporosa, ma all'insulto dell'alito della bocca; nulla del mezzo singolare di spegnerla cotesta ostinata elettricità ec. Torno a dire, non son punto soddisfatto del ragguaglio, che il Sig. Ab. Iacquet si è accinto a dare del mio Elettroforo, comechè egli ne abbia molto innalzato il pregio, dichiarandolo un nuovo apparecchio, che stordisce i più abili Elettrizzanti. Riconosco che questa espressione è alquanto esagerata: e apprendo da voi, Sig., che lo stordimento non fu, nè è di tutti, conciossiachè abbiate saputo tenervene voi così in guardia, che preso non ne rimaneste. Avete fatto ancor più: sorto siete colla vostra lettera stampata a fare svenir cotesto abbagliante stupore dagli occhi pure dei prevenuti; e io non dubito punto, che la riputazion grande di cui godete, non abbia prodotto l'effetto preteso, e forse, chi sa? oltre il giusto. Non intendo quì parlare della scoperta dell'Elettricità vindice: ho abbastanza palesato sopra ciò i miei sentimenti, cioè, che ben lungi di dolermi con voi d'alcun torto, ho occasione anzi d'esservi tenuto. Mi lagno soltanto di ciò, che questo vostro scritto tende di più a diminuire il pregio dell'Elettroforo, preso anche in qualità di semplice apparecchio, o stromento, giacchè ne lo fa comparire senza il corredo de' suoi più singolari vantaggi: mi lagno, dico, unicamente dello scritto, non già di voi, Signore, cui fo la giustizia di credere, che non avete voi cercato di celare questi
- 76. vantaggi, ma che non li conoscevate per anco, giudicato avendo dell'Elettroforo dietro la lettera di Vienna, e un piccol numero di sperienze. Or dunque, Signore, io mi prometto da voi un giudizio più favorevole, quando ricavate abbiate delle notizie più complete da questa parte di descrizione accompagnata da alcune figure, che vi trasmetto, e dopo che ripetute avrete da voi medesimo le mie sperienze più capitali. Sono in vero impaziente d'intendere ciò che sarete per dire di quel giuoco singolare della boccetta per rianimare l'elettricità languente, ritorcendola a modo di dire contro se stessa; e della durazione perpetua dei segni, che per tal mezzo si viene a procurare. Dopo la descrizione succinta, che voi quì vedete nei fogli stampati, ho fatto un gran numero di sperienze, le quali somministrano molto lume per la teoria delle Atmosfere, e dell'Elettricità vindice, che ho pubblicate in parte, e in più gran parte riservo per la Memoria, che ho promesso. Amerei pure farvene parte, se i limiti di una lettera me lo permettessero: per angusti però che siano vuò farmi luogo a comunicarvi un'osservazione, che concerne direttamente la costruzione dell'Elettroforo. Con tutta la buona fede deggio confessar un inganno da me preso. Ho inculcato in più d'un luogo, che lo strato resinoso debba essere sottile, in difetto di che non agirebbe di lunga mano così bene: in vero io riguardava ciò come il più essenziale alla grandezza degli effetti; m'ingannai. Non mi rincresce la confessione d'un errore, massime che a rinvenir sul giusto m'insegnarono le sperienze d'un Principe illuminato, che in mezzo alle cognizioni estese in ogni genere di utili, e sublimi scienze, e a quella più difficile di governare, nutre un gusto particolare per le naturali cose e sa trovar de' momenti da consecrare ai trattenimenti di Fisica, e che non ha poco contribuito a dar grido, e voga al mio Elettroforo, per mezzo d'uno che ne inviò al Sig. Ingen-housz. Egli è dunque provato, e costante, che la spessezza di più linee, e fin d'alcuni pollici nello strato resinoso non toglie all'Elettroforo di agire vigorosissimamente, come io avea avanzato; sebbene poi, a dir tutto, una minore spessezza sia preferibile per altri riguardi e sono:
- 77. primieramente che uno strato sottile, oltre l'uso come Elettroforo, può servire di un buon Quadro Magico, vale a dire ricevere una grande carica, e dare una violenta esplosione; ciò che uno strato troppo grosso non giugne mai a fare, com'è noto per i principj delle cariche. Per un medesimo principio lo strato sottile vi offrirà lo spettacolo della comparsa dei segni elettrici dalla parte del piatto, o lastra inferiore tenendola isolata, pressochè tanto vivi quanto quelli che dà lo scudo ossia lastra superiore; ma se lo strato di resina sia assai grosso, il giuoco del piatto verrà meno in tutto, o in parte della forza. Da ultimo quello che ancor più merita d'essere considerato si è, che la virtù di ritenere l'elettricità è minore in uno strato grosso, che in un sottile; in un di questi potrete trovar elettricità ancor inerente dopo tre o quattro mesi senza averla mai in tutto quell'intervallo rianimata, come ho io esperimentato, laddove in quelli non vi si manterrà un mese. Del rimanente per quanto riguarda le sperienze ordinarie dell'Elettroforo, lo strato di resina grosso può servir a un dipresso egualmente, col vantaggio anzi di non essere così soggetto a screpolare: le scintille che darà lo scudo sollevato saranno abbastanza forti per mettere in vista l'errore, in che io son caduto avanzando il contrario, e di cui ho avuto già luogo a disingannarmi, ed or l'ho di ritrattarmi, e ne godo, come anche godrò di farlo pubblicamente. Ho l'onore di essere ec.
- 78. SOPRA LA CAPACITÀ DEI CONDUTTORI ELETTRICI e sulla commozione che anche un semplice Conduttore è atto a dare eguale a quella della boccia di Leyden LETTERA AL SIGNOR DE SAUSSURE
- 79. DEI CONDUTTORI ELETTRICI[41] Da molto tempo io mi era proposto di lavorare a un'Opera sull'Elettricità, in cui avrei ridotto la massima parte de' fenomeni all'azione, e giuoco delle atmosfere elettriche. Molte altre occupazioni, e ricerche di genere diverso me ne hanno distolto: non ne ho però deposto il pensiero. Ma perchè io vedo che la cosa potrà andare in lungo, e Voi già mostraste desiderio, o Signore, che io vi facessi parte delle mie idee, ed osservazioni, ho pensato intanto di soddisfarvi in qualche maniera, staccando dal resto questa particella che può in certo modo stare da se; le altre cose tutte essendo così legate, che non potrebbero una senza l'altra, e senza l'intiero complesso, essere, nè spiegate a dovere, nè abbastanza intese. §. 1. Della capacità dei Conduttori Elettrici. È stato dimostrato, e niuno più de' Fisici Elettrizzanti dubita, essere la capacità de' Conduttori in ragione non già della massa, ma del volume, e superficie di essi. Tralle altre la bella, e originale sperienza di Franklin della catena ammucchiata, e accolta in un catino elettrizzato, la quale quando esce fuori, e si dispiega nell'aria accresce capacità al Conduttore, e come vi ricada ne lo riduce all'angusta capacità di prima[42] ma singolarmente, e soprattutto le sperienze fatte intorno al così detto pozzo elettrico di cui Voi foste il primo, o Signore, a darci una bella analisi[43], ci fan vedere, e toccar con mano come l'elettricità sull'esterna faccia solamente de' Conduttori si dispieghi[44]. Quindi è che nelle nostre macchine per uso de' Conduttori comodi a un tempo, e capaci soglionsi in oggi adoperare grossi cilindri, e sfere vuote d'ottone (giacchè il fargli
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