Competition Theory in Ecology Peter A. Abrams
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- 6. Oxford Series in Ecology and Evolution The Comparative Method in Evolutionary Biology Paul H. Harvey and Mark D. Pagel The Cause of Molecular Evolution JohnH.Gillespie Dunnock Behaviour and Social Evolution N.B.Davies Natural Selection: Domains, Levels, and Challenges GeorgeC.Williams Behaviour and Social Evolution of Wasps: The Communal Aggregation Hypothesis YosiakiItô Life History Invariants: Some Explorations of Symmetry in Evolutionary Ecology EricL.Charnov Quantitative Ecology and the Brown Trout J.M.Elliott Sexual Selection and the Barn Swallow AndersPapeMøller Ecology and Evolution in Anoxic Worlds TomFenchelandBlandJ.Finlay Anolis Lizards of the Caribbean: Ecology, Evolution, and Plate Tectonics JonathanRoughgarden From Individual Behaviour to Population Ecology WilliamJ.Sutherland Evolution of Social Insect Colonies: Sex Allocation and Kin Selection RossH.CrozierandPekkaPamilo Biological Invasions: Theory and Practice NanakoShigesadaandKohkichiKawasaki Cooperation Among Animals: An Evolutionary Perspective LeeAlanDugatkin Natural Hybridization and Evolution MichaelL.Arnold The Evolution of Sibling Rivalry DouglasW.MockandGeoffreyA.Parker Asymmetry, Developmental Stability, and Evolution AndersPapeMøllerandJohnP.Swaddle Metapopulation Ecology IlkkaHanski Dynamic State Variable Models in Ecology: Methods and Applications ColinW.ClarkandMarcMangel The Origin, Expansion, and Demise of Plant Species DonaldA.Levin The Spatial and Temporal Dynamics of Host–Parasitoid Interactions MichaelP.Hassell The Ecology of Adaptive Radiation DolphSchluter Parasites and the Behavior of Animals JaniceMoore
- 7. Evolutionary Ecology of Birds PeterBennettandIanOwens The Role of Chromosomal Change in Plant Evolution DonaldA.Levin Living in Groups JensKrauseandGraemeD.Ruxton Stochastic Population Dynamics in Ecology and Conservation RussellLande,SteinerEngen,andBernt-ErikSæther The Structure and Dynamics of Geographic Ranges KevinJ.Gaston Animal Signals JohnMaynardSmithandDavidHarper Evolutionary Ecology: The Trinidadian Guppy AnneE.Magurran Infectious Diseases in Primates: Behavior, Ecology, and Evolution CharlesL.NunnandSoniaAltizer Computational Molecular Evolution ZihengYang The Evolution and Emergence of RNA Viruses EdwardC.Holmes Aboveground–Belowground Linkages: Biotic Interactions, Ecosystem Processes, and Global Change RichardD.BardgettandDavidA.Wardle Principles of Social Evolution AndrewF.G.Bourke Maximum Entropy and Ecology: A Theory of Abundance, Distribution, and Energetics JohnHarte Ecological Speciation PatrikNosil Energetic Food Webs: An Analysis of Real and Model Ecosystems JohnC.MooreandPeterC.deRuiter Evolutionary Biomechanics: Selection, Phylogeny, and Constraint GrahamK.TaylorandAdrianL.R.Thomas Quantitative Ecology and Evolutionary Biology: Integrating Models with Data OtsoOvaskainen,HenrikJohandeKnegt,andMariadelMarDelgado Mitonuclear Ecology GeoffreyE.Hill The Evolutionary Biology of Species TimothyG.Barraclough Game Theory in Biology: Concepts and Frontiers JohnM.McNamaraandOlofLeimar Adaptation and the Brain SusanD.Healy Competition Theory in Ecology PeterA.Abrams
- 8. Competition Theory in Ecology PETER A. ABRAMS Department of Ecology and Evolutionary Biology, University of Toronto, Canada
- 9. Great Clarendon Street, Oxford, OX2 6DP, United Kingdom Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries © Peter A. Abrams 2022 The moral rights of the author have been asserted Impression: 1 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, by licence or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this work in any other form and you must impose this same condition on any acquirer Published in the United States of America by Oxford University Press 198 Madison Avenue, New York, NY 10016, United States of America British Library Cataloguing in Publication Data Data available Library of Congress Control Number: 2022936370 ISBN 978–0–19–289552–3 (hbk) ISBN 978–0–19–289553–0 (pbk) DOI: 10.1093/oso/9780192895523.001.0001 Printed and bound by CPI Group (UK) Ltd, Croydon, CR0 4YY Links to third party websites are provided by Oxford in good faith and for information only. Oxford disclaims any responsibility for the materials contained in any third party website referenced in this work.
- 10. Acknowledgements This book arose from a planned review article that grew too long. Charley Krebs and Tom Schoener encouraged me to turn it into a book. It was an idea that I had resisted for quite some time, so the book would likely not have come into existence without their influence. Tom also used some preliminary chapter drafts in a graduate seminar course, which furnished some much-needed motivation for speeding up my writing schedule. Chris Klausmeier, Bob Holt, and Mark McPeek early on provided valuable feedback, and Michael Cortez sent comments on the longest chapter. I am grateful to Ian Sherman, Charlie Bath, and Giulia Lipparini at Oxford University Press for their input into this project. I am also very much indebted to my wife, Janet Pelley, for her forbearance as I spent an inordinate amount of time writing this work, and for providing feedback and copy editing on many of the chapters. The book was writ- ten during the first two years of the SARS-CoV2 epidemic, which limited access to libraries and people who could have made the writing process easier. Weekly dis- cussions with Tom Reimchen, Don Kramer, and Larry Dill have helped keep me informed of recent developments in ecology and evolution during that period. The Natural Sciences and Engineering Research Council of Canada provided financial support through a Discovery Grant.
- 12. Contents 1 Introduction: competition theory past and present 1 1.1 A short history 1 1.2 The need for resources in competition theory 3 1.3 The Lotka–Volterra model 4 1.4 The first revival of competition theory 7 1.5 Recent competition theory 8 1.6 General themes of this book 9 1.7 Necessary background and a look ahead 12 2 Defining and describing competition 13 2.1 Introduction 13 2.2 Historical definitions of competition 14 2.3 What should the definition be? 22 2.4 Implications of the definition 24 2.5 Competition within the framework of food webs 29 3 Measuring and describing competition: a consumer – resource framework 33 3.1 The measurement of competition (and other interactions) 33 3.2 Methods of measuring and describing competition 36 3.3 Arguments against resource-based definitions and models 40 3.4 MacArthur’s connection of LV to consumer–resource models 42 3.5 What do coexistence and exclusion mean? 47 3.6 What distinguishes a single resource from others? 49 3.7 Functional forms for the model components 49 3.7.1 Resource growth 52 3.7.2 Consumer functional responses 53 3.7.3 Consumer numerical responses 56 3.8 Analysis of models of competition 58 3.9 Summary 61
- 13. viii • Contents 4 Competition theory: its present state 63 4.1 Introduction 63 4.2 Questions for assessing recent influential theory 64 4.3 Choosing articles to represent current competition theory 66 4.4 Forgotten results in ‘modern competition theory’ 70 4.5 Why the Lotka–Volterra and MacArthur models are insufficient 72 4.6 Reasons for including resource dynamics 74 4.7 Appendix: Problematic features in the focal articles 75 5 Understanding intraspecific and apparent competition 79 5.1 Introduction 79 5.2 Intraspecific competition 80 5.2.1 The definition and mechanism of intraspecific competition 81 5.2.2 Describing, measuring, and modelling intraspecific competition 82 5.2.3 Models of density dependence 86 5.2.4 One-consumer–multi-resource systems 93 5.2.5 A more mechanistic approach to density dependence 101 5.3 Apparent competition 101 6 The negativity, constancy, and continuity of competitive effects 109 6.1 Introduction 109 6.2 Resource extinction and quasi-extinction in MacArthur’s model 111 6.3 Consequences of non-logistic resource growth 122 6.4 Consequences of nonlinear functional responses 125 6.4.1 Effects of nonlinear functional responses on consumer competition in systems with stable equilibria 126 6.4.2 Interactions in unstable systems with type II responses 132 6.5 Interdependence of competitive effects with more consumers 137 6.6 Other neglected aspects of consumer–resource models 138 7 Resource use and the strength of interspecific competition 143 7.1 Theory regarding the strength of competition 143 7.1.1 Theory from the early 1970s 144 7.1.2 Early questioning of MacArthur’s limiting similarity 147
- 14. Contents • ix 7.1.3 Recent and potential future theory on overlap and competition 149 7.1.4 Continued use of outdated similarity–competition relationships 153 7.2 Laboratory studies of competition 154 7.3 Field studies of competition 155 7.3.1 A historical review 156 7.3.2 An illustrative example: competition between hermit crabs 157 7.3.3 Current status of field studies of competition 159 7.4 Does competitive neutrality occur? 160 7.5 Interspecific competition in a food web context 162 7.6 Competition between species in theory and reality 169 8 Competition in seasonal environments: temporal overlap 171 8.1 Introduction 171 8.1.1 A brief history of work on seasonal competition 172 8.1.2 Aspects of seasonal variation in competition treated here 174 8.1.3 Why are the dynamics of seasonal systems important? 175 8.2 A modelling framework and a seasonal MacArthur system 176 8.2.1 General features of the models 176 8.2.2 Resource lags and mutual invasibility of MacArthur systems 178 8.2.3 Coexistence in a 2-consumer MacArthur system 184 8.2.4 How robust and representative is the example? 188 8.2.5 Coexistence of a seasonal and an aseasonal consumer 189 8.2.6 A more complete description of seasonal interactions 192 8.2.7 Seasonality resource conversion efficiency, b 195 8.2.8 A 3-consumer system with variation in c 197 8.2.9 A 2-resource system with temporal and non-temporal partitioning 199 8.3 Competition in other 2-consumer–1-resource models 200 8.3.1 Systems with abiotic resources 201 8.3.2 Biotic resources with type II functional responses 203 8.3.3 Abiotic resources with type II functional responses 204 8.4 Discussion 204 9 Relative nonlinearity and seasonality 209 9.1 Introduction 209 9.2 Inherently unstable consumer–resource interactions 210 9.3 Differences in nonlinearity with seasonal resource growth 213 9.4 Differences in the nonlinearity of numerical responses 222
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- 16. x • Contents 9.5 Other types of environmental variation 225 9.5.1 Nonlinear numerical responses 225 9.5.2 Nonlinear functional responses 226 9.5.3 Remaining unknowns 229 9.6 Systems with two or more resources 230 9.7 Discussion 230 10 Consumers and resources in space 233 10.1 The nature of spatial competition 233 10.2 A history of metapopulation competition models 237 10.3 Space and the global shape of intraspecific competition 238 10.4 Random movement and coexistence 241 10.4.1 Competition when only one trophic level moves 242 10.4.2 Competition with mobile consumers and interference competition 244 10.5 Adaptive movements and their effects on competition 245 10.5.1 General aspects of adaptive movement 245 10.5.2 The shape of competition under adaptive consumer movement 247 10.5.3 Adaptive movement by the resource 251 10.6 Adaptive movement of both species 253 10.7 Extending our current understanding of spatial competition 255 11 Evolution and its ecological consequences 257 11.1 Evolution’s many effects on interspecific competition 257 11.2 A brief history of work on the evolutionary responses to competition 261 11.2.1 Empirical studies of competitive coevolution 261 11.2.2 A history of theoretical models of competitive coevolution 262 11.3 A simplified approach to evolution 265 11.4 Examples of non-standard questions and outcomes 267 11.4.1 Evolution in the resource population(s) 267 11.4.2 Evolution with imperfectly or non-substitutable resources 268 11.4.3 Evolution of other consumer parameters 270 11.5 Evolution of apparent competitors 270 11.6 Evolution with both exploitative and interference competition 272 11.7 Evolution of competitors in a food web context 273 11.8 Evolution and coexistence: current theory and the future 274 12 Overview 277 12.1 A range of viewpoints on theory 277
- 17. Contents • xi 12.2 Theory’s roles in ecology and competition 280 12.2.1 The goals of theory 280 12.2.2 The relationship between theory and experiment 281 12.2.3 What will a more comprehensive theory look like? 282 12.3 Omitting intermediate entities in models of indirect interactions 283 12.4 Important aspects of consumer–resource relationships 285 12.5 Food web structure and its influence on competition 287 12.6 Forces that have biased research on competition 288 12.7 Conclusions 290 References 295 Index 321
- 19. 1 Introduction Competition theory past and present 1.1 A short history This book is a critical look at current competition theory, which constitutes a signif- icant fraction of theoretical ecology. My general view of the purpose of ecological theory is similar to that expressed by Michel Loreau (Loreau, 2010, p. 268): ‘It is my firm belief that ecological theory should be both a guide for basic research and a guide for action’. It is likely that very few professional ecologists would dispute Loreau’s statement. Given the unprecedented rates of loss of species and natural biological communities, most ecologists hope that ecological theory will provide practical advice on altering the dynamics of natural populations undergoing unde- sired changes, such as declines towards extinction. Certainly, as Loreau states, it ‘should’ do so. Nevertheless, ecological theory in its present state has largely failed to make predictions or contribute to plans that could help to avert the collapse of ecological systems. This book will examine the reasons for these shortcomings by focusing on competition theory, a subset of ecological theory. Competition theory is central to most of the other branches of ecological theory and has a particularly long history in the field. Investigating its current state and why it has not progressed more rapidly may provide more general insights for ecological theory and for ecology as a whole. Understanding ecology’s current state requires some history. Ecology, the scien- tific study of the distribution and abundance of living organisms, developed out of natural history. Natural history had provided an accounting and description of the organisms in natural communities long before ecology arose as a scientific disci- pline.Ecology soughtto explainthe properties of those communities andpredict their future. Accounting for or predicting either the population size or geographic range of almost any species on Earth represents a major challenge. It was clear to some biolo- gists in the early twentieth century that the natural history knowledge of that period would not be sufficient to answer most of the major questions about abundance, even for a single species. Because distributions and abundances are constantly changing, those biologists recognized that the mathematics of dynamical systems was clearly important for understanding ecology. As the scope and magnitude of human impacts Competition Theory in Ecology. Peter A. Abrams, Oxford University Press. © Peter A. Abrams (2022). DOI: 10.1093/oso/9780192895523.003.0001
- 20. 2 • Competition Theory in Ecology on natural systems have escalated, mathematical models have become increasingly important tools to provide insights and predictive power. Ecological theory began to appear in the 1920s, some of it spurred by applied ques- tions in fisheries. However, in spite of a few developments over the next three decades, largely in fisheries, pest control, and human demography, a mathematical framework for understanding ecological communities was still largely absent from ecological lit- erature in the 1960s. At that point quantitative ecology started to receive renewed attention from biology departments in universities in North America. In part this was because of the perceived insufficiency of the theory that existed at the time; it cer- tainly had a poor track record in applied fields like fisheries management. The 1960s were also a time of expansion in biology departments and increased interest in ecol- ogy among the general population. Now most major universities have a department devoted to ecology, evolution, and behaviour, and many have one or more faculty members engaged in developing ecological theory. The scientific literature on ecology and evolution has expanded enormously. In spite of this expansion of the field as a whole, my impression is that theory in ecology has not lived up to its promise at the time I started graduate work half a century ago. It has definitely not provided the type of predictive and explanatory power that I and many others at that time were expecting to develop quickly. This book will examine both the history and the current state of theory on one of the major types of ecological interactions, competition. Competition theory provides a case study of some of the problems in developing theory in ecology more generally. It was the central interaction studied by many of the ecologists who were responsible for the revival of theoretical ecology in the 1960s and early 1970s. Focusing on competi- tion theory can still be justified, because an adequate understanding of competition either requires or implies a good understanding of all other interactions. Competition occurs within and between species. It therefore has an effect on the abundance of every organism. Competition between species sets limits on the num- ber of species that can coexist. Competition between individuals within a species determines the maximum abundance of a species and how rapidly it is approached. Within-species competition is also the driver of natural selection and its resulting evolutionary change. Competition is at least part of the mechanism behind divergent selection that leads to speciation. Thus, competition is responsible for generating new species as well as for limiting the number of species that can be present locally. All of these considerations contributed to making competition a central focus of the math- ematical approaches to ecological interactions that developed in the 1960s and 70s. Competition had been a major area of interest for decades before this, with major arguments in the 1940s and 1950s about how important it was in determining the abundance of species (see Hutchinson, 1978). Most ecologists who have studied this interaction have come to the study of com- petition with some preconceptions. All humans have some personal experience with competition. It often begins with issues such as, ‘Who gets to play with a favourite toy?’, and continues throughout life, involving money and various other needed or desired ‘items’ that are in limited supply. Most of economics is about competition, and
- 21. Introduction: competition theory past and present • 3 a Web of Knowledge search for articles about ‘competition’ from the past five years yields more publications from economics than from ecology. Thus, most students in an introductory ecology class have some preconceived notions about competition. In spite of (or perhaps because of) this, the meaning of competition in ecology has remained something of a grey area. To address this confusion, the next chapter in this book is devoted to documenting the history of definitions and arguing for one based solely on shared use of resources that influence population growth. 1.2 The need for resources in competition theory One central thesis of this book is an idea that was more widely accepted four decades ago than it is today; i.e. that understanding competition requires an understand- ing of its underlying consumer–resource interactions. Resources are substances that are required for survival and/or reproduction. For example, in predators, resources always include their prey, but they may also include sources of water, shelter, or cam- ouflage. This means that a proper ecological understanding of competition between predators requires, at a minimum, some study of prey population dynamics, the rates of consumption by predators, and the effects of that consumption on the preda- tors’ birth and death rates. The last of these requires some knowledge of the supply and workings of those other factors influencing the predator’s birth and death rates. Competition between plant species involves exploitation of water, light, and miner- al nutrients. However, all of these are tied to the space where they occur, and the nature of the consumer–resource interaction may differ greatly with the physical characteristics of the place where the water, light, and nutrients are found. Detri- tivores, parasites, pathogens, and other groups are also consumers, and they often require different types of models of competition. This is particularly true of the lat- ter two groups, which inhabit their ‘resource’, and their survival or reproduction may be adversely affected by overly high consumption rates. Consumer–resource inter- actions are also an essential component of many mutualistic interactions between species. A more complete theory of competition, based on a better understanding of consumer–resource interactions should help to provide a foundation for predict- ing future changes in distribution and abundance of all of these groups. A theory that includes resources explicitly is also needed for understanding the evolution of ecologically important characteristics in any species. Acknowledging the centrality of consumer–resource interactions in competition leads directly to the question of the adequacy of existing consumer–resource theory. Thus, another theme of this book will be that, for both competition theory and consumer–resource theory, there has been an over-emphasis on historical models and overly simplistic formulations for understanding the interactions. In competi- tion theory this has meant a continuing reliance on the Lotka–Volterra model, which is discussed below. In consumer–resource theory, the legacy of simple models with a long history means, inter alia, a concentration on cases with a single resource, or
- 22. 4 • Competition Theory in Ecology just two resources in the minority of studies that consider more than one. For those branches of competition theory that explicitly include resources, the most common assumption is that there are just two consumers and two resources, and the resources are assumed not to interact with one another. Simple models also omit adaptive behaviour and phenotypic plasticity from the set of processes determining the shape of consumption rate functions. Existing consumer–resource and competition the- ories have additionally tended to ignore the impacts of the abundances of species occupying higher and lower trophic levels on a focal consumer–resource pair. Linear relationships between resource abundance and consumption rate are often assumed as the default, as are linear relationships between resource consumption and per individual birth and death rates. In competition theory, there is still a large body of new work produced every year using the oldest and simplest possible model of competition in which each species has an instantaneous per capita growth rate that declines linearly and independently with the abundance of every one of its competitor species. The result is that many ecologists have expectations based on theoretical systems that are likely to have prop- erties that are extremely uncommon, even within the vast domain of different natural communities. 1.3 The Lotka–Volterra model Because this book will be mainly about theory, it is necessary to begin with a brief review of the foundational mathematical model of interspecific competition, even though that model lacks any representation of resources. This is the simple model independently developed by Alfred Lotka and Vito Volterra, in the mid-1920s (see Volterra, 1931). As late as the mid-1960s, this was still the only model of competition referred to in most of the literature (Hutchinson 1965). This model has played such a major role in past research I will begin by reviewing its basic form and properties for any readers who may not remember their undergraduate ecology course. The Lotka–Volterra (LV) model notably lacks any explicit representation of resources. It assumes that the per individual rate of increase of each consumer (com- petitor) species declines linearly with increases in its own abundance and declines linearly (usually with a different slope) with increases in the abundances of the second consumer species. The effects of changes in abundance on per individual growth rates are immediate. The most common representation of the LV model of two-species competition describes the rates of change in their abundances (N1, N2) as follows: dN1 dt = r1N1 ( 1 − N1+α12N2 K1 ) dN2 dt = r2N2 ( 1 − N2+α21N1 K2 ) (1.1a, b) The parameters ri and Ki are respectively the maximum per individual growth rate and the equilibrium population size (‘carrying capacity’) of species i when it is present
- 23. Introduction: competition theory past and present • 5 alone. The effect of interspecific relative to intraspecific competition is measured by αij, which is the ratio of the effect of the abundance of species j on the per capita rate of increase of species i, relative to the effect of the abundance of species i on its own per capita growth rate. The competition coefficient αij increases with the similarity of the two species in their relative use of different resources; it also increases as the absolute ability of species j to harvest all resources increases relative to that of species i. This model can be expanded to encompass more species; in this case there is a summation over all other species j of αijNj in the numerator of the fractional terms. Whether both species coexist can be determined by assessing whether the per capita growth rate of each species (the quantity in parentheses in eqs 1.1a, b) is positive when the focal species is at near-zero abundance and its competitor is at its carrying capacity. Thus, under the specific form of eqs (1.1), the maximum per capita growth rates, r1 and r2, have no impact on whether the two species will both persist. If the product α12α21 is greater than one, it is impossible for the species to coexist; i.e. no values of K1 and K2 allow each species to persist together indefinitely. It is possible that one species always excludes the other; this may occur for a small difference in the K values when the product of the competition coefficients is close to unity. When the product of the α’s is small, a larger ratio of K’s is required to bring about exclusion of the low-K species, but this is always a possibility. One outcome that was not widely appreciated before the development of the LV model was that in some cases when interspecific competition is stronger than intraspecific (α12α21 > 1), either species is capable of excluding the other, with the outcome depending on initial abundances. In the two-species LV model, it is possi- ble to determine whether the species will coexist by examining the growth rate of each species when it is very rare and the other species is at its carrying capacity. If both of these ‘invasion growth rates’ are positive, the two species will coexist, and if not, coex- istence is impossible. Both invasion growth rates are negative in the case of alternative outcomes. Alternative outcomes were observed in later laboratory experiments. The sets of outcomes in the LV model are usually illustrated using ‘isocline dia- grams’. This involves setting the per capita growth rates equal to zero, solving each equation for one variable in terms of the other, and then plotting the resulting two lines on a graph whose axes are the two population densities (sizes). The equilibrium densities are given by where the two lines intersect. The equilibrium is stable if arrows originating at points near the equilibrium, and whose direction is given by the pair of growth rates at that point, are directed back towards the equilibrium. However, if the arrows indicate a cycle around the equilibrium (never true for eqs (1.1)), isocline analysis is inconclusive. Although 3-D diagrams can be drawn for 3-variable systems (e.g. McPeek 2019a), these are usually not sufficient for determining stability, and are certainly not the easiest way to do so. Unfortunately, the conditions for coexistence in the two-species LV model do not apply universally to models that have explicit resource dynamics, or to models with temporal variability, or to a range of other models and the consumer–resource interactions that underlie them. There is no analogue to the two-species coexistence condition LV model with three or more competitors. In any LV model, each species’
- 24. 6 • Competition Theory in Ecology population growth rate responds immediately to a change in the other species, something that is usually not the case for real consumer–resource interactions. Even when the LV model is being used as a rough approximation, estimating the parame- ters of the model from first principles—particularly the strength of competition given by the α values—requires a consumer–resource model. These and many other limi- tations of models lacking explicit resource dynamics will be discussed in this book. However, it should be noted that Volterra did include resources in his conceptualiza- tion of competition, even though he did not use the term. This is evident in his idea that only a single species could persist indefinitely if there was only a single limiting factor, or, as it later came to be known, the ‘competitive exclusion principle’. The limitation to a single consumer on a single resource follows from the two- species competition model when the product of the competition coefficients is equal to or greater than one. If there is purely exploitative competition for a single resource by two consumers, the product of their competition coefficients is unity, and there will be either no equilibrium point with positive densities of both, or, for a unique ratio of carrying capacities, a line of neutrally stable points. Volterra pointed out that the species that persist at the lowest level of that factor would prevent the existence of (i.e., exclude) all the others. Hardin (1960) notes that some authors later attributed this idea to Gause (1936), who had carried out a laboratory experiment in which competitive exclusion occurred. Hardin also noted that a wide range of authors had proposed similar ideas before and after Volterra. Many more recent authors attribute the idea to Tilman (1982). In any case, the issue of coexistence on a single resource has remained a topic of continued interest, largely because early authors did not devote much thought to what exactly constitutes a single resource. Haigh and Maynard Smith (1972) suggest- ed that the same resource species (or substance) at different times could constitute different resources, as could different parts of an individual of the resource species. Stewart and Levin (1973) and Armstrong and McGehee (1976a, b) showed that the prohibition of coexistence on a single resource type did not apply to consumer species in seasonal environments or species undergoing sustained population cycles. There has now been a large body of work (summarized in Chesson 2020b) on the potential for environmental variation to allow coexistence on a single resource. However, this requires that the consumers differ in their temporal responses to changing resource densities, in which case resource items becoming available at different times could be divided into different classes of resources. It has repeatedly been shown that space and time are both involved in the separation of distinct resources. All of the work over the years that has actually demonstrated coexistence on what seemed initially to be a single resource depends on the competitors responding differently to resource items based on place or time (or simple failure of the author to consider all limiting factors). These issues will be discussed further in the chapters that follow. In spite of its limitations, the LV model did reveal some properties of at least some two-competitor systems, which were not widely appreciated in the 1920s. In addition, Lotka and Volterra’s works inspired some early experimental explorations of competi- tion in the laboratory by Georgy Gause (1936), who studied competition between two
- 25. Introduction: competition theory past and present • 7 protozoans, and by Thomas Park (1948), who did the same for a pair of flour beetle species. These were the first influential experimental approaches to understanding competition in biological communities. Each of these authors related their results to the LV model. However, they were mainly concerned with examining whether or not competitive exclusion occurred in pairs of species, and did not really provide a challenging test for the adequacy of the model. While the LV model played a key role in the birth of competition theory, it was clearly too simple to understand the composition of natural communities, or predict changes in those communities. Its assumption of linear effects on abundance, its focus on only two competing species, and the absence of an explicit accounting of resources combine to greatly restrict the ability of the LV model to describe any natural sys- tem, or even the majority of laboratory systems. This became clear many years later, after Francisco Ayala (1969) published a study on competition between Drosophila species in the laboratory in the journal Nature. His assumption that the LV mod- el applied exactly to his two-species competition experiments led him to conclude that his observation of coexistence invalidated the competitive exclusion principle. This misinterpretation was later corrected in Gilpin and Ayala (1973) and Ayala et al. (1973). It had been assumed that the Drosophila had only a single resource in the jars in which the competing larval flies were raised, but later work showed that the species differed in the use of drier and moister areas within the medium (Pomerantz et al. 1980). Ecology is certainly not alone in attempting to understand very complex systems in which it would be unrealistic to develop a quantitative understanding of all of the dynamic components that could influence changes in variables of interest. The normal course of theoretical development of a scientific field would have seen an exploration of the consequences of the most basic elaboration of the model; in this case that elaboration is clearly to include the dynamics of the resources that are the subject of the competitive interaction. This second stage of development was initiated in the late 1960s and early 1970s, but it seems to have been largely abandoned before it was given a chance to restructure the field. 1.4 The first revival of competition theory The theoretical approach to understanding competitive systems, initiated by Lotka and Volterra, was not advanced significantly in the biological literature until a young professor of biology at Princeton University, Robert MacArthur, revived interest in mathematical studies of competition in the 1960s and early 1970s. Richard Levins (1968) independently stressed the importance of resources for understanding com- petition, and, in joint work, these two authors tried to relate competition between species to their similarity in resource use. MacArthur’s final (1972) book, Geograph- ical Ecology contained a large section that was devoted to interspecific competition. Two years earlier he had published an article on this topic, which was the very first
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