Emergent global patterns_of_ecosystem_structure_and_function_form_a_mechanistic_general_ecosystem_model
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This document summarizes a new mechanistic general ecosystem model (GEM) called the Madingley Model. The model simulates ecological processes like primary production, eating, growth, reproduction and dispersal for individual organisms ranging in size from 10 mg to 150,000 kg across terrestrial and marine environments globally. Emergent properties observed at individual, community, ecosystem and global scales, such as trophic structure and body size distributions, generally agree with empirical data without direct constraints. The model provides novel predictions about relationships between net primary productivity, trophic chain length and herbivore pressure. It indicates ecologists now have sufficient information to build realistic global models of ecosystem structure and function to predict impacts of human pressures.
![Emergent Global Patterns of Ecosystem Structure and
Function from a Mechanistic General Ecosystem Model
Michael B. J. Harfoot1,2.*, Tim Newbold1,2., Derek P. Tittensor1,2,3., Stephen Emmott2, Jon Hutton1,
Vassily Lyutsarev2, Matthew J. Smith2, Jo¨ rn P. W. Scharlemann1,4, Drew W. Purves2
1 United Nations Environment Programme World Conservation Monitoring Centre, Cambridge, United Kingdom, 2 Computational Science Laboratory, Microsoft Research,
Cambridge, United Kingdom, 3 Dalhousie University, Halifax, Nova Scotia, Canada, 4 School of Life Sciences, University of Sussex, Falmer, Brighton, United Kingdom
Abstract
Anthropogenic activities are causing widespread degradation of ecosystems worldwide, threatening the ecosystem services
upon which all human life depends. Improved understanding of this degradation is urgently needed to improve avoidance
and mitigation measures. One tool to assist these efforts is predictive models of ecosystem structure and function that are
mechanistic: based on fundamental ecological principles. Here we present the first mechanistic General Ecosystem Model
(GEM) of ecosystem structure and function that is both global and applies in all terrestrial and marine environments.
Functional forms and parameter values were derived from the theoretical and empirical literature where possible.
Simulations of the fate of all organisms with body masses between 10 mg and 150,000 kg (a range of 14 orders of
magnitude) across the globe led to emergent properties at individual (e.g., growth rate), community (e.g., biomass turnover
rates), ecosystem (e.g., trophic pyramids), and macroecological scales (e.g., global patterns of trophic structure) that are in
general agreement with current data and theory. These properties emerged from our encoding of the biology of, and
interactions among, individual organisms without any direct constraints on the properties themselves. Our results indicate
that ecologists have gathered sufficient information to begin to build realistic, global, and mechanistic models of
ecosystems, capable of predicting a diverse range of ecosystem properties and their response to human pressures.
Citation: Harfoot MBJ, Newbold T, Tittensor DP, Emmott S, Hutton J, et al. (2014) Emergent Global Patterns of Ecosystem Structure and Function from a
Mechanistic General Ecosystem Model. PLoS Biol 12(4): e1001841. doi:10.1371/journal.pbio.1001841
Academic Editor: Michel Loreau, Centre National de la Recherche Scientifique, France
Received December 19, 2013; Accepted March 10, 2014; Published April 22, 2014
Copyright: 2014 Harfoot et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits
unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: This research was funded by United Nations Environment Programme World Conservation Monitoring Centre and the Computational Science
Laboratory, Microsoft Research. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing Interests: The authors have declared that no competing interests exist.
Abbreviations: DGVMs, dynamic global vegetation models; DOC, dissolved organic carbon; ESMs, Earth System Models; EwE, Ecopath With Ecosim; GEM,
General Ecosystem Model; NBS, normalised body mass spectra; NPP, net primary productivity; POC, particulate organic carbon
* E-mail: mike.harfoot@unep-wcmc.org
. These authors contributed equally to this work.
Introduction
The pace and scale of anthropogenic environmental change has
caused the widespread degradation of ecosystems and the services
they provide that ultimately support human life on Earth [1].
Understanding and mitigating these impacts necessitates the
development of a suite of tools, including policy instruments,
practical conservation measures, and empirical research. At
present, a variety of models are used to assist decision-making in
relation to biodiversity and ecosystem services. Most are correl-ative,
relying on statistical relationships derived from limited
observational data without explicit reference to the underlying
mechanisms; examples include the GLOBIO model, species
distribution models, and models of local extinction based on
species–area relationships [2–4]. All of these models are useful, for
different purposes. However, what is urgently needed is mecha-nistic
models, which explicitly represent the biological, physiolog-ical,
and ecological mechanisms underlying the systems in question
[5]. One of the key benefits of mechanistic models is that they are
likely to make more accurate predictions under novel conditions
[6]. For example, Earth System Models (ESMs), containing
mechanistic descriptions of multiple interacting components of
the climate, atmosphere, and ocean, are used to project properties
and dynamics under future climate conditions that have not been
observed previously (at least in relation to historical data) [7].
Similarly, mechanistic models of ecosystems would allow us to
predict a given combination of human pressures on a given
ecosystem, even when there is no or little historical data on which
to rely. Mechanistic models can also improve our understanding of
the systems being modelled, allowing predictions to be understood
in relation to the underlying mechanisms that generate them [8].
This in turn might lead to novel ways to mitigate or even reverse
the degradation of ecosystems.
We present the first process-based, mechanistic General
Ecosystem Model (GEM) (called the Madingley Model). It is
general in the sense that it strives to use a unified set of
fundamental ecological concepts and processes for any ecosystem
to which it is applied, either terrestrial or marine, and it can be
simulated at any spatial resolution from local up to global scales.
Applying a general modelling approach globally has three main
advantages: (1) it allows testing of whether the same set of
ecological mechanisms and concepts can adequately capture
broad-scale ecosystem behaviour in both the marine and terrestrial
realms; (2) it enables the development of a suite of predictive
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![outputs common to both realms, from which standardised metrics
of ecosystem health can be calculated; and (3) it enables links
between marine and terrestrial ecosystems, both natural and
human-driven, to be modelled. The model is also spatially explicit,
with dynamics in a given location driven by the climate and other
local factors, as well as by connections with other ecosystems
through dispersal, and is mechanistic, with dynamics being driven
by ecological processes defined at the level of individual organisms.
Specifically, we model autotroph (plant) stocks, and individual
herbivorous, omnivorous, and carnivorous animals of all body
sizes, and their interactions. From these interactions, patterns
emerge at larger spatial and temporal scales, including commu-nities,
ecosystems, and global macroecological gradients, without
any direct model constraints imposed on those properties.
Such a GEM has great potential if it can, at a minimum,
reproduce the observed properties of ecosystem structure and
function, and enable the formation of valuable, novel hypotheses,
and precise, testable predictions. Here, we test the model’s ability
to simulate ecosystems that persist over long time scales (1,000 y)
by comparing model predictions with empirical data and test two
theoretical predictions that to date have not been assessed
empirically and have only been studied with simple trophic
models: that the net primary productivity (NPP) of ecosystems
determines the length of trophic chains [9,10] and that herbivore
pressure on autotrophs will reduce once a critical level of carnivore
biomass is supported (‘‘trophic release hypothesis’’ [11]). Finally,
we provide a suite of other novel predictions that demonstrate the
potential utility of the model as an operational tool with which the
effects of human impacts on ecosystems can be explored.
Mechanistic models of specific ecosystems have been developed
previously, and to date these have been constrained to particular
spatial locations or to particular sets of organisms within
ecosystems. For example, dynamic global vegetation models
(DGVMs) are used to represent the physiological and ecological
processes driving plant community dynamics on the global land
surface, enabling investigations into how terrestrial vegetation
interacts with climate [12]. However, these do not include animals
or other heterotrophs, and so are limited in the extent to which
they can be used to understand the roles of heterotrophs in
ecosystems, or to address questions about the conservation of
organisms other than plants. For the marine realm, ‘‘end-to-end’’
ecosystem models have been developed, which include most
trophic levels for particular regions [13]. Examples are the
Ecopath With Ecosim (EwE) [14] and Atlantis [15] models. But
marine models tend to focus either on biogeochemical cycles or on
organisms of economic importance, such as fish, rather than on
the properties of the ecosystem as a whole. They also generally
either use a stock-and-flow formulation [14,15], making them
unable to follow trajectories of individual organisms, or are
restricted to simulating particular guilds of organisms [16].
There have also been previous theoretical examinations of the
potential effect of select processes on select ecosystem metrics, such
as the role of bioenergetics in determining size distributions [17].
Such theoretical studies have been very useful in providing insight
into the potential mechanisms underlying ecosystem structure; but
they have tended to be carried out for single, abstract locations
that are not tied to any real geographical location and to omit
most of the key processes affecting ecosystem structure and
function in reality. We are not aware of any previous attempt to
model emergent ecosystem structure and function by identifying a
minimal, but putatively complete, set of key processes and then
simulating these processes for all organisms globally, over the
actual climate and geography of all marine and terrestrial
environments. It is for these reasons that we refer to the model
presented here as a GEM.
Methods
Model Scope
We identified a set of core biological and ecological processes
necessary to predict ecosystem-level properties: primary produc-tion
for autotrophs, and eating, metabolism, growth, reproduction,
dispersal, and mortality for heterotrophs (Figure 1 and Box 1). We
modelled both marine and terrestrial environments but excluded
freshwater ecosystems. We included all photoautotrophs, and all
heterotrophs that feed on living organisms (i.e., we did not include
chemoautotrophs and detritivores). We generally represented only
macroscopic organisms (.161023 g), except that we included
plankton in the marine realm because of their known importance
to the marine food web [18]. All plant biomass in the terrestrial
realm was modelled, but only leaves, flowers, fruits, and seeds were
available as a food source for herbivores and omnivores. The
marine component included phytoplanktonic autotrophs, which
provide more than 90% of primary productivity in the oceans
[18]. Seagrasses, mangroves, macroalgae, and corals, which are
important autotrophs in coastal systems, are not yet included. In
this proof-of-concept model, we consider a world without any
human impacts, except that we used modern-day climatic
conditions. The model and user guide can be downloaded from
www.madingleymodel.org, and simulation outputs for main
manuscript figures can be downloaded from the Dryad Digital
Repository: doi:10.5061/dryad.5m96v [19].
Traits, Cohorts, and Stocks
Traditional approaches to mechanistic modelling in community
ecology focus on densities or abundances of individuals belonging
to different species [16,20]. These are well suited to modelling a
small set of focal species, but are unfeasible for modelling whole
ecosystems at a global scale, because the vast majority of the
world’s species remain to be described, or are at best represented
by few data describing their distribution and ecology [21–23].
Author Summary
Ecosystems across the world are being rapidly degraded.
This threatens their provision of natural goods and
services, upon which all life depends. To be able to
reduce—and one day reverse—this damage, we need to
be able to predict the effects of human actions on
ecosystems. Here, we present the first example of a
General Ecosystem Model (GEM)—called the Madingley
Model—a novel class of computational model that can be
applied to any ecosystem, marine or terrestrial, and can be
simulated at any spatial scale from local up to global. It
covers almost all organisms in ecosystems, from the
smallest to the largest, encoding the underlying biology
and behaviour of individual organisms to capture the
interactions between them and with the environment, to
model the fate of each individual organism, and to make
predictions about ecosystem structure and function.
Predictions made by the Madingley Model broadly
resemble what we observe in real-world ecosystems across
scales from individuals through to communities, ecosys-tems,
and the world as a whole. Our results show that
ecologists can now begin modelling all nonhuman life on
earth, and we suggest that this type of approach may hold
promise for predicting the ecological implications of
different future trajectories of human activity on our
shared planet.
A Mechanistic General Model of Global Ecosystems
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![A Mechanistic General Model of Global Ecosystems
Figure 1. Schematic of the model. Ecosystem structure and function (B) emerges from a combination of processes operating on individual
organisms within a grid cell (A), and exchange of individuals among grid cells via dispersal (C). Life histories (e.g., average lifespan, lifetime
reproductive success, and generation length) are also emergent (not shown in this diagram, but see Figure 3). Fundamental ecological processes
affect the ecological properties (principally body mass and abundance; represented as the diameter and number of black dots in A, respectively) of
organisms. For computational efficiency, organisms with similar properties are grouped into cohorts (coloured circles in all panels). Graphs in (A)
show illustrative examples of functional forms used to model each ecological process; full mathematical details can be found in the main text and in
Text S1. Panel (C) illustrates how dispersal links different grid cells through the exchange of cohorts via dispersal. As result of the within-grid-cell
processes, and dispersal, the state of the ecosystem—that is, the collection of cohorts within each grid cell—changes dynamically through time.
Panel (B) shows two example measures of ecosystem structure that can be calculated at any time: the relative biomasses in different trophic levels,
and the body-mass abundance distribution of heterotrophs. All such community-level properties and metrics emerge from bottom-up processes in
the model without any model-imposed constraints beyond those processes operating on individual organisms.
doi:10.1371/journal.pbio.1001841.g001
Instead, we adopted a trait-based approach [24] where
individuals are characterized by their functional traits: categorical
traits, such as feeding mode, which determine the mechanisms by
which organisms exist and which were used to define functional
groups; and continuous traits, such as body mass, which modulate
those mechanisms but do not determine functional grouping.
Taxonomic identity of individuals is ignored for three reasons.
First, there is insufficient species-level information to model whole
ecosystems worldwide. Second, it is more feasible to model the role
of individuals in ecosystems in terms of their traits than in terms of
their taxonomic identity, because of limited taxonomic knowledge
and data [21–23]. Third, in comparison to taxonomic identity,
organisms’ functional traits are more directly relevant to most
ecosystem functions and ecosystem services [25,26].
A separate issue is whether to define the model in terms of
population densities and biomasses within functional groups (i.e.,
‘‘stocks’’ or ‘‘pools’’), or as collections of interacting individuals
each characterized by their combination of functional traits
(individual-based). For all organisms except autotrophs, we used
an individual-based approach, because this allowed the model to
be more finely resolved, and because it enabled us to capture
variation in body mass—one of the most important traits for
determining the rates of ecological processes [27–29] over the
lifetime of an individual. It also enabled us to follow the fates of
individual organisms. Higher level ecosystem properties emerge
from these individual-based rules. Capturing this emergence was a
central aim of this initial work.
Autotrophs were represented as stocks—that is, the total
biomasses of such organisms—because either the definition of an
individual was problematic (terrestrial plants) or rates of turnover
were faster than the modelled time step (marine phytoplankton).
For heterotrophs, simulating every individual separately would
have been computationally intractable given the vast number of
individuals in global ecosystems. Therefore, we adopted a
computational approach based on cohorts. A cohort consisted of a
group of organisms occurring within the same grid cell, with
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![Box 1. Running simulations within our GEM.
Each simulation is initialised with environmental informa-tion
from multiple datasets (as described in the Methods
section and in Table S1) and spatially distributed stocks
and cohorts (see Methods) according to user specifications
(functional groups and grid locations). During a simulation,
the stocks and cohorts then interact through time and
space. For each time step and each grid cell, the first
computation is to increment the biomass of autotrophs
according to the relevant growth function (Table 5). Next,
the ecology of the heterotroph cohorts is modelled (see
functions in Table 6). The order in which heterotroph
cohorts act is randomised at each time step. Each
heterotroph cohort performs multiple ecological processes
per time step (Figure 1A): Individuals in the cohort (i)
metabolise biomass to sustain their activities; (ii) eat
biomass from either autotrophs if herbivorous or other
heterotrophs if carnivorous, or from both if omnivorous;
(iii) use net biomass gain to grow, if juvenile, or store
biomass for future reproduction if they have reached
sufficient body mass to be reproductively mature; (iv) give
birth to a separate, offspring cohort if sufficient reproduc-tive
biomass has been accumulated; (v) suffer mortality as
a result of being eaten by other cohorts feeding on them,
or as a result of background mortality processes, starva-tion,
or senescence; and (vi) disperse from their current
grid cell to another grid cell. As a result of these
interactions across space and time, communities of
cohorts possessing different functional traits, individual
biomasses, and abundances self-assemble (Figure 1B and
1C).
identical traits—that is, in the same functional group and with
identical continuous traits—but not necessarily belonging to the
same taxon. This cohort-based approach allowed us to define the
model in exactly the way that one would do in a fully individual-based
model (i.e., processes defined at an individual level), but also
allowed us to keep the number of computations low enough to be
feasible.
Functional Groups
All stocks and cohorts belong to a functional group, defined
according to the categorical traits of the individuals in that stock or
cohort (Tables 1 and 2).
Individuals in the same functional group interact with one
another and with their environment in a qualitatively similar
manner. Therefore, cohorts within the same functional group are
modelled using the same mathematical representations of the
ecological processes, though the rates predicted by those functions
differ according to continuous traits that differ between cohorts,
A Mechanistic General Model of Global Ecosystems
such as body mass. Individuals belonging to different functional
groups have at least one qualitatively different interaction with
other individuals or with their environment. We use the same
functional forms for analogous functional groups in the ocean and
on land, but with different parameter values, where justified by
previous research.
Body mass affects many individual properties and interactions,
including feeding preferences and rates, metabolic rates, and
dispersal [27–29]. Therefore, body mass was included as a
parameter in nearly all ecological processes of heterotrophs
(Figure 1).
The Environment
The environment is defined as a two-dimensional layer
representing the land surface and the upper mixed layer (top
100 m) of the oceans. This layer is divided into grid cells within
which individuals and stocks are assumed to be well mixed. The
ecological processes can be affected by the size of the grid cell, the
physical environment at that cell, and dispersal of organisms
among adjacent grid cells. The model can be employed for any
number of grid cells, at any resolution, locally or globally, subject
to computational limitations. For the results presented here, we
used either simulations for individual 1u61u grid cells, or a 2u62u
grid covering the whole globe (see below, and Tables 3 and 4)
except for high latitudes (.65u) because remotely sensed,
exogenous environmental data currently used are not available
for the polar regions. Each grid cell in the model is assigned to
either the terrestrial or marine realm based on a land/ocean mask
[30]. Environmental conditions for each grid cell are read as
model inputs from publicly available datasets: for the terrestrial
realm air temperature [31], precipitation [31], soil water
availability [32], number of frost days [31], and seasonality of
primary productivity [33]; and for the marine realm sea-surface
temperature [34], NPP [35], and ocean current velocity (Table S1)
[34]. The model is flexible with respect to the specific environ-mental
data used, and future simulated environmental conditions
can be used.
The Ecology
We provide a summary of how simulations are run in Figure 1
and Box 1, and an overview of how the ecological processes are
modelled, with the main mathematical functions, is summarised in
Tables 5 and 6. Full details are provided in Text S1.
Autotroph Ecology. In the marine realm, one stock of
phytoplankton per grid cell is modelled, characterised by a total
wet matter biomass at time t, Bp,(t). For terrestrial autotrophs, we
track two stocks of leaves, l, one deciduous and one evergreen,
each characterized by a total biomass at time t, Bl,(t). The biomass
of an autotroph stock s, which could be either phytoplankton (p) or
leaves (l), is incremented in each time step (of length Dt) as follows:
Table 1. Stock functional group definitions.
Realm Nutrition Source Mobility Leaf Strategy
Marine Photosynthesis Planktonic N/A
Terrestrial Photosynthesis Sessile Deciduous
Terrestrial Photosynthesis Sessile Evergreen
Categorical trait values (column names) with the specific trait values for each stock functional group modelled.
N/A values reflect traits that are not applicable to a functional group.
doi:10.1371/journal.pbio.1001841.t001
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![Bs,(tzDt)~Bs,(t)zDBGrowth
s {DBMort
s , ð1Þ
where DBGrowth
s and DBMort
s are the gain and loss of biomass from
stock s over the time interval Dt, respectively. DBMort
s includes
losses due to herbivory. We use different approaches to model the
gain and loss of biomass from marine and terrestrial autotroph
stocks (Table 5).
In the marine realm, we model growth of the phytoplankton
stock by incrementing the total biomass of phytoplankton in each
cell using satellite-derived estimates of NPP (Table 5). This avoids
us having to adopt computationally impractical time-steps (days) in
order to accurately simulate the dynamics of phytoplankton, which
have rapid turnover rates (in our opinion, an explicit nutrient–
phytoplankton–zooplankton model would be a major improve-ment
to the marine part of the model; see Table 7). Loss of
phytoplankton arises directly from modelling grazing by marine
organisms (Table 5; Equations 3 and 4 in Text S1).
Terrestrial autotrophs are modelled using the climate-driven
terrestrial carbon model of Smith et al. [36]. We selected this
model because it has been parameterized and tested against
empirical data on carbon stocks and flows more rigorously than
similar models of which we are aware (Equations 5–19 in Text S1)
[36]. Moreover, it has a similar level of complexity to that used to
represent heterotrophic organisms. However, like the other model
components we adopted, the vegetation model could be replaced
by alternatives in future studies, including more complex models
able to address particular issues like CO2 fertilization (e.g.,
[12,37]). Terrestrial plant growth is modelled as a function of
NPP, the proportion of NPP that is produced by evergreen or
deciduous leaves, and the fraction of NPP allocated to structural
tissues (Table 5), all of which depend on the local climate. The loss
of plant biomass is determined by leaf mortality rate, which is also
function of the climate, as well as the consumption of biomass by
herbivorous terrestrial organisms (Table 5).
Heterotroph Ecology. Heterotrophs are modelled as co-horts.
Each cohort i is characterized by a functional group
(Table 2), by two traits that do not change through time—body
mass at birth, MJuvenile
i , and body mass at reproductive maturity
MAdult
i (for cohort, i)—and by three state variables whose values
do change through time—the abundance of individuals Ni,(t), the
wet matter body mass of each individual within the cohort Mi,(t),
and a stored reproductive mass of each individual, Ri,(t) (Figure 1).
The values of these state variables are updated each time step
according to the effects of ecological processes (Table 6).
Individuals in each cohort are assumed to interact only with
stocks and cohorts in the same grid cell.
The growth of individual body mass is modelled as follows:
i {DMMetab
i {DMReproAlloc
Mi,(tzDt)~Mi,(t)zDMAss
i , ð2Þ
Table 3. Settings used for the six model studies conducted in this research article.
Study Description Spatial Extent Length (y) Ensemble Number Output Detail
1 Grid-cell numerical analyses Four 1u61u focal grid cells (Table 4) 1,000 10 Biomass and abundance densities
by functional groups
2 Grid-cell individual- and
community-level predictions
Four 1u61u focal grid cells (Table 4) 100 1 Detailed individual-level process
diagnostics
3 Grid-cell community-level
predictions at empirically
observed locations
Fourteen 1u61u grid cells at
locations where ecosystem structure
has been empirically estimated
(Table S3)
100 10 Biomass and abundance densities
by functional group
4 Global predictions Global grid of 2u62u cells extending
from 65uN to 65uS in latitude and
from 180uE to 180uW in longitude
100 1 Biomass and abundance densities
by functional group
5 Effects of dispersal on marine
trophic structure
Global grid of 2u62u cells in the
marine realm only extending
from 65uN to 65uS in latitude and
from 180uE to 180uW in longitude
100 1 Biomass and abundance densities
by functional group
6 Effects of biomass turnover
rates on marine trophic
structure
Grid cell M1 (Table 4) 100 10 Biomass and abundance densities
by functional group for simulations
with differing biomass turnover
rates.
doi:10.1371/journal.pbio.1001841.t003
Table 4. Descriptions and coordinates of the focal grid cells for which detailed numerical-, individual-, and community-level model
simulations were made.
Cell Number Cell Description Latitude Longitude Location
T1 Terrestrial:tropical, aseasonal 0uN 32.5uE Southern Uganda
T2 Terrestrial:temperate, seasonal 52.5uN 0.5uE Central England
M1 Marine: low productivity, aseasonal 225.5uS 2119.5uW South Pacific Ocean
M2 Marine: high productivity, seasonal 42.5uN 245.5uW North Atlantic Ocean
doi:10.1371/journal.pbio.1001841.t004
A Mechanistic General Model of Global Ecosystems
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![Table 5. Summary of how autotroph ecological processes are modelled (for full details, see Text S1 and Table S2).
Process Realm Main Mathematical Functions Eqn(s). Assumptions
where DMAss
( )
( )
i is the total biomass assimilated as food, which is the
sum of the biomasses assimilated through herbivory and preda-tion,
DMAss,Herb
i and DMAss,Pred
i , respectively; DMMetab
i is mass
lost through metabolism; and DMReproAlloc
i is mass lost by
allocation to reproduction (Table 6, see also Figure 1).
Predation and herbivory are modelled using a Holling’s Type
III functional response, which assumes that the number (or
biomass) of prey (or plant material) eaten by an individual
predator (or herbivore) is a sigmoidal function of prey density (or
biomass density) (Table 6) [38]. The Holling’s functions require
definition of the attack rate and handling time for each predator
(or herbivore) cohort on each prey cohort (or plant stock). Attack
rates of herbivores on plants scaled according to the body mass of
herbivore. Attack rates of predators on animals were derived from
the size-structured model of Williams et al. [39], where the
probability of predation is a Gaussian function around an optimal
prey body size (as a proportion of predator size) (see Equations 35
and 36 in Text S1) estimated from large empirical datasets on
feeding relationships [40]. This size-structured model is an
extension of the long-standing niche model [41] but could be
replaced with other predator–prey interaction models in future
studies if desired. For carnivores and omnivores, the handling time
of each predator on each prey increases linearly with prey body
mass (larger prey take longer to eat) but decreases as defined by a
power-law relationship with predator body mass (larger predators
handle prey more quickly) (Equation 40 in Text S1). For
herbivores, handling time depends on herbivore body mass only
(a decreasing power-law relationship) (Equation 32 in Text S1).
Metabolic costs are modelled as a power-law relationship with
body mass, following Brown [29], using parameter values derived
from field metabolic rates (Table 6) [42]. We assume that each
cohort is active for some proportion of each time step according to
ambient temperature (Equations 41–47 in Text S1). Endotherms
are assumed to thermoregulate, and thus are active for 100% of
each time step. Marine ectotherms are active for 100% of each
time step. Terrestrial ectotherms do not thermoregulate, and thus
are only active for the proportion of each time step during which
ambient temperature was within their upper and lower activity
temperature limits, estimated following Deutsch et al. [43].
Once an individual reaches its adult mass, we assume that
all further mass gained is stored as reproductive potential.
An individual’s reproductive potential mass is incremented as
follows:
Ri,(tzDt)~Ri,(t)zDMReproAlloc
i {DRReproEvent
i , ð3Þ
where DRReproEvent
i is the potential reproductive biomass lost by
each individual of cohort i through reproductive events (Figure 1).
Reproductive events occur when an individuals’ stored reproduc-tive
potential reaches a threshold proportion of adult mass
(Table 6). During reproductive events, iteroparous organisms
devote all of their stored reproductive potential mass to producing
offspring; semelparous organisms devote all of their stored
reproductive potential mass, and also a proportion (Equations
50–52 in Text S1, Table S2) of their adult mass.
The number of individuals in each cohort is incremented as
follows:
Ni,(tzDt)~Ni,(t){DNMort
i {
X
k
(DNPred
k,i ), ð4Þ
Growth Marine The growth of phytoplankton, p, biomass in marine cell, M, during month, m, is given by:
DBGrowth
p ~NPPMm
:j:Acell :dtNPP,
where NPPMm
is a remotely sensed estimate of monthly marine NPP; j converts from
carbon to wet matter biomass; Acell is the grid cell area; dtNPP converts from monthly values
to the model time step.
3 in Text S1 The modelled standing
biomass of
phytoplankton is
capable of generating
the remotely sensed
productivity in any given
time step
Growth Terr. The growth of biomass in autotroph stock, l, in terrestrial cell, T, during month, m, is given
by:
DBGrowth
l ~
NPPT
m:Acell :y:dtNPP:(1{fstruct):fLeafMort:fever , ½if l is evergreen
NPPT
m:Acell :y:dtNPP:(1{fstruct):fLeafMort:(1{fever) , ½if l is deciduous
where NPPT
m is a remotely sensed estimate of monthly terrestrial NPP; Acell is the grid cell area;
y converts from carbon to wet matter biomass; dtNPP converts from monthly values to the
model time step; fstruct is the fractional allocation of primary production to structural tissue;
fever is the proportion of NPP produced by evergreen leaves at a particular location; and
fLeafMort is the proportion of total mortality that is leaf mortality.
5, 7–19 in Text S1 Annual mean
environmentally
determined NPP is
allocated to months in
the same relative
proportions as that
observed in remotely
sensed NPP data.
Mortality Marine The loss of phytoplankton biomass is given by:
DBMort
p ~Lp,Herbivory,
where Lp,Herbivory is the cumulative phytoplankton biomass consumed through herbivory.
4 in Text S1 Background mortality of
phytoplankton is
negligible compared to
losses from herbivory
Mortality Terr. The loss of biomass from autotroph stock, l, is given by:
DBMort
l ~
dtm,l :mever:Bl,(t) :feverzLl,Herbivory ,½if l is evergreen
dtm,l :mdecid :Bl,(t) :(1{fever)zLl,Herbivory ,½if l is deciduous
where Bl,(t) is the biomass of stock l at time t; mever and mdecid are annual leaf mortality
rates for evergreen and deciduous stocks, respectively; dtm,l converts annual leaf mortality
rates to the model time step; Ll,Herbivory is the cumulative biomass of stock, l, consumed
through herbivory; and fever is the proportion of NPP produced by evergreen leaves at a
particular location.
6, 10–15 in Text S1 Herbivory rates do not
affect plant allocation
strategies and plants do
not have the capacity for
defensive strategies
doi:10.1371/journal.pbio.1001841.t005
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![where DNMort
,
i is the number of individuals of cohort i lost to
nonpredation mortality, and
P
k (DNPred
k,i ) is the total number of
individuals of cohort i lost through predation, summed over all
predator cohorts k as outlined above (Figure 1). We model three
sources of nonpredation mortality: a constant proportional rate of
background mortality, which applies to all individuals; starvation
mortality, which is applied according to how much body mass has
been lost compared to the maximum body mass ever obtained
by an individual; and senescence mortality, which increases
exponentially after maturity with a functional form similar to the
Gompertz model (e.g., [44,45]) (Table 6). Note that abundance
only ever decreases within a cohort. New individuals generated
through reproduction produced new offspring cohorts (see below)
(Equations 52–54 in Text S1). For computational efficiency, once
A Mechanistic General Model of Global Ecosystems
the number of cohorts exceeds a user-specified, computationally
tractable threshold, a number of pairs of cohorts equal to the
excess are merged together. On merging, the biomass of one of the
cohort pair is converted into an equivalent number of individuals
of the other cohort in the pair (Equations 68–69 in Text S1). The
cohort pairs identified for merging are those lying closest together
in continuous trait space, and belonging to the same functional
group (Equation 67 in Text S1).
Individuals were exchanged among the grid cell via three types
of dispersal: (1) random diffusive dispersal of newly produced
(juvenile) cohorts, (2) active dispersal of individuals determined by
the degree of starvation experienced, and (3) advective-diffusive
dispersal driven by ocean currents (in the marine realm only)
(Table 6). Dispersal occurred via the movement of whole cohorts,
Table 6. Cont.
Process Main Mathematical Functions Eqn(s). Assumptions
Reprodn. The biomass allocated to reproduction for cohort i is modelled as:
DMRe proAlloc
i ~max 0, Mi,(t)zDMAss
i {DMMetab
i {MAdult
i
,
where DMAss
i is the total biomass assimilated as food; DMMetab
i is mass lost through
metabolism; MAdult
i is the body mass at which an individual of cohort i reaches
reproductive maturity.
A reproductive event was assumed to occur when the following threshold condition
was met:
Mi,(t )zRi,(t )
MAdult
i
wb,
where MAdult
i is the mass at which an individual of cohort i reaches reproductive
maturity; Ri,(t ) is the stored reproductive potential biomass of each individual in
cohort i at the current time; b is the threshold value for accumulation of reproductive
potential biomass.
S49–S54 Semelparous organisms can
allocate a fraction of their adult
mass to reproductive events.
Mortality The instantaneous rate of senescence mortality was modelled as:
mse~lse :exp
tpm=tbm
,
where lse is the instantaneous rate of senescence mortality for a cohort at the point of
maturity; tpm is the time that it took for the cohort to reach maturity; tbm is the time since
the cohort reached maturity.
The instantaneous rate of starvation mortality is given by:
lmax
mst~
1zexp{ Mi,(t ){qst :Mmax
i
fstMmax
i
where lmax is the maximum possible instantaneous fractional starvation mortality rate; qst
determines the inflection point of the logistic function describing the ratio of the realised
mortality rate to the maximum rate; fst is the scaling parameter for the logistic function
describing the ratio of realised mortality rate to the maximum rate; Mmax
i is the maximum
body mass ever achieved by individuals in cohort i.
The instantaneous rate of background mortality, mbg, was modelled as a constant value.
S55–S58 There is no senescence mortality
applied to cohorts that have not
reached maturity.
Dispersal Three types of dispersal were included in the model, two of which—diffusive
natal dispersal and responsive dispersal—applied across all realms, whereas advective
dispersal applied in the marine realm and to planktonic size
organisms only.
Diffusive natal dispersal modelled the characteristic dispersal distance of each cohort as a
function of body mass as follows:
di~ndiffusive :
Mi,(t )
Mdisp
ref
!odisp
,
where ndiffusive is the dispersal speed of an individual of body mass equal to the dispersal
reference mass Mdisp
ref ; odisp dispersal distance body mass exponent. Active dispersal in adults is
attempted if intracohort density of adult individuals is below a mass-related density threshold:
Ni,(t )
Acellvbresponsive
density
.
MAdult
i
,
or if the proportion of body mass lost in a time step exceeds a starvation threshold:
Mi,(t )
MAdult
i
vbresponsive
bodymass ,
where the betas represent those thresholds.
The final, advectively driven dispersal is applicable solely to planktonic organisms in the
marine realm and modelled using the two-dimensional advective vector at that time step
and location, with an additional diffusive component of random direction and length.
S59–S61 Cohorts are spread
homogeneously across grid cells.
Cohorts disperse in entirety not
as fractions.
The diffusive dispersal of
immature organisms is assumed
to represent them searching for
new territory.
Note that the same processes apply in the terrestrial and marine realms. For full details, see Text S1 and Table S2.
doi:10.1371/journal.pbio.1001841.t006
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![Table 7. The major development needs for the Madingley Model organised by development category.
such that cohorts remained intact. This was necessary numerically
to keep the number of cohorts manageable. We carried out some
targeted simulations to explore the effects of allowing cohorts to
split on dispersal, and found that could have quantitative effects,
but does not fundamentally alter dynamics (Figure S1). Assump-tions
and functional forms about dispersal, and numerical schemes
to implement them, are another potentially important area for
future research.
When the model was applied to a specific grid cell in isolation,
dispersal into or out of the grid cell was not modelled.
Emergent Properties
The properties of individuals and communities that we present
below are ‘‘emergent’’; that is, they are not prescribed, but instead
emerge through time as a result of the large number of interactions
that take place between individual organisms (approximated
as cohorts). As a result of these interactions, life histories of
individuals are formed over time and can be tracked, and com-munities
and ecosystems of individuals self-assemble. Moreover,
the dynamics of any one grid cell are affected by the exchange of
individuals with other grid cells, which occurs due to dispersal.
Thus macroscale predictions (e.g., over the generation length of an
individual cohort, across functional groups, or across entire
ecosystems) emerge from microscale biological mechanisms. The
macroscale predictions differ for ecosystems in different climates,
but only because the microscale biology is sensitive to the climate.
Similarly, the macroscale predictions differ between the land
and sea, but only because microscale biology differs between land
and sea. We compared these emergent properties to empirical
data.
Model Simulations and Comparison to Data
We carried out four distinct types of simulations for different
assessments of model capabilities (Table 3).
Terrestrial grid cells were seeded with two autotroph stocks,
deciduous and evergreen, as detailed above, and marine grid cells
were seeded with a single phytoplankton stock. Grid cells were
seeded with around 1,000 cohorts each, with 112 cohorts in each
of nine functional groups in the terrestrial realm and 100 cohorts
in each of 10 functional groups in the marine realm. Juvenile and
adult body masses of cohorts were drawn at random from a
prespecified range (Table 2), and initial abundance was scaled
negatively with initial body mass to provide reasonable initial
densities (see Text S1 for full details).
Detailed numerical analyses were conducted on four focal grid
cells (Study 1, Table 3) to investigate ecosystem dynamics over
longer time scales. These simulations were used to check for the
persistence of key community components (autotrophs, herbivores,
carnivores, and omnivores), and to determine the typical time
scales for the dynamics to reach some form of equilibrium. These
Category Development Need
Data 1. Source individual organism-level data with which to constrain ecological processes such as mortality from disease and environmental
disturbance, reproductive behaviour, dispersal behaviour, and activity rates in response to environmental or food stress.
2. Gather information on local community structure to evaluate community-level predictions, such as total biomass of functional or trophic
groups, whole communities, individual size distributions for entire communities in the terrestrial realm, and biomass fluxes through ecosystems.
3. Collect data detailing ecosystems across space and through time to evaluate emergent ecosystem-level properties—for example, latitudinal
or longitudinal transects of biomass and/or abundance, total biomass and/or abundance within a region, and changes in ecosystem structure in
response to environmental change through space and/or time.
4. Assemble data on quantified interaction networks for communities with which to compare the individual-level interaction networks predicted
by the model.
Ecology 1. Include detritivores as a functional group, including the ecological processes that link detritivores to the organic matter inputs from the
ecosystem and cycle that processed organic matter back to form inputs for the primary producers of the system, as well as representing
detritivore-based food chains.
2. Resolve sub-grid-cell habitat structure and organismal preferences within that structure that will likely lead to patterns of interactions among
organisms that violate the well-mixed assumption, for example, by providing refugia for prey: in forests for instance, canopy-dwelling predators
encounter canopy-dwelling prey more often than expected, but ground-dwelling prey less often than expected.
3. Incorporate an explicitly resolved, mechanistic model of phytoplankton dynamics with two-way linking between phytoplankton and
zooplankton.
4. Incorporate a three-dimensional spatial structure in the oceans with a temporally and spatially varying mixed-layer and deep chlorophyll
maxima
5. Represent nonphytoplanktonic coastal NPP (seagrass beds or coral reefs) in order to more realistically capture biodiverse and productive
coastal ecosystems.
6. Capture varying organismal ecological stoichiometry to account for biochemical limitations on performance and also to being able to explore
biogeochemical cycling through entire ecosystems; useful starting points include ecological stoichiometric [112] and dynamic energy budget
[113] concepts.
7. Simulate freshwater ecosystems in addition to terrestrial and marine, and source necessary datasets to constrain ecological parameters and
evaluate outputs.
8. Introduce the concept of intelligent behaviour—for example, directed dispersal (e.g., along a gradient of resources), hibernation and stasis
strategies, or complex predator–prey and herbivore–plant interactions
Methods 1. How does underlying behaviour feed up to mathematical representations of ecological functions? For example, how does the intelligent
behaviour of predators and prey affect the Hollings’ functions employed to model this interaction?
2. Analysis of the model framework to identify analytical solutions for emergent properties such as size distributions or trophic structure.
3. Study the implications of the numerical methods employed in the model such as the time step of ecological processes and the cohort
approximation.
4. Implement a variable time-scale method wherein smaller, more metabolically rapid organisms have a faster time step [14], which may stabilise
the marine realm and will be needed to implement a fully coupled dynamic and mechanistic phytoplankton model.
5. Formally constrain the model against data (data needs are described above) in order to rigorously select the most appropriate assumptions,
functional forms, and parameter values.
doi:10.1371/journal.pbio.1001841.t007
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![analyses used the same climatological time series per year to
remove the effects of interannual environmental variation. For
each focal grid cell, we ran 10 model simulations for 1,000 y at a
monthly time step. To test the effect of the cohort-merging regime
on modelled dynamics, we repeated the simulation ensembles for
each focal grid cell with the threshold number of cohorts at which
merging is activated set at 500, 1,000, 5,000, and 10,000 cohorts
and for a shorter period of 100 y.
Additional detailed simulations were carried out for the focal
grid cells over a 100-y period to generate highly resolved
predictions of emergent ecosystem properties at two levels of
biological organisation: individual and ecosystem level (Study 2,
Table 3).
We compared the properties of individual organisms with
empirical data. Importantly, none of these properties were defined
in the model as parameters, but rather they emerged as a result of
the ecological interactions among individuals. The predicted
relationship between body mass and growth rates was compared to
estimates for reptiles, mammals, birds, and fish [46–48], and the
relationship between body mass and time to reach maturity to
estimates for invertebrates, reptiles, mammals, birds, and fish [49–
57] (where necessary body masses were estimated from body
lengths using relationships in [58–61]). The predicted relationship
between body mass and mortality rates was compared with data
for invertebrates, mammals, birds, and fish, taken from a single
study [62]. The predicted relationship between body mass and
lifetime reproductive success was compared with data for
mammals, birds, and a few insect species [63–71]. Of these
emergent properties, the growth rate of organisms derives most
closely from the functional forms and input parameters. Specif-ically,
growth rate could theoretically be a simple sum of food
assimilation rates under conditions of saturating prey density
minus metabolic costs. To test whether this was the case, we
calculated the theoretical growth rate for organisms of a range of
body masses under these conditions.
We compared our novel predictions of complete ecosystem
structure in two grid cells (T1 and M1) (Table 4) to empirical data:
the biomass density of large herbivores with an estimate for
Uganda [72], and the predicted herbivore to autotroph biomass
ratios with average observed ratios for similar ecosystems [73]. We
further compared the modelled relationships between body mass
and population density with empirical estimates derived from fish
assemblages [74,75].
To test the ability of our model to capture broad-scale patterns
in the basic trophic structure of ecosystems, we compared our
model predictions (Study 3, Table 3) to empirical estimates from
the same dataset used to calculate the global average trophic
structure ([73]; see above), but this time using specific values for 14
sites for which we could identify the spatial location (Table S3).
This dataset is the most geographically wide-ranging dataset on
ecosystem structure that we are aware of, including sites in both
the terrestrial and marine realms.
We also generated model outputs at a global scale (Study 4,
Table 3). These were used in two ways: firstly, to investigate the
mechanisms giving rise to variation in ecosystem structure by
assessing the relationship between trophic structure and produc-tivity
in the model along large gradients of autotroph productivity
in both terrestrial (along a meridional transect from the low
productivity Saharan desert to high productivity Congo Basin
tropical forest region) and marine (along a meridional transect
from low productivity Antarctic waters to high productivity East
Atlantic upwelling zones) realms; and secondly, to make novel
predictions of as-yet unmeasured global properties (e.g., latitudinal
gradients in total biomass) and to compare to other modelled
A Mechanistic General Model of Global Ecosystems
estimates of total biomass and density at a global scale [76]. We
also compared modelled global average ratios of herbivore to
autotroph biomass with the average ratios observed in the same
dataset that we used to test the predictions made by individual cells
[73]. Finally, we investigated how modelled marine ecosystem
structure responded to mechanisms that have been proposed to
cause inverted trophic biomass pyramids, such as dispersal [77],
turnover rate of autotrophs, and turnover rate of consumers [77–
79]. To do this, we simulated the global marine realm with no
dispersal permitted between grid cells (Study 5, Table 3) and the
effects of reducing the turnover rate of biomass through the
ecosystem (Study 6, Table 3).
Results
Grid Cell: Dynamics
For the 1,000-y simulations (Study 1), model dynamics
converged rapidly (,100 y) to dynamic equilibria for all 10
replicates in all four focal grid cells (Figure 2). Autotrophs,
herbivores, omnivores, and carnivores persisted in all simulations.
The dynamics of total biomass by functional group differed
markedly among the four grid cells. Terrestrial grid cells were
dominated by autotroph biomass and, among heterotrophic
organisms, by herbivores, with lower biomasses of omnivores
and carnivores. Marine grid cells, in comparison, had much lower
biomasses of autotrophs, and omnivorous and carnivorous
organisms were more dominant. Unsurprisingly, the seasonal grid
cells in both the terrestrial and marine realms (Figure 2B and 2D)
exhibited much greater fluctuations in biomasses within years,
particularly for lower trophic levels. The high-productivity marine
grid cell exhibited large-amplitude, high-frequency variations in
zooplankton abundance. Biomass dynamics were robust to the
choice of the threshold number of cohorts at which to activate
merging above a threshold of 1,000 cohorts (Figure S2).
Grid Cell: Individuals
The power-law relationships between body mass and the
properties of individual organisms that emerged from the model
were generally consistent with empirical data (Figure 3). For
growth rates and times taken to reach reproductive maturity, the
modelled and empirical values were very similar, although the
slope of the relationship between predicted growth rates and body
mass was steeper. In absolute terms the predicted growth rates
tended to be higher and the predicted times to maturity tended to
be lower than those observed in the empirical data (Table S4).
Our assumptions about underlying ecological processes, such as
handling times and metabolic rates, place a fundamental limit on
the growth rate of organisms of a given body mass (i.e., the net
growth rate of individuals that are feeding at the maximum rate). If
most individuals attained this maximum, then the growth rates
would not be emergent, so much as defined by the model
assumptions. But this was not the case. The emergent relationship
between body mass and growth rate was not a simple function of
maximum possible food assimilation and metabolic costs: mod-elled
growth rates were typically one-tenth of theoretical
maximum model growth rates and showed large variation for
any given body mass (Figure S3). This variation resulted from the
many other factors that affected growth rate, most notably the
abundance and body masses of potential prey and predators
competing for the same prey.
Predicted mortality rates showed a negative power-law
relationship with body mass (Figure 3C), qualitatively consistent
with empirical data, although the relationship was generally
shallower and absolute rates were higher (Table S4). Finally,
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![A Mechanistic General Model of Global Ecosystems
Figure 2. 1,000-year dynamics for four locations. Medians from ensembles of 10 replicate simulations (lines) and absolute ranges (shaded
regions) of biomass densities for autotrophs (dark green lines), herbivores (light green), omnivores (blue), and carnivores (red) within four 1u61u focal
grid cells; T1, terrestrial aseasonal (A); T2, terrestrial seasonal (B); M1, marine aseasonal (C); and M2, marine seasonal (D) (Table 4). The temporal
dynamics in these metrics emerges from underlying ecological processes that affect a large number of cohorts within each grid cell. Insets zoom in
on medians for the last 5 y of the simulations, demonstrating the seasonal variability in each cell.
doi:10.1371/journal.pbio.1001841.g002
predicted reproductive rates in the terrestrial realm showed a weak
positive power-law relationship with body mass, broadly consistent
with empirical estimates (Figure 3D, Table S4), whereas predicted
reproductive rates in the marine realm were weakly negative.
Predicted reproductive rates were substantially more variable than
the empirical data (Figure 3D).
Grid Cell: Community
For the four focal grid cells, terrestrial ecosystems exhibited a
pyramid of biomass across the different trophic levels (Figure 4A),
which is widely accepted to be present in terrestrial systems [80].
The predicted herbivore biomass as a proportion of producer
biomass (0.98%) was consistent with empirical terrestrial estimates
(median value=0.93%) (Table S5) [73]. However, predicted
biomass of large-bodied herbivores was four to six times higher
than estimated from a field study [72]. Consistent with current
opinion and observations [78,81–84], marine ecosystems exhibited
an inverted pyramid of biomass structure [73,82], with the highest
biomasses in the highest trophic levels (Figure 4C). Marine systems
exhibited relatively faster flow rates of productivity from autotrophs
to higher trophic levels compared with terrestrial ecosystems—and
at rates much higher than those estimated to date (Figure 4A and
4C) [85]. Predicted herbivore biomass as a proportion of producer
biomass for the marine grid cells was much higher than in terrestrial
ecosystems (63%), and of a similar magnitude to empirical estimates
(median value=52%) (Table S5) [73].
Expressed as abundance rather than biomass, and consistent
with theoretical expectations [86,87], trophic pyramids were not
inverted in either realm: that is, communities contained a greater
number of herbivores than carnivores (Figure S4).However,
omnivores were more abundant than herbivores, by a factor of
3 in the terrestrial cell and by two orders of magnitude in the
marine cell. This was because the average size of omnivores was
smaller than the average size of herbivores or carnivores.
In both terrestrial and marine grid cells, densities of organisms
showed a negative, approximately log-linear relationship with
individual body mass (Figure 4B and 4D), the slopes of which fell
within observed ranges in fish community assemblages from some
sources (Figure S5) [75], although not from others (Table S6) [74].
Geographical Patterns in Ecosystem Structure Across 14
Sites
Predicted ratios of heterotroph to autotroph biomass were
broadly consistent with empirical estimates in many of the
terrestrial and marine locations (Figure 5). For terrestrial
ecosystems, the model and empirical data were in closest
agreement in the two savannah ecosystems (Figure 5J and N).
For the other ecosystem types—desert, tundra, deciduous forest,
and tropical forest—there was lower agreement between model
and empirical estimates of trophic structure, with modelled
heterotroph to autotroph biomass ratios generally greater than
empirical estimates, sometimes by orders of magnitude (Figure 5).
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![A Mechanistic General Model of Global Ecosystems
Figure 3. Comparison of emergent life history metrics with empirical data. Empirical (black) and emergent model (grey) relationships
between body mass and (A) growth rate, (B) maturity, (C) individual mortality rates, and (D) lifetime reproductive success. These life history metrics
are not part of the model definition. Rather, they emerge from underlying ecological processes such as metabolism and feeding (see main text). Life
history metrics were sampled from 100-y model runs for the four focal grid cells (Table 4). Individual mortality rates are estimated as the inverse of
lifespan, and because the minimum simulated lifespan is one model time step (1 mo), estimated individual mortality rates were bounded at 12.
doi:10.1371/journal.pbio.1001841.g003
Modelled ecosystems in the marine realm generally showed
closer agreement with empirical estimates than in the terrestrial
realm. However, in both Santa Monica Bay, San Francisco
(Figure 5A), and the Swartkops estuary in South Africa (Figure 5F),
median modelled herbivore to autotroph biomass ratios were three
orders of magnitude larger than empirical estimates.
Trophic Structure Along Productivity Gradients
The structure of both marine and terrestrial ecosystems showed
marked changes along a gradient of increasing NPP (Figure 6).
Marine ecosystems showed increasing biomass for all three
heterotroph types (carnivores, omnivores, and herbivores), and
flat then declining and highly variable autotroph standing biomass
(Figure 6A). Terrestrial ecosystems also showed a trend of
increasing heterotrophic biomass with productivity (Figure 6B).
Carnivores increased in biomass with productivity more steeply
than for other trophic levels, and were entirely absent from the
lowest productivity desert ecosystem. In the most productive
terrestrial ecosystems, carnivores typically had higher biomass
densities than omnivores.
Global Ecosystems
Global patterns of total heterotroph biomass, averaged across
the final year of the simulation (Figure 7A), were similar to
patterns of primary productivity (Figure S6). In the marine realm,
our modelled estimate of median heterotroph biomass density was
167,147 kg km22, approximately 7–30 times greater than previ-ous
modelled estimates, which range from 5,500–25,000 kg km22
[76,88–90]. However, a recent empirical study into mesopelagic
fish biomass suggests that some fish biomass densities are likely to
be an order of magnitude higher than these previous estimates
[90] and so our prediction is plausible. Global median ratios of
herbivore to primary producer biomass estimated by the model
were 0.8% for terrestrial and 189% for marine ecosystems,
compared to 0.93% and 52% for empirical estimates (Table S5)
[73]. Our modelled estimate of median total terrestrial hetero-troph
biomass density was 151,089 kg km22, a prediction which,
as far as we are aware, has never been made previously.
In the marine realm, high heterotroph biomass is predicted in
upwelling systems and areas of high annual productivity (e.g., the
North Atlantic). In the terrestrial realm, predicted heterotroph
biomass was highest in naturally forested areas and lowest in
deserts. There was no clear latitudinal gradient of biomass density
in either system, but latitudinal variability was substantially greater in
the terrestrial realm. At subtropical latitudes in the northern
hemisphere in the terrestrial realm, there was a band in which
carnivores had higher biomass density than omnivores, whereas
elsewhere omnivores had greater biomass density. This switch in the
relative dominance of omnivores in the northern hemisphere
coincided with a decline in mean herbivore biomass density. No
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![A Mechanistic General Model of Global Ecosystems
Figure 5. Global heterotroph:autotroph biomass ratios. Comparisons of modelled (open) and empirical (filled) heterotroph to autotroph
biomass ratios in marine (A–F) and terrestrial (G–N) environments (Table S3). Green squares are herbivore to autotroph ratios, blue triangles are
omnivore to autotroph ratios, and red diamonds are carnivore to autotroph ratios. Modelled ratios are medians from 10 simulations, and vertical lines
are 1 standard deviation over these simulations. Empirical ratios are individual estimates or, where more than one estimate was available, the median
of these with sample sizes of H (n = 5), K (n = 2), L (n = 2), and N (n = 3), and vertical lines indicate maximum and minimum empirical estimates.
Comparison locations are shown on a map of the predicted ratio of herbivore to autotroph biomass constructed from the global simulation (Study 4,
Table 3).
doi:10.1371/journal.pbio.1001841.g005
Discussion
We have shown that it is possible to derive global predictions
about the emergent properties of ecosystem structure and function
from a GEM based on processes of, and interactions among,
individual organisms, without any model-imposed constraints on
those properties.
Stability of Emergent Dynamics
The model reached a dynamic steady state in all grid cells, with
the persistence of all trophic levels, which is expected in the
absence of perturbation [91]. Real ecosystems are not expected to
exhibit such stable dynamics because they are subject to numerous
interannual environmental fluctuations and perturbations. These
were not incorporated for this study, but could be in the future.
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![or biomes, might help us to better diagnose discrepancies in the
future.
Growth rates were slightly faster and times to maturity slightly
shorter than those from observation. Modelled rates of biomass
transfer calculated for the two focal grid cells were higher than
empirically observed rates, particularly in the marine realm
(Figure 4) [85]. At least in part, this discrepancy may result from
a bias in the data toward larger organisms, leading to empirical
estimates underestimating real biomass flow rates.
Similarly, the negative log-linear relationship between individ-ual
body mass and organism density is consistent with ecological
theory [92], although uni- [93,94] or multimodal [95,96] relationships
have been observed. The modelled slopes were shallower than
empirical estimates for a log-linear relationship, which again might
indicate that turnover rates in the model were overestimated, causing
greater suppression of smaller organism abundance and higher
abundance of larger organisms than in real ecosystems.
Another difference between the model and data was that the
modelled biomass of large-bodied herbivores was several times
higher than observations [72]. Modelled ratios of herbivore to
autotroph biomass were also higher than empirical estimates in
most cases, especially for terrestrial ecosystems. There are three
potential explanations for this. The first is that herbivores, like
predators, are eating too efficiently in the model, which might
result from incorrect functional forms or missing processes. The
second explanation is that because the available data are extremely
sparse, the data are thus potentially not representative of the
system. Thirdly, human impacts might have reduced large
herbivore biomass in the empirical data compared to the
undisturbed ecosystem assumed in these simulations of the model.
The closer match between modelled and empirical trophic
structure for marine and savannah ecosystems, compared to
forests, might be because these ecosystems conform much better to
the assumption that individuals are well mixed. This assumption
implies that herbivores can find all plant material and predators
can find all prey. In all ecosystems, but most obviously in forests,
many leaves are physically out of reach of many herbivores, and
many prey are able to find refuge from predation. This may act to
slow down biomass turnover in forests in comparison to the ocean
and savannas, in a way that cannot be captured by a model that
assumes complete mixing within a grid cell. On the other hand,
the discrepancy could also be caused by incomplete empirical
data. It is easier to estimate whole-ecosystem properties in
savannas (where animals tend to be highly visible) and in the
ocean (which can be trawled with nets) compared with forests.
Alternatively, the terrestrial plant model might be inaccurately
capturing the allocation of productivity to structural or nonstruc-tural
matter at these specific forest sites. However, this appears less
likely, as the allocation function of this model has been rigorously
constrained using a global dataset, and evaluation shows the model
predicts well for this property [36]. We note, however, that at
finer, site-level scales, plant allocation strategies will certainly be
more heterogeneous and will certainly be different from the larger
scale average predicted by the global model.
It is important to note that differences between the marine and
terrestrial realms were not imposed on the model as top-down
limits on the structure of ecosystems but rather emerged from
individual-scale ecology. A necessarily different set of representa-tive
functional groups was defined for the marine environment
compared to the terrestrial environment, but all functional groups
in the model followed the same fundamental ecological functions.
The only other encoded differences between marine and terrestrial
cohorts were the proportion of total autotroph biomass available
for consumption by a given herbivore cohort, the different optimal
A Mechanistic General Model of Global Ecosystems
prey body sizes for predators, and the assumption that marine
ectotherms are not thermally restricted in their capacity to
function. The primary cause of the much lower ratio of herbivore
biomass to autotroph biomass in the focal terrestrial cells versus in
the oceans was the allocation by terrestrial plants of primary
productivity to structural tissues, which are inedible to all
herbivores in the model (Figure S11). This assumption probably
made it more likely that terrestrial cells would exhibit a
conventional pyramid of biomass structure. However, the model
predicted considerable variation in the shape of the trophic
biomass pyramid across terrestrial and marine cells, including an
inverted structure in some terrestrial cells and a noninverted
structure in some marine cells (Figure S7).
Emergent Global Patterns: Model Results and Predictions
The modelled global estimates of biomass density represent the
first attempt to assess the scaling of ecosystem properties from
individuals to communities at a global level, and to apply a general
ecological modelling methodology consistently across both the
marine and terrestrial realms.
Some of these properties have been estimated previously in
specific locations, but none have been estimated globally using
mechanistic models (although marine animal biomass and biomass
densities have been predicted mechanistically [76,88,89]). In
addition, we have calculated emergent properties that are, as far as
we are aware, unprecedented (Table 8), and we discuss these
below.
Heterotroph Biomass and NPP. At a global scale, the
spatial pattern of heterotroph biomass was broadly consistent with
observed NPP [97], which is unsurprising, as NPP is the basal
resource in all of the modelled ecosystems. However, the
relationship between primary productivity and heterotroph
biomass was not simple: a given level of primary productivity
could result in a wide range of heterotroph biomass (Figure S6A–
D). This variation arises from differences in climate, which lead to
differences in biomass allocation to different plant tissues and to
variation in animal metabolic rates and levels of activity. The
predicted peak in terrestrial heterotroph biomass densities
observed in locations with intermediate levels of NPP is also likely
to result from these factors; for example, plants in the most
productive areas allocate a greater proportion of biomass to
structural tissues, whereas plants in intermediate productivity
ecosystems such as grasslands have a greater relative allocation to
nonstructural tissues. Autotroph biomass was also influenced by
herbivory, as demonstrated by removing all heterotrophs from the
model and representing mortality of plants through herbivory
using a constant loss term (Figure S6E and F). This experiment
suggests the impact of herbivory on plants varies significantly
across the world, indicating the potential importance of explicitly
considering herbivores in carbon cycle models, such as DGVMs,
or models of ocean biogeochemistry, which is not done at present.
Exploring the impacts of heterotrophs on carbon cycling and
predicted carbon dynamics is an important avenue of research for
future development of GEMs.
Emergent Structure and Productivity. Modelled variation
in trophic structure along gradients of productivity supported
theoretical expectations that the NPP of systems will determine the
length of trophic chains [9,10,98]. In low-productivity terrestrial
systems, there is insufficient autotrophic biomass propagating to
higher trophic levels to support carnivores, whereas in high-productivity
ecosystems, carnivore biomass is greater than
omnivore biomass. In the marine realm, autotroph biomass
decreased with increasing primary productivity beyond NPP of
40,000 kg km22 y21, inconsistent with expectations from the
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![Table 8. Novel predictions and datasets needed to evaluate them.
Prediction Data to Evaluate
trophic release hypothesis (Figure 6B) [11]. The model predicts for
marine ecosystems that with increasing primary productivity
herbivore biomass increases and carnivore biomass, as a propor-tion
of total biomass, decreases. For terrestrial ecosystems,
herbivore biomass increased to around 40,000 kg km22 and then
decreased, whereas the carnivore biomass proportion decreased
only after around 550,000 kg km22. The relationship predicted
for marine ecosystems is in agreement with the general findings
from available empirical data on changes in trophic structure
associated with changes in productivity, derived from freshwater,
intertidal, and reef fish communities [99–103]. However, our
results indicate that a qualitatively different relationship between
trophic structure and productivity appears to exist in the terrestrial
realm. There are additional factors that influence modelled
community structure along productivity gradients that will require
detailed investigation in the future, including (i) seasonality, which will
vary among different modelled locations with similar productivity; (ii)
climatic differences, which might affect the composition of autotroph
biomass in terrestrial ecosystems; and (iii) dispersal regimes.
Emergent Latitudinal Patterns of Community Stru-cture.
Predictions of latitudinal variation in community struc-ture
(as shown in Figure 7B and 7C) give an insight into the
mechanistic basis of these patterns at a global scale. On land, there
was greater variation in the biomass density of all trophic groups,
both latitudinally and longitudinally, compared to in the oceans
(Table 8). The greater variation in terrestrial biomass densities was
likely driven by greater environmental heterogeneity in the
terrestrial realm and the greater range and speed of dispersal
processes (e.g., advective dispersal) in the oceans. For example,
both temporal [104,105] and spatial variability [106] in environ-mental
temperature is higher on land versus the ocean.
In the mid to high latitudes of the terrestrial northern
hemisphere, omnivorous organisms account for greater biomass
than carnivores. However, in equatorial latitudes and extending to
30uS, carnivorous organisms constituted a greater fraction of the
total ecosystem biomass than omnivores (Figure 7C and Table 8).
The equatorial and low southern hemisphere latitudes correspond
to more stable environmental conditions [106] compared with mid
to high northern latitudes. Therefore, the model appears, in the
terrestrial realm, to be selecting for generalist feeding strategies in
more variable environments, while favouring specialism where the
environment is more stable.
Mechanisms Giving Rise to Inverted Marine Trophic
Structure. The model showed that dispersal of organisms plays
an important role in the spatial extent and frequency of inversion
of marine trophic structure (Figures S8 and S9), which is consistent
with the hypothesis that the import of allocthonous organic matter
supports relatively higher heterotrophic biomass in oligotrophic
freshwater systems, which has been postulated previously but not
investigated in detail [77]. Furthermore, we show that noninverted
trophic biomass structure is more frequent when the turnover rate
of phytoplankton is reduced and when the rate and efficiency of
biomass transfer through the ecosystem is lower (Figure S10), in
agreement with current theory [77–79]. The generality of inverted
trophic pyramids in the marine realm remains unknown, but
there are numerous examples of herbivore biomass being larger
than producer biomass in ocean environments [73]. Inversion at
the top of the trophic pyramid has apparently been observed in
some near-pristine reef habitats [84], though this may simply
be an overestimation artefact of the visual census approach
used [107].
Future Model Development
In developing the first global GEM, our strategy was to start
with a ‘‘simple’’ model that can be improved later. To keep it
simple, we excluded numerous aspects of ecology—some of which
are captured by existing models of particular ecosystems [14,15].
Adding this ecology back into our model would, arguably, make it
more realistic. Then again, attempting to include all known
ecological processes occurring in every ecosystem around the
world would not only be completely impractical but would also be
excessive for most of the purposes for which a GEM is intended.
Thus, we would expect the set of ecological processes represented
in GEMs to evolve over time and to depend on the ways in which
GEMs come to be used. Moreover, there are several other
important ways in which our model could be improved, as
outlined in Table 7, and discussed below.
Future Model Development: Ecology. The physical envi-ronment
is currently represented very simply in the model. For
example, in reality, variation in habitat structure within grid cells
will alter interactions between organisms. And a fully integrated
and explicitly resolved mechanistic model of phytoplankton is
required in future iterations of the model, as is representation of
nonphytoplanktonic coastal autotrophs (e.g., seagrass beds or coral
Median terrestrial total heterotrophic biomass density is predicted to be
151,089 kg km22 and maximum terrestrial heterotrophic biomass densities are
found in ecosystems with intermediate levels of NPP (Figure 7A and Figure S6A)
Empirical or modelled information on the total biomass of heterotrophic
organisms in a sample of terrestrial biomes, from which median terrestrial
biomass density could be inferred
Median marine total heterotophic biomass density is predicted to be 167,147 kg km22,
approximately 7–30 times greater than previous modelled estimates
Empirical information on the total biomass of heterotrophic organisms in
a sample of marine locations, from which median marine biomass density
could be inferred
Omnivorous organisms account for greater biomass than carnivores in low to mid
productivity terrestrial environments, for example in the Saharan desert—Sahelian
savanna transition (Figure 6B), or more widely in the mid to high latitudes in the
northern hemisphere (Figure 7C). At equatorial latitudes and extending to 30uS,
carnivorous organisms constitute greater biomass than omnivores on average
Ecosystem trophic structure or food web structure for low to mid
productivity terrestrial environments in equatorial latitudes and mid
latitudes in both hemispheres
Terrestrial biomass densities vary more than marine biomass densities across latitudes
(Figure 7B and C)
Observations of total biomass contained in trophic groups at a set of sites
within the same latitude band, carried out across a range of latitude
bands. For the terrestrial realm, the band between 20u and 30uN has
potentially substantial latitudinal variation in total biomass.
doi:10.1371/journal.pbio.1001841.t008
A Mechanistic General Model of Global Ecosystems
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![reefs) and detritivores. The detrital loop in particular is important
in ‘‘closing the system.’’ Other ecological processes that should be
incorporated in future iterations of the model include ecological
stoichiometry; intelligent behaviour, such as directed dispersal,
hibernation, and stasis; and complex predator–prey and herbi-vore–
plant interactions (Table 7).
Future Model Development: Data. Robust data-con-strained
parameterisation of the model and rigorous evaluation
of our novel but testable outputs was not possible because the
necessary data were not generally available. Therefore, another set
of developments are needed around the acquisition and collation
of data for use in GEM modelling (Table 8 and Table 7), which
are reflected by the biodiversity informatics community [108].
Future Model Development: Numerical and Math-ematical
Methods. The development of the Madingley Model
was enabled by combination of numerical methods that is, far as
we are aware, novel (e.g., the cohort approach to trait-driven
interactions, combined with cohort merging, randomly ordered
updating, the treatment of autotrophs as continuous state
variables, and exponential differencing of loss rates within time
steps; see Text S2 for further examples). Given the novelty of this
modelling paradigm in ecology, at least five areas of development
will be required: detailed analysis and understanding of the
mathematical representations of ecology, analytical tractability of
predicted ecosystem properties, the implications of alternative
abstractions and numerical methods used to implement them, the
infrastructure to allow flexibility in scale, and the infrastructure to
constrain and evaluate the model so that the benefits of additional
components or realism can be assessed objectively (Table 7). In
addition, it would be interesting to explore the approach referred
to as ‘‘parameterization’’ in the biogeosciences modelling commu-nity—
that is, to fit phenomenological relationships to the output of
GEMs, thus allowing approximate versions of them to be run much
more quickly, or within the context of more general ESMs.
Future Model Development: Community. The further
development of GEMs discussed above will be expedited by a
community of researchers improving upon the model presented
here or developing alternative GEMs. We call for such a
community of ecologists, biologists, mathematicians, and comput-er
scientists to form around the GEM concept so that this class of
model can be rapidly advanced to better meet the pressing needs
of conservationists and policymakers. In this spirit, we have
developed our model architecture in such a way that it is relatively
easy to alter the representation of ecological processes and have
made our model code freely available to the community (www.
madingleymodel.org).
Use of GEMs
Our model is the first step towards the development of a more
ecologically refined GEM (and GEMs) that occupies a very
different niche to the more specialised modelling approaches that
have been used to inform biodiversity policy to date, and is more
akin to the global climate models that inform global climate
science and policy [8]. Our GEM necessarily made numerous
simplifying assumptions in order to capture a broad range of
ecological processes and organisms. This nevertheless provides a
new approach to answering important outstanding questions in
ecology and with which to begin to ask entirely new questions—
questions that require an integrated, mechanistic understanding of
whole ecosystems; the connections among them; and their
response to environmental variation and natural or human
perturbations. In the following sections, we briefly discuss how
GEMs could be used to inform ecological science and conservation
policy.
A Mechanistic General Model of Global Ecosystems
Use of GEMs: Ecology. GEMs will help in the development
of ecological theory. The study of ecology is so broad that most
pieces of ecological research necessarily focus on a small subset,
whether in terms of scale, taxa, or the processes concerned. The
implications of the findings in these disparate research areas for
the longer term and larger scale dynamics of whole communities
and ecosystems are hard to assess. This has led some ecologists to
call for a renewed interest in ‘‘systems ecology,’’ which aims to
study important ecological processes within the context of other
important ecosystem and earth-system processes to enable a better
understanding of the natural environment [109]. Models like ours
provide one way to do this: new ecological findings can be used to
modify the model, or different competing formulations of
ecological theories (e.g., prey density or ratio-dependent predation
functions [110]) can be represented in the model and the results
assessed against known ecosystem structure. By doing so, the
processes of critical importance for ecosystem structure and
functioning could be identified and priorities for development of
new ecological hypotheses or data-gathering determined. Our
preliminary investigations of community trophic structure along
productivity gradients and of the mechanisms giving rise to the
inversion of marine cells illustrate the potential of GEMs in this
regard.
Use of GEMs: Conservation. The simulations presented
here are not directly relevant to conservation decision-making, as
the model currently does not directly include anthropogenic
influences. In principle, a model of this kind could be used to
better inform the management of the world’s ecosystems, in much
the same way that mechanistic ESMs are used to predict and
explore scenarios of anthropogenic climate change [7]. Forcing the
model with time-varying historic or future projections of
environmental variables would provide the kinds of novel and
highly relevant outputs that could enable a mechanistic approach
to conservation decision-making.
By taking a system-level approach, GEMs are uniquely able to
simulate the interacting relationships between various simulta-neous
human pressures (such as climate change, land use change,
and harvesting of wild animals) and various metrics of ecosystem
structure and function, exploring the trajectories derived from
external scenarios of human pressure. For example, they could
predict (1) static measures of ecosystem properties, such as the
variation in the functional traits represented in ecosystems, an
important measure of biodiversity thought to be related to
ecosystem functioning [26]; (2) metrics that are currently used to
monitor the state of ecological systems, such as the total
abundance of large endotherms as an analogue of the Living
Planet Index [111]; (3) metrics relating to focal species, by
examining the fate of organisms with similar traits to those species,
although important species-specific factors may not be captured
that way; and (4) dynamic ecosystem measures, such as stability
(the magnitude of temporal variation in ecosystem properties) or
resilience (predicted time to recover from a perturbation). A
unique advantage of GEM-like models relative to statistical
modelling approaches is their capacity to model completely novel
perturbation scenarios—that is, perturbations for which there are
no data, experiments, or observations.
The structure of this type of model also allows for a wide set of
anthropogenic perturbations to be considered simultaneously. For
example, such models will be able to simulate how whole
ecosystems respond to, and feed back upon, the effects of changes
in atmospheric carbon dioxide concentrations on plants; altered
climate on all organisms and ecological processes; harvesting of
animals, land-use change, and harvesting of vegetation; invasive
species; and toxic pollutants. The effects of these disparate
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![perturbations could be measured using a common set of metrics.
Considering these impacts together in a GEM should allow for
much more holistic understanding, and management, of the
world’s ecosystems, which will make GEMs a powerful tool for
bodies such as the Intergovernmental Platform on Biodiversity and
Ecosystem Services.
Conclusions
We have developed the first General Ecosystem Model (GEM)
that synthesizes fundamental aspects of ecological theory, to
model, simulate, and predict how the structure and function of
ecosystems at multiple scales emerges from the biology and
interactions of individual organisms. Our model matches a broad
range of empirical data well, to a first approximation. Where it
departs from either observations or expectations, it does so in ways
that afford interesting avenues for future ecological research,
future model development, and empirical data collection. It also
provides a set of novel predictions that can be independently
assessed. We anticipate that this will be the beginning of a long-term
exploration of GEMs, and we call upon ecologists, biologists,
mathematicians, and computer scientists to join in creating a
modelling community surrounding GEMs that can catalyse the
development of more realistic, sophisticated, yet better understood
models of ecosystems worldwide. Our hope is that GEMs will form
the basis of new science in ecology and, in particular, science that
proves actionable to those charged with conserving the biosphere
on which we all depend.
Supporting Information
Figure S1 Cohort dispersal effects on autotrophic and
heterotrophic biomass. The difference between fracturing
cohort and whole cohort dispersal expressed as a percentage of the
whole cohort dispersal value. Percentage differences were
calculated over a 10610 grid of 1u61u marine grid cells extending
from 30u to 40uN and 40u to 30uW, using median and annual
mean biomasses from an ensemble of 10 simulations for both
fracturing cohort and whole cohort dispersal. Negative values
therefore indicate lower biomass in the fracturing cohort ensemble
median, whereas positive values indicate the opposite.
(TIFF)
Figure S2 Cohort number effects on long-term means of
trophic-level biomass. Medians from the mean over the last
5 y of ensembles of 20 replicate simulations (points) and absolute
ranges (error bars) of biomass densities for autotrophs (dark
green lines and dark green squares), herbivores (green lines and
green circles), omnivores (blue lines and blue triangles), and
carnivores (red lines and red diamonds). Ensembles of replicates
were run with a threshold of 500, 1,000, 5,000, or 10,000
cohorts per grid cell for terrestrial cell T1 and marine cell M1
(Table 4).
(TIFF)
Figure S3 Emergent model growth rates compared to
theoretical maximum rates. (A) Absolute emergent model
growth rate (grey crosses and diamonds) relationship with body
mass compared with empirical (black points) and theoretical
maximum (red line). (B) The relationship between emergent model
growth rate as a fraction of theoretical maximum growth rate (grey
open circles) and body mass for each trophic level in terrestrial or
marine cells. Modelled emergent individual-level properties are
sampled from 100-y model runs for the four focal grid cells
(Table 4).
(TIFF)
A Mechanistic General Model of Global Ecosystems
Figure S4 Trophic abundance pyramids. Community-level
abundance pyramids across all cohorts belonging to each
trophic level emergent from the model for an example of terrestrial
and marine grid cell (grid cells T1 and M1 from Table 4). Results
are from the final year of a 100-y model run. Light green
represents herbivores, blue represents omnivores, and red
represents carnivores. Total abundance densities (1,000 s individ-uals/
km2) are indicated by the widths (after log-transformation)
and numbers within the boxes.
(TIF)
Figure S5 Comparison of model predicted with empir-ical
normalised body mass spectra (NBS). Frequency
distribution of the slope of NBS from [75] with model-derived
NBS slope values, calculated following Sprules and Munawar
[114], for carnivores (red), omnivores (blue), and herbivores
(green). Triangles correspond to slopes for the low productivity,
aseasonal marine cell (M1, Table 4) and circles to the high
productivity, aseasonal terrestrial cell (T1, Table 4).
(TIF)
Figure S6 Relationships between predicted biomass
densities and NPP. The global relationship between total
heterotrophic biomass and NPP split between terrestrial and
marine realms (A). The global relationship between the ratio of
herbivore to autotroph biomasses and NPP split between
terrestrial and marine realms (B). The relationships between
different trophic levels and NPP across terrestrial (C) and marine
(D) environments. The relationship between autotroph biomass
and NPP across terrestrial (E) and marine environments (F) with
heterotrophs modelled explicitly ‘‘full’’ and constant proportional
autotroph herbivory loss rates of 0.25, 0.5, and 0.75.
(TIFF)
Figure S7 Frequency distributions of trophic biomass
structure. Frequency distributions of log-transformed ratios of
trophic-level biomasses in terrestrial grid cells (brown) and marine
grid cells (blue), for H:A= herbivore to autotroph, O:H = omni-vore
to herbivore, C:H =carnivore to herbivore, and C:O= car-nivore
to omnivore biomass ratio. Red dashed lines indicate where
the biomass ratio equals 1.0, which means equality of the two
trophic-level biomasses.
(TIFF)
Figure S8 Spatial extent of un-inverted marine trophic
structure for the bottom two trophic levels: herbivores
and autotrophs. Spatial locations (green points) of un-inverted
herbivores to autotroph trophic structure (i.e., where there is less
herbivore than autotroph biomass) in (A) a simulation where
dispersal was permitted (Study 4, Table 3) and (B) when dispersal
is not modelled.
(TIFF)
Figure S9 Frequency distribution of marine trophic
structure in the absence of dispersal. Frequency distribu-tions
of log-transformed ratios of trophic-level biomasses in marine
grid cells with dispersal (upper set of histograms—Study 4, Table 3)
and marine grid cells without any dispersal modelled (lower set of
histograms). H:A, herbivore to autotroph; O:H, omnivore to
herbivore; C:H, carnivore to herbivore; C:O, carnivore to
omnivore biomass ratio. Red dashed lines indicate where the
biomass ratio equals 1.0, which means equality of the two trophic-level
biomasses.
(TIFF)
Figure S10 The effects of turnover rates and trophic
transfer efficiencies on marine trophic structure. Box
PLOS Biology | www.plosbiology.org 21 April 2014 | Volume 12 | Issue 4 | e1001841](https://image.slidesharecdn.com/emergentglobalpatternsofecosystemstructureandfunctionformamechanisticgeneralecosystemmodel-141206110842-conversion-gate01/85/Emergent-global-patterns_of_ecosystem_structure_and_function_form_a_mechanistic_general_ecosystem_model-21-320.jpg)
![and whisker plots of the predicted ratios of trophic levels (H:A,
herbivore to autotroph; O:H, omnivore to herbivore; C:H,
carnivore to herbivore; C:O, carnivore to omnivore biomass
ratio) for ensembles of 10 replicate simulations with different
model assumptions investigating the mechanisms giving rise to
inverted marine trophic biomass structure: N, the full model for a
single grid cell; H, herbivore assimilation efficiency reduced to
20% (from 60–70% omnivore–herbivore); HP, herbivore and
predator assimilation efficiency reduced to 20% (from 60–80%
omnivore–carnivore); A, attack rates of herbivores and predators
decreased by two orders of magnitude; AHP, combined reduction
of attack rates, herbivore assimilation, and predator assimilation as
above. Dark bars indicate median values, boxes the interquartile
ranges, and whiskers the maximal range. Upper panels correspond
to grid cell M1 and lower panels to grid cell M2 (Table 4).
(TIFF)
Figure S11 Community-level properties for cell T1 with
all edible plant matter available for herbivory. Trophic
pyramid and size distribution spectra for focal cell T1 with the
value of parameter wherb,f equal to 1 for terrestrial herbivores,
which means that each terrestrial herbivore cohort experiences
100% of the edible plant matter in the grid cell when it is eating.
The release of this parameter does not affect the low herbivore to
primary producer ratio for terrestrial communities. Here, the ratio
is 1.0%, marginally higher than that calculated for the same
location using a value for wherb,f of 10% (Figure 4).
(TIFF)
Table S1 Environmental data sources. External global
environmental data sources used within the model. Units represent
those used within the Madingley model, not those of the original
source data. a Environmental variables were long-term/multi-decadal
average values.
(DOCX)
Table S2 Model parameters and their values.
(DOCX)
Table S3 Empirical estimates of trophic-level biomass-es
in globally widespread ecosystems in both marine
and terrestrial environments. Notes: 1. Consider only the
pelagic producers. Assume that dissolved organic carbon (DOC)
and suspended particulate organic carbon (POC) are available to
the pelagic community. Do not include benthic suspension feeders.
Assume micro-zooplankton are herbivores (as defined in our
model). For omnivores and carnivores, assume that the proportion
of biomass that is supported originally by pelagic primary
production is equal to the proportional rate of consumption of
pelagically derived foods relative to consumption of foods from all
sources. 2. From Table 12.2 (plants taken as above ground
vascular + Moss + Algae + Lichens) of Chapin et al [115].
3. Herbivore biomass taken from [73]. 4. Producer and herbivore
biomasses from [73]. 5. Producer biomass of 9,999 g C m-2 comes
from Figure 8 of Frangi and Lugo [116]. Montane palm floodplain
forest; herbivore biomass taken from [73].
(DOCX)
A Mechanistic General Model of Global Ecosystems
Table S4 Comparison of emergent individual-level
properties from the model with observations. The slopes
and intercepts of the relationships between predicted properties
and body mass compared to empirical data. The probability that
the slope and intercept of the predicted relationship were different
from those for the empirical data was calculated as the t statistic of
linear models fitted to combined model and empirical data for
each emergent property using a categorical factor to indicate a
model or empirical datum. The probability that the t statistic for
the model including the categorical factor indicates the signifi-cance
of the difference.
(DOCX)
Table S5 Summary statistics of empirical community
herbivore and primary producer biomasses. Summary
statistics, derived from [73], for those ecosystem types most closely
representing the ecosystems within the two grid cells shown in
Figure 3. PB, primary producer biomass; HB, herbivore biomass.
Median herbivore biomass in temperate and tropical grassland
ecosystems is 52.3% of that in communities of marine phyto-plankton,
whereas median primary producer biomass is 57 times
larger in the terrestrial compared to the marine ecosystem.
(DOCX)
Table S6 Comparison of abundance–density slopes
predicted by the model with observed slopes. Abun-dance–
density relationships predicted by the model (for cells T1
and M1, Table 4) compared with observations. Empirical
abundance–density relationships were derived from Jennings et
al. [74]. The reported total biomass versus body mass relationships
were converted to abundance versus body mass relationships, by
dividing the total biomass in each mass bin by the central mass of
that mass bin, which can be approximated as subtracting 1 from
the slope of total biomass against body mass.
(DOCX)
Text S1 Technical and mathematical details of the
model.
(DOCX)
Text S2 Model time step effects.
(DOCX)
Acknowledgments
We thank L. Joppa for engaging in discussion and ideas that helped us to
conceptualize the model and A. Blandon, K. Boughey, and E. Pynegar for
compiling empirical data with which to compare the model.
Author Contributions
The author(s) have made the following declarations about their
contributions: Conceived and designed the experiments: MH TN DT SE
JH VL MJS JPWS DWP. Performed the experiments: MH TN DT.
Analyzed the data: MH TN DT MS DP. Contributed reagents/materials/
analysis tools: MH TN DT MS VL DP. Wrote the paper: MH TN DT SE
JH MJS JPWS DWP. Contributed equally to this manuscript: MH TN
DT.
References
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Emergent global patterns_of_ecosystem_structure_and_function_form_a_mechanistic_general_ecosystem_model
- 1. Emergent Global Patterns of Ecosystem Structure and Function from a Mechanistic General Ecosystem Model Michael B. J. Harfoot1,2.*, Tim Newbold1,2., Derek P. Tittensor1,2,3., Stephen Emmott2, Jon Hutton1, Vassily Lyutsarev2, Matthew J. Smith2, Jo¨ rn P. W. Scharlemann1,4, Drew W. Purves2 1 United Nations Environment Programme World Conservation Monitoring Centre, Cambridge, United Kingdom, 2 Computational Science Laboratory, Microsoft Research, Cambridge, United Kingdom, 3 Dalhousie University, Halifax, Nova Scotia, Canada, 4 School of Life Sciences, University of Sussex, Falmer, Brighton, United Kingdom Abstract Anthropogenic activities are causing widespread degradation of ecosystems worldwide, threatening the ecosystem services upon which all human life depends. Improved understanding of this degradation is urgently needed to improve avoidance and mitigation measures. One tool to assist these efforts is predictive models of ecosystem structure and function that are mechanistic: based on fundamental ecological principles. Here we present the first mechanistic General Ecosystem Model (GEM) of ecosystem structure and function that is both global and applies in all terrestrial and marine environments. Functional forms and parameter values were derived from the theoretical and empirical literature where possible. Simulations of the fate of all organisms with body masses between 10 mg and 150,000 kg (a range of 14 orders of magnitude) across the globe led to emergent properties at individual (e.g., growth rate), community (e.g., biomass turnover rates), ecosystem (e.g., trophic pyramids), and macroecological scales (e.g., global patterns of trophic structure) that are in general agreement with current data and theory. These properties emerged from our encoding of the biology of, and interactions among, individual organisms without any direct constraints on the properties themselves. Our results indicate that ecologists have gathered sufficient information to begin to build realistic, global, and mechanistic models of ecosystems, capable of predicting a diverse range of ecosystem properties and their response to human pressures. Citation: Harfoot MBJ, Newbold T, Tittensor DP, Emmott S, Hutton J, et al. (2014) Emergent Global Patterns of Ecosystem Structure and Function from a Mechanistic General Ecosystem Model. PLoS Biol 12(4): e1001841. doi:10.1371/journal.pbio.1001841 Academic Editor: Michel Loreau, Centre National de la Recherche Scientifique, France Received December 19, 2013; Accepted March 10, 2014; Published April 22, 2014 Copyright: 2014 Harfoot et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Funding: This research was funded by United Nations Environment Programme World Conservation Monitoring Centre and the Computational Science Laboratory, Microsoft Research. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The authors have declared that no competing interests exist. Abbreviations: DGVMs, dynamic global vegetation models; DOC, dissolved organic carbon; ESMs, Earth System Models; EwE, Ecopath With Ecosim; GEM, General Ecosystem Model; NBS, normalised body mass spectra; NPP, net primary productivity; POC, particulate organic carbon * E-mail: mike.harfoot@unep-wcmc.org . These authors contributed equally to this work. Introduction The pace and scale of anthropogenic environmental change has caused the widespread degradation of ecosystems and the services they provide that ultimately support human life on Earth [1]. Understanding and mitigating these impacts necessitates the development of a suite of tools, including policy instruments, practical conservation measures, and empirical research. At present, a variety of models are used to assist decision-making in relation to biodiversity and ecosystem services. Most are correl-ative, relying on statistical relationships derived from limited observational data without explicit reference to the underlying mechanisms; examples include the GLOBIO model, species distribution models, and models of local extinction based on species–area relationships [2–4]. All of these models are useful, for different purposes. However, what is urgently needed is mecha-nistic models, which explicitly represent the biological, physiolog-ical, and ecological mechanisms underlying the systems in question [5]. One of the key benefits of mechanistic models is that they are likely to make more accurate predictions under novel conditions [6]. For example, Earth System Models (ESMs), containing mechanistic descriptions of multiple interacting components of the climate, atmosphere, and ocean, are used to project properties and dynamics under future climate conditions that have not been observed previously (at least in relation to historical data) [7]. Similarly, mechanistic models of ecosystems would allow us to predict a given combination of human pressures on a given ecosystem, even when there is no or little historical data on which to rely. Mechanistic models can also improve our understanding of the systems being modelled, allowing predictions to be understood in relation to the underlying mechanisms that generate them [8]. This in turn might lead to novel ways to mitigate or even reverse the degradation of ecosystems. We present the first process-based, mechanistic General Ecosystem Model (GEM) (called the Madingley Model). It is general in the sense that it strives to use a unified set of fundamental ecological concepts and processes for any ecosystem to which it is applied, either terrestrial or marine, and it can be simulated at any spatial resolution from local up to global scales. Applying a general modelling approach globally has three main advantages: (1) it allows testing of whether the same set of ecological mechanisms and concepts can adequately capture broad-scale ecosystem behaviour in both the marine and terrestrial realms; (2) it enables the development of a suite of predictive PLOS Biology | www.plosbiology.org 1 April 2014 | Volume 12 | Issue 4 | e1001841
- 2. outputs common to both realms, from which standardised metrics of ecosystem health can be calculated; and (3) it enables links between marine and terrestrial ecosystems, both natural and human-driven, to be modelled. The model is also spatially explicit, with dynamics in a given location driven by the climate and other local factors, as well as by connections with other ecosystems through dispersal, and is mechanistic, with dynamics being driven by ecological processes defined at the level of individual organisms. Specifically, we model autotroph (plant) stocks, and individual herbivorous, omnivorous, and carnivorous animals of all body sizes, and their interactions. From these interactions, patterns emerge at larger spatial and temporal scales, including commu-nities, ecosystems, and global macroecological gradients, without any direct model constraints imposed on those properties. Such a GEM has great potential if it can, at a minimum, reproduce the observed properties of ecosystem structure and function, and enable the formation of valuable, novel hypotheses, and precise, testable predictions. Here, we test the model’s ability to simulate ecosystems that persist over long time scales (1,000 y) by comparing model predictions with empirical data and test two theoretical predictions that to date have not been assessed empirically and have only been studied with simple trophic models: that the net primary productivity (NPP) of ecosystems determines the length of trophic chains [9,10] and that herbivore pressure on autotrophs will reduce once a critical level of carnivore biomass is supported (‘‘trophic release hypothesis’’ [11]). Finally, we provide a suite of other novel predictions that demonstrate the potential utility of the model as an operational tool with which the effects of human impacts on ecosystems can be explored. Mechanistic models of specific ecosystems have been developed previously, and to date these have been constrained to particular spatial locations or to particular sets of organisms within ecosystems. For example, dynamic global vegetation models (DGVMs) are used to represent the physiological and ecological processes driving plant community dynamics on the global land surface, enabling investigations into how terrestrial vegetation interacts with climate [12]. However, these do not include animals or other heterotrophs, and so are limited in the extent to which they can be used to understand the roles of heterotrophs in ecosystems, or to address questions about the conservation of organisms other than plants. For the marine realm, ‘‘end-to-end’’ ecosystem models have been developed, which include most trophic levels for particular regions [13]. Examples are the Ecopath With Ecosim (EwE) [14] and Atlantis [15] models. But marine models tend to focus either on biogeochemical cycles or on organisms of economic importance, such as fish, rather than on the properties of the ecosystem as a whole. They also generally either use a stock-and-flow formulation [14,15], making them unable to follow trajectories of individual organisms, or are restricted to simulating particular guilds of organisms [16]. There have also been previous theoretical examinations of the potential effect of select processes on select ecosystem metrics, such as the role of bioenergetics in determining size distributions [17]. Such theoretical studies have been very useful in providing insight into the potential mechanisms underlying ecosystem structure; but they have tended to be carried out for single, abstract locations that are not tied to any real geographical location and to omit most of the key processes affecting ecosystem structure and function in reality. We are not aware of any previous attempt to model emergent ecosystem structure and function by identifying a minimal, but putatively complete, set of key processes and then simulating these processes for all organisms globally, over the actual climate and geography of all marine and terrestrial environments. It is for these reasons that we refer to the model presented here as a GEM. Methods Model Scope We identified a set of core biological and ecological processes necessary to predict ecosystem-level properties: primary produc-tion for autotrophs, and eating, metabolism, growth, reproduction, dispersal, and mortality for heterotrophs (Figure 1 and Box 1). We modelled both marine and terrestrial environments but excluded freshwater ecosystems. We included all photoautotrophs, and all heterotrophs that feed on living organisms (i.e., we did not include chemoautotrophs and detritivores). We generally represented only macroscopic organisms (.161023 g), except that we included plankton in the marine realm because of their known importance to the marine food web [18]. All plant biomass in the terrestrial realm was modelled, but only leaves, flowers, fruits, and seeds were available as a food source for herbivores and omnivores. The marine component included phytoplanktonic autotrophs, which provide more than 90% of primary productivity in the oceans [18]. Seagrasses, mangroves, macroalgae, and corals, which are important autotrophs in coastal systems, are not yet included. In this proof-of-concept model, we consider a world without any human impacts, except that we used modern-day climatic conditions. The model and user guide can be downloaded from www.madingleymodel.org, and simulation outputs for main manuscript figures can be downloaded from the Dryad Digital Repository: doi:10.5061/dryad.5m96v [19]. Traits, Cohorts, and Stocks Traditional approaches to mechanistic modelling in community ecology focus on densities or abundances of individuals belonging to different species [16,20]. These are well suited to modelling a small set of focal species, but are unfeasible for modelling whole ecosystems at a global scale, because the vast majority of the world’s species remain to be described, or are at best represented by few data describing their distribution and ecology [21–23]. Author Summary Ecosystems across the world are being rapidly degraded. This threatens their provision of natural goods and services, upon which all life depends. To be able to reduce—and one day reverse—this damage, we need to be able to predict the effects of human actions on ecosystems. Here, we present the first example of a General Ecosystem Model (GEM)—called the Madingley Model—a novel class of computational model that can be applied to any ecosystem, marine or terrestrial, and can be simulated at any spatial scale from local up to global. It covers almost all organisms in ecosystems, from the smallest to the largest, encoding the underlying biology and behaviour of individual organisms to capture the interactions between them and with the environment, to model the fate of each individual organism, and to make predictions about ecosystem structure and function. Predictions made by the Madingley Model broadly resemble what we observe in real-world ecosystems across scales from individuals through to communities, ecosys-tems, and the world as a whole. Our results show that ecologists can now begin modelling all nonhuman life on earth, and we suggest that this type of approach may hold promise for predicting the ecological implications of different future trajectories of human activity on our shared planet. A Mechanistic General Model of Global Ecosystems PLOS Biology | www.plosbiology.org 2 April 2014 | Volume 12 | Issue 4 | e1001841
- 3. A Mechanistic General Model of Global Ecosystems Figure 1. Schematic of the model. Ecosystem structure and function (B) emerges from a combination of processes operating on individual organisms within a grid cell (A), and exchange of individuals among grid cells via dispersal (C). Life histories (e.g., average lifespan, lifetime reproductive success, and generation length) are also emergent (not shown in this diagram, but see Figure 3). Fundamental ecological processes affect the ecological properties (principally body mass and abundance; represented as the diameter and number of black dots in A, respectively) of organisms. For computational efficiency, organisms with similar properties are grouped into cohorts (coloured circles in all panels). Graphs in (A) show illustrative examples of functional forms used to model each ecological process; full mathematical details can be found in the main text and in Text S1. Panel (C) illustrates how dispersal links different grid cells through the exchange of cohorts via dispersal. As result of the within-grid-cell processes, and dispersal, the state of the ecosystem—that is, the collection of cohorts within each grid cell—changes dynamically through time. Panel (B) shows two example measures of ecosystem structure that can be calculated at any time: the relative biomasses in different trophic levels, and the body-mass abundance distribution of heterotrophs. All such community-level properties and metrics emerge from bottom-up processes in the model without any model-imposed constraints beyond those processes operating on individual organisms. doi:10.1371/journal.pbio.1001841.g001 Instead, we adopted a trait-based approach [24] where individuals are characterized by their functional traits: categorical traits, such as feeding mode, which determine the mechanisms by which organisms exist and which were used to define functional groups; and continuous traits, such as body mass, which modulate those mechanisms but do not determine functional grouping. Taxonomic identity of individuals is ignored for three reasons. First, there is insufficient species-level information to model whole ecosystems worldwide. Second, it is more feasible to model the role of individuals in ecosystems in terms of their traits than in terms of their taxonomic identity, because of limited taxonomic knowledge and data [21–23]. Third, in comparison to taxonomic identity, organisms’ functional traits are more directly relevant to most ecosystem functions and ecosystem services [25,26]. A separate issue is whether to define the model in terms of population densities and biomasses within functional groups (i.e., ‘‘stocks’’ or ‘‘pools’’), or as collections of interacting individuals each characterized by their combination of functional traits (individual-based). For all organisms except autotrophs, we used an individual-based approach, because this allowed the model to be more finely resolved, and because it enabled us to capture variation in body mass—one of the most important traits for determining the rates of ecological processes [27–29] over the lifetime of an individual. It also enabled us to follow the fates of individual organisms. Higher level ecosystem properties emerge from these individual-based rules. Capturing this emergence was a central aim of this initial work. Autotrophs were represented as stocks—that is, the total biomasses of such organisms—because either the definition of an individual was problematic (terrestrial plants) or rates of turnover were faster than the modelled time step (marine phytoplankton). For heterotrophs, simulating every individual separately would have been computationally intractable given the vast number of individuals in global ecosystems. Therefore, we adopted a computational approach based on cohorts. A cohort consisted of a group of organisms occurring within the same grid cell, with PLOS Biology | www.plosbiology.org 3 April 2014 | Volume 12 | Issue 4 | e1001841
- 4. Box 1. Running simulations within our GEM. Each simulation is initialised with environmental informa-tion from multiple datasets (as described in the Methods section and in Table S1) and spatially distributed stocks and cohorts (see Methods) according to user specifications (functional groups and grid locations). During a simulation, the stocks and cohorts then interact through time and space. For each time step and each grid cell, the first computation is to increment the biomass of autotrophs according to the relevant growth function (Table 5). Next, the ecology of the heterotroph cohorts is modelled (see functions in Table 6). The order in which heterotroph cohorts act is randomised at each time step. Each heterotroph cohort performs multiple ecological processes per time step (Figure 1A): Individuals in the cohort (i) metabolise biomass to sustain their activities; (ii) eat biomass from either autotrophs if herbivorous or other heterotrophs if carnivorous, or from both if omnivorous; (iii) use net biomass gain to grow, if juvenile, or store biomass for future reproduction if they have reached sufficient body mass to be reproductively mature; (iv) give birth to a separate, offspring cohort if sufficient reproduc-tive biomass has been accumulated; (v) suffer mortality as a result of being eaten by other cohorts feeding on them, or as a result of background mortality processes, starva-tion, or senescence; and (vi) disperse from their current grid cell to another grid cell. As a result of these interactions across space and time, communities of cohorts possessing different functional traits, individual biomasses, and abundances self-assemble (Figure 1B and 1C). identical traits—that is, in the same functional group and with identical continuous traits—but not necessarily belonging to the same taxon. This cohort-based approach allowed us to define the model in exactly the way that one would do in a fully individual-based model (i.e., processes defined at an individual level), but also allowed us to keep the number of computations low enough to be feasible. Functional Groups All stocks and cohorts belong to a functional group, defined according to the categorical traits of the individuals in that stock or cohort (Tables 1 and 2). Individuals in the same functional group interact with one another and with their environment in a qualitatively similar manner. Therefore, cohorts within the same functional group are modelled using the same mathematical representations of the ecological processes, though the rates predicted by those functions differ according to continuous traits that differ between cohorts, A Mechanistic General Model of Global Ecosystems such as body mass. Individuals belonging to different functional groups have at least one qualitatively different interaction with other individuals or with their environment. We use the same functional forms for analogous functional groups in the ocean and on land, but with different parameter values, where justified by previous research. Body mass affects many individual properties and interactions, including feeding preferences and rates, metabolic rates, and dispersal [27–29]. Therefore, body mass was included as a parameter in nearly all ecological processes of heterotrophs (Figure 1). The Environment The environment is defined as a two-dimensional layer representing the land surface and the upper mixed layer (top 100 m) of the oceans. This layer is divided into grid cells within which individuals and stocks are assumed to be well mixed. The ecological processes can be affected by the size of the grid cell, the physical environment at that cell, and dispersal of organisms among adjacent grid cells. The model can be employed for any number of grid cells, at any resolution, locally or globally, subject to computational limitations. For the results presented here, we used either simulations for individual 1u61u grid cells, or a 2u62u grid covering the whole globe (see below, and Tables 3 and 4) except for high latitudes (.65u) because remotely sensed, exogenous environmental data currently used are not available for the polar regions. Each grid cell in the model is assigned to either the terrestrial or marine realm based on a land/ocean mask [30]. Environmental conditions for each grid cell are read as model inputs from publicly available datasets: for the terrestrial realm air temperature [31], precipitation [31], soil water availability [32], number of frost days [31], and seasonality of primary productivity [33]; and for the marine realm sea-surface temperature [34], NPP [35], and ocean current velocity (Table S1) [34]. The model is flexible with respect to the specific environ-mental data used, and future simulated environmental conditions can be used. The Ecology We provide a summary of how simulations are run in Figure 1 and Box 1, and an overview of how the ecological processes are modelled, with the main mathematical functions, is summarised in Tables 5 and 6. Full details are provided in Text S1. Autotroph Ecology. In the marine realm, one stock of phytoplankton per grid cell is modelled, characterised by a total wet matter biomass at time t, Bp,(t). For terrestrial autotrophs, we track two stocks of leaves, l, one deciduous and one evergreen, each characterized by a total biomass at time t, Bl,(t). The biomass of an autotroph stock s, which could be either phytoplankton (p) or leaves (l), is incremented in each time step (of length Dt) as follows: Table 1. Stock functional group definitions. Realm Nutrition Source Mobility Leaf Strategy Marine Photosynthesis Planktonic N/A Terrestrial Photosynthesis Sessile Deciduous Terrestrial Photosynthesis Sessile Evergreen Categorical trait values (column names) with the specific trait values for each stock functional group modelled. N/A values reflect traits that are not applicable to a functional group. doi:10.1371/journal.pbio.1001841.t001 PLOS Biology | www.plosbiology.org 4 April 2014 | Volume 12 | Issue 4 | e1001841
- 5. Table 2. Cohort functional group definitions. Realm Feeding Mode Mobility Reproductive Strategy Thermoregulation Mode Log10 Minimum Mass for Functional Group (kg) Log10 Maximum Mass for Functional Group (kg) Herbivory Proportional Assimilation Efficiency Carnivory Proportional Assimilation Efficiency Marine Herbivore (plankton) Planktonic Iteroparity Ectotherm 28.00 24.00 0.7 0 Marine Herbivore (plankton) Planktonic Semelparity Ectotherm 28.00 24.00 0.7 0 Marine Herbivore (plankton) Mobile Iteroparity Ectotherm 27.00 1.00 0.7 0 Marine Herbivore (plankton) Mobile Semelparity Ectotherm 27.00 1.00 0.7 0 Marine Omnivore Mobile Iteroparity Endotherm 1.00 5.18 0 0.8 Marine Omnivore Mobile Iteroparity Ectotherm 28.00 2.00 0.6 0.64 Marine Omnivore Mobile Semelparity Ectotherm 28.00 2.00 0.6 0.64 Marine Carnivore Mobile Iteroparity Endotherm 21.00 4.70 0 0.8 Marine Carnivore Mobile Iteroparity Ectotherm 27.00 3.30 0 0.8 Marine Carnivore Mobile Semelparity Ectotherm 27.00 3.30 0 0.8 Terrestrial Herbivore Mobile Iteroparity Endotherm 22.82 3.70 0.5 0 Terrestrial Herbivore Mobile Semelparity Ectotherm 26.40 0.00 0.5 0 Terrestrial Herbivore Mobile Iteroparity Ectotherm 23.00 2.48 0.5 0 Terrestrial Omnivore Mobile Iteroparity Endotherm 22.52 3.18 0.4 0.64 Terrestrial Omnivore Mobile Semelparity Ectotherm 26.40 0.30 0.4 0.64 Terrestrial Omnivore Mobile Iteroparity Ectotherm 22.82 1.74 0.4 0.64 Terrestrial Carnivore Mobile Iteroparity Endotherm 22.52 2.85 0 0.8 Terrestrial Carnivore Mobile Semelparity Ectotherm 26.10 0.30 0 0.8 Terrestrial Carnivore Mobile Iteroparity Ectotherm 22.82 3.30 0 0.8 Categorical trait values (column names) and specific trait values for each cohort functional groups modelled. Organisms with body mass less than 1025 kg are only found in the marine realm and are dispersed planktonically, whereas all organisms with body mass greater than 1025 kg moved through mobile dispersal. doi:10.1371/journal.pbio.1001841.t002 A Mechanistic General Model of Global Ecosystems PLOS Biology | www.plosbiology.org 5 April 2014 | Volume 12 | Issue 4 | e1001841
- 6. Bs,(tzDt)~Bs,(t)zDBGrowth s {DBMort s , ð1Þ where DBGrowth s and DBMort s are the gain and loss of biomass from stock s over the time interval Dt, respectively. DBMort s includes losses due to herbivory. We use different approaches to model the gain and loss of biomass from marine and terrestrial autotroph stocks (Table 5). In the marine realm, we model growth of the phytoplankton stock by incrementing the total biomass of phytoplankton in each cell using satellite-derived estimates of NPP (Table 5). This avoids us having to adopt computationally impractical time-steps (days) in order to accurately simulate the dynamics of phytoplankton, which have rapid turnover rates (in our opinion, an explicit nutrient– phytoplankton–zooplankton model would be a major improve-ment to the marine part of the model; see Table 7). Loss of phytoplankton arises directly from modelling grazing by marine organisms (Table 5; Equations 3 and 4 in Text S1). Terrestrial autotrophs are modelled using the climate-driven terrestrial carbon model of Smith et al. [36]. We selected this model because it has been parameterized and tested against empirical data on carbon stocks and flows more rigorously than similar models of which we are aware (Equations 5–19 in Text S1) [36]. Moreover, it has a similar level of complexity to that used to represent heterotrophic organisms. However, like the other model components we adopted, the vegetation model could be replaced by alternatives in future studies, including more complex models able to address particular issues like CO2 fertilization (e.g., [12,37]). Terrestrial plant growth is modelled as a function of NPP, the proportion of NPP that is produced by evergreen or deciduous leaves, and the fraction of NPP allocated to structural tissues (Table 5), all of which depend on the local climate. The loss of plant biomass is determined by leaf mortality rate, which is also function of the climate, as well as the consumption of biomass by herbivorous terrestrial organisms (Table 5). Heterotroph Ecology. Heterotrophs are modelled as co-horts. Each cohort i is characterized by a functional group (Table 2), by two traits that do not change through time—body mass at birth, MJuvenile i , and body mass at reproductive maturity MAdult i (for cohort, i)—and by three state variables whose values do change through time—the abundance of individuals Ni,(t), the wet matter body mass of each individual within the cohort Mi,(t), and a stored reproductive mass of each individual, Ri,(t) (Figure 1). The values of these state variables are updated each time step according to the effects of ecological processes (Table 6). Individuals in each cohort are assumed to interact only with stocks and cohorts in the same grid cell. The growth of individual body mass is modelled as follows: i {DMMetab i {DMReproAlloc Mi,(tzDt)~Mi,(t)zDMAss i , ð2Þ Table 3. Settings used for the six model studies conducted in this research article. Study Description Spatial Extent Length (y) Ensemble Number Output Detail 1 Grid-cell numerical analyses Four 1u61u focal grid cells (Table 4) 1,000 10 Biomass and abundance densities by functional groups 2 Grid-cell individual- and community-level predictions Four 1u61u focal grid cells (Table 4) 100 1 Detailed individual-level process diagnostics 3 Grid-cell community-level predictions at empirically observed locations Fourteen 1u61u grid cells at locations where ecosystem structure has been empirically estimated (Table S3) 100 10 Biomass and abundance densities by functional group 4 Global predictions Global grid of 2u62u cells extending from 65uN to 65uS in latitude and from 180uE to 180uW in longitude 100 1 Biomass and abundance densities by functional group 5 Effects of dispersal on marine trophic structure Global grid of 2u62u cells in the marine realm only extending from 65uN to 65uS in latitude and from 180uE to 180uW in longitude 100 1 Biomass and abundance densities by functional group 6 Effects of biomass turnover rates on marine trophic structure Grid cell M1 (Table 4) 100 10 Biomass and abundance densities by functional group for simulations with differing biomass turnover rates. doi:10.1371/journal.pbio.1001841.t003 Table 4. Descriptions and coordinates of the focal grid cells for which detailed numerical-, individual-, and community-level model simulations were made. Cell Number Cell Description Latitude Longitude Location T1 Terrestrial:tropical, aseasonal 0uN 32.5uE Southern Uganda T2 Terrestrial:temperate, seasonal 52.5uN 0.5uE Central England M1 Marine: low productivity, aseasonal 225.5uS 2119.5uW South Pacific Ocean M2 Marine: high productivity, seasonal 42.5uN 245.5uW North Atlantic Ocean doi:10.1371/journal.pbio.1001841.t004 A Mechanistic General Model of Global Ecosystems PLOS Biology | www.plosbiology.org 6 April 2014 | Volume 12 | Issue 4 | e1001841
- 7. Table 5. Summary of how autotroph ecological processes are modelled (for full details, see Text S1 and Table S2). Process Realm Main Mathematical Functions Eqn(s). Assumptions where DMAss ( ) ( ) i is the total biomass assimilated as food, which is the sum of the biomasses assimilated through herbivory and preda-tion, DMAss,Herb i and DMAss,Pred i , respectively; DMMetab i is mass lost through metabolism; and DMReproAlloc i is mass lost by allocation to reproduction (Table 6, see also Figure 1). Predation and herbivory are modelled using a Holling’s Type III functional response, which assumes that the number (or biomass) of prey (or plant material) eaten by an individual predator (or herbivore) is a sigmoidal function of prey density (or biomass density) (Table 6) [38]. The Holling’s functions require definition of the attack rate and handling time for each predator (or herbivore) cohort on each prey cohort (or plant stock). Attack rates of herbivores on plants scaled according to the body mass of herbivore. Attack rates of predators on animals were derived from the size-structured model of Williams et al. [39], where the probability of predation is a Gaussian function around an optimal prey body size (as a proportion of predator size) (see Equations 35 and 36 in Text S1) estimated from large empirical datasets on feeding relationships [40]. This size-structured model is an extension of the long-standing niche model [41] but could be replaced with other predator–prey interaction models in future studies if desired. For carnivores and omnivores, the handling time of each predator on each prey increases linearly with prey body mass (larger prey take longer to eat) but decreases as defined by a power-law relationship with predator body mass (larger predators handle prey more quickly) (Equation 40 in Text S1). For herbivores, handling time depends on herbivore body mass only (a decreasing power-law relationship) (Equation 32 in Text S1). Metabolic costs are modelled as a power-law relationship with body mass, following Brown [29], using parameter values derived from field metabolic rates (Table 6) [42]. We assume that each cohort is active for some proportion of each time step according to ambient temperature (Equations 41–47 in Text S1). Endotherms are assumed to thermoregulate, and thus are active for 100% of each time step. Marine ectotherms are active for 100% of each time step. Terrestrial ectotherms do not thermoregulate, and thus are only active for the proportion of each time step during which ambient temperature was within their upper and lower activity temperature limits, estimated following Deutsch et al. [43]. Once an individual reaches its adult mass, we assume that all further mass gained is stored as reproductive potential. An individual’s reproductive potential mass is incremented as follows: Ri,(tzDt)~Ri,(t)zDMReproAlloc i {DRReproEvent i , ð3Þ where DRReproEvent i is the potential reproductive biomass lost by each individual of cohort i through reproductive events (Figure 1). Reproductive events occur when an individuals’ stored reproduc-tive potential reaches a threshold proportion of adult mass (Table 6). During reproductive events, iteroparous organisms devote all of their stored reproductive potential mass to producing offspring; semelparous organisms devote all of their stored reproductive potential mass, and also a proportion (Equations 50–52 in Text S1, Table S2) of their adult mass. The number of individuals in each cohort is incremented as follows: Ni,(tzDt)~Ni,(t){DNMort i { X k (DNPred k,i ), ð4Þ Growth Marine The growth of phytoplankton, p, biomass in marine cell, M, during month, m, is given by: DBGrowth p ~NPPMm :j:Acell :dtNPP, where NPPMm is a remotely sensed estimate of monthly marine NPP; j converts from carbon to wet matter biomass; Acell is the grid cell area; dtNPP converts from monthly values to the model time step. 3 in Text S1 The modelled standing biomass of phytoplankton is capable of generating the remotely sensed productivity in any given time step Growth Terr. The growth of biomass in autotroph stock, l, in terrestrial cell, T, during month, m, is given by: DBGrowth l ~ NPPT m:Acell :y:dtNPP:(1{fstruct):fLeafMort:fever , ½if l is evergreen NPPT m:Acell :y:dtNPP:(1{fstruct):fLeafMort:(1{fever) , ½if l is deciduous where NPPT m is a remotely sensed estimate of monthly terrestrial NPP; Acell is the grid cell area; y converts from carbon to wet matter biomass; dtNPP converts from monthly values to the model time step; fstruct is the fractional allocation of primary production to structural tissue; fever is the proportion of NPP produced by evergreen leaves at a particular location; and fLeafMort is the proportion of total mortality that is leaf mortality. 5, 7–19 in Text S1 Annual mean environmentally determined NPP is allocated to months in the same relative proportions as that observed in remotely sensed NPP data. Mortality Marine The loss of phytoplankton biomass is given by: DBMort p ~Lp,Herbivory, where Lp,Herbivory is the cumulative phytoplankton biomass consumed through herbivory. 4 in Text S1 Background mortality of phytoplankton is negligible compared to losses from herbivory Mortality Terr. The loss of biomass from autotroph stock, l, is given by: DBMort l ~ dtm,l :mever:Bl,(t) :feverzLl,Herbivory ,½if l is evergreen dtm,l :mdecid :Bl,(t) :(1{fever)zLl,Herbivory ,½if l is deciduous where Bl,(t) is the biomass of stock l at time t; mever and mdecid are annual leaf mortality rates for evergreen and deciduous stocks, respectively; dtm,l converts annual leaf mortality rates to the model time step; Ll,Herbivory is the cumulative biomass of stock, l, consumed through herbivory; and fever is the proportion of NPP produced by evergreen leaves at a particular location. 6, 10–15 in Text S1 Herbivory rates do not affect plant allocation strategies and plants do not have the capacity for defensive strategies doi:10.1371/journal.pbio.1001841.t005 A Mechanistic General Model of Global Ecosystems PLOS Biology | www.plosbiology.org 7 April 2014 | Volume 12 | Issue 4 | e1001841
- 8. Table 6. Summary of how heterotroph ecological processes are modelled. A Mechanistic General Model of Global Ecosystems Process Main Mathematical Functions Eqn(s). Assumptions Herbiv. The total biomass assimilated as food by cohort i through herbivory on all stocks is calculated as follows: DMAss,Herb i ~eherb f : PNS k Bk,(t ) : 1{e{Fi,k :Dtd :tf :zf ,(t) , where eherb f is the fractional herbivore assimilation efficiency for the functional group, f, to which cohort i belongs; Bk,(t ) is the biomass of stock k at time t* when herbivore cohort i acts; Dtd is the length of the model time step in days; tf is the proportion of the time step for which functional group f is typically active; zf t ð Þ is the proportion of the time step that is suitable for a cohort of functional group f to be active; and Fi,k the instantaneous rate at which stock k is eaten by an individual from herbivore cohort i is determined by: Fi,k~ 2 ai,k: wherb,f :Bk,(t ) Acell 1z PNS l 2 ai,l : wherb,f :Bl,(t ) Acell :Hi,l , where ai,k is the effective rate at which an individual herbivore searches its environment in hectares per day, and which is assumed to scale linearly with herbivore body mass; wherb,f is the proportion of the current biomass of stock k that is experienced by cohort i; Bk,(t ) is the biomass of stock k at time t* herbivore cohort i acts; Acell is the area of the cell; Hi,l is the time taken for an individual in cohort i to handle a unit mass of autotroph stock l. S23, S24, S26, S30–S32 Autotroph biomass and herbivore cohorts are well mixed throughout each cell. Each herbivore cohort encounters a separate fraction, wherb,f , of the total autotroph biomass available. Predation The total biomass assimilated as food by cohort i through predation on all cohorts is calculated as follows: DMAss,Pred i ~epred f : PNC j Mj,(t ) :Nj,(t ) : 1{e{Fi,j :Dtd :tf :zf ,(t) , where epred f is the fractional herbivore assimilation efficiency for the functional group, f, to which cohort i belongs; Mj,(t ) is the body mass of an individual of cohort j at time t* when predator cohort i acts; Nj,(t ) is the abundance of individuals in cohort j at time t*; and Fi,j , the instantaneous rate at which a prey cohort j is eaten by an individual predator from cohort i, is determined by: Fi,j~ ai,j : Nj,(t ) Acell :Hi,j 1z XNS m ai,m: Nm,(t ) Acell :Hi,m:Hi,m , where ai,j is the effective rate at which an individual predator searches its environment and successfully kills prey; Nj,(t ) is the abundance of cohort i at time t* when predator cohort i acts; Hi,j is the cumulative density of organisms with a body mass lying within the same predator-specific mass bin as cohort j; Hi,m is the time taken for an individual in cohort i to handle one individual prey individual in cohort m, per unit time spent searching for food. S23, S25, S28, S34–S39 Predator and prey cohorts are well mixed throughout each cell. Predator cohorts can experience all other cohorts sharing the same cell. While searching for one prey, predators can be simultaneously encountering another prey—that is, they are not limited by search time. Omniv. The total biomass assimilated as food by an omnivore cohort is the sum of the assimilation terms for herbivory and predation as described above but with Fi,k, the instantaneous rate at which stock k is eaten by an individual from an omnivorous cohort i determined by: Fi,k~ ai,k: 2 wherb,f :Bk,(t ) Acell 1z PNS 2 l ai,l : wherb,f :Bl,(t ) Acell :Hi,lz PNS m ai,m: Nm,(t ) Acell :Hi,m:Hi,m , and Fi,j , the instantaneous rate at which a prey cohort j is eaten by an individual omnivore from cohort i, given by: Fi,j~ ai,j : Nj,(t ) Acell :Hi,j 1z PNS l ai,l : 2 wherb,f :Bl,(t ) Acell :Hi,lz PNS m ai,m: Nm,(t ) Acell :Hi,m:Hi,m : Where variables and parameters are as described for herbivory and predation above. S23–S25, S27, S29, S30–S32, S34–S39 As described above for herbivory and predation. Omnivores spend a fixed fraction of each time step engaged in each of herbivory and predation. Metab. The metabolic loss of biomass from each individual of cohort i, each with body mass Mi,(t), was modelled as follows: DMmetab i ~ES: zf ,(t) :IFMR 0,f :exp { EA=kB:TK,body bmetab,FMR : Mi,(t) f ! z 1{zf ,(t) { EA=kB:TK,body :IBMR 0,f :exp bmetab,BMR : Mi,(t) f ! 2 666664 3 777775 :Dtd , where Mi,(t) is the body mass of an individual in cohort i; ES converts from energy to biomass; zf ,(t) ; IFMR 0,f and IBMR 0,f are mass- and temperature-independent metabolic rate constants for field and basal metabolic rates, respectively; EA is aggregate activation energy of metabolic reactions; kB is the Boltzmann constant; TK,body is the body temperature of the individual; bmetab,FMR f and bmetab,BMR f are body mass exponents for field and basal metabolic rates, respectively. S48 Body temperature, TK,body, is assumed to be 310 K for endothermic organisms and equal to ambient temperature for ectothermic functional groups. PLOS Biology | www.plosbiology.org 8 April 2014 | Volume 12 | Issue 4 | e1001841
- 9. where DNMort , i is the number of individuals of cohort i lost to nonpredation mortality, and P k (DNPred k,i ) is the total number of individuals of cohort i lost through predation, summed over all predator cohorts k as outlined above (Figure 1). We model three sources of nonpredation mortality: a constant proportional rate of background mortality, which applies to all individuals; starvation mortality, which is applied according to how much body mass has been lost compared to the maximum body mass ever obtained by an individual; and senescence mortality, which increases exponentially after maturity with a functional form similar to the Gompertz model (e.g., [44,45]) (Table 6). Note that abundance only ever decreases within a cohort. New individuals generated through reproduction produced new offspring cohorts (see below) (Equations 52–54 in Text S1). For computational efficiency, once A Mechanistic General Model of Global Ecosystems the number of cohorts exceeds a user-specified, computationally tractable threshold, a number of pairs of cohorts equal to the excess are merged together. On merging, the biomass of one of the cohort pair is converted into an equivalent number of individuals of the other cohort in the pair (Equations 68–69 in Text S1). The cohort pairs identified for merging are those lying closest together in continuous trait space, and belonging to the same functional group (Equation 67 in Text S1). Individuals were exchanged among the grid cell via three types of dispersal: (1) random diffusive dispersal of newly produced (juvenile) cohorts, (2) active dispersal of individuals determined by the degree of starvation experienced, and (3) advective-diffusive dispersal driven by ocean currents (in the marine realm only) (Table 6). Dispersal occurred via the movement of whole cohorts, Table 6. Cont. Process Main Mathematical Functions Eqn(s). Assumptions Reprodn. The biomass allocated to reproduction for cohort i is modelled as: DMRe proAlloc i ~max 0, Mi,(t)zDMAss i {DMMetab i {MAdult i , where DMAss i is the total biomass assimilated as food; DMMetab i is mass lost through metabolism; MAdult i is the body mass at which an individual of cohort i reaches reproductive maturity. A reproductive event was assumed to occur when the following threshold condition was met: Mi,(t )zRi,(t ) MAdult i wb, where MAdult i is the mass at which an individual of cohort i reaches reproductive maturity; Ri,(t ) is the stored reproductive potential biomass of each individual in cohort i at the current time; b is the threshold value for accumulation of reproductive potential biomass. S49–S54 Semelparous organisms can allocate a fraction of their adult mass to reproductive events. Mortality The instantaneous rate of senescence mortality was modelled as: mse~lse :exp tpm=tbm , where lse is the instantaneous rate of senescence mortality for a cohort at the point of maturity; tpm is the time that it took for the cohort to reach maturity; tbm is the time since the cohort reached maturity. The instantaneous rate of starvation mortality is given by: lmax mst~ 1zexp{ Mi,(t ){qst :Mmax i fstMmax i where lmax is the maximum possible instantaneous fractional starvation mortality rate; qst determines the inflection point of the logistic function describing the ratio of the realised mortality rate to the maximum rate; fst is the scaling parameter for the logistic function describing the ratio of realised mortality rate to the maximum rate; Mmax i is the maximum body mass ever achieved by individuals in cohort i. The instantaneous rate of background mortality, mbg, was modelled as a constant value. S55–S58 There is no senescence mortality applied to cohorts that have not reached maturity. Dispersal Three types of dispersal were included in the model, two of which—diffusive natal dispersal and responsive dispersal—applied across all realms, whereas advective dispersal applied in the marine realm and to planktonic size organisms only. Diffusive natal dispersal modelled the characteristic dispersal distance of each cohort as a function of body mass as follows: di~ndiffusive : Mi,(t ) Mdisp ref !odisp , where ndiffusive is the dispersal speed of an individual of body mass equal to the dispersal reference mass Mdisp ref ; odisp dispersal distance body mass exponent. Active dispersal in adults is attempted if intracohort density of adult individuals is below a mass-related density threshold: Ni,(t ) Acellvbresponsive density . MAdult i , or if the proportion of body mass lost in a time step exceeds a starvation threshold: Mi,(t ) MAdult i vbresponsive bodymass , where the betas represent those thresholds. The final, advectively driven dispersal is applicable solely to planktonic organisms in the marine realm and modelled using the two-dimensional advective vector at that time step and location, with an additional diffusive component of random direction and length. S59–S61 Cohorts are spread homogeneously across grid cells. Cohorts disperse in entirety not as fractions. The diffusive dispersal of immature organisms is assumed to represent them searching for new territory. Note that the same processes apply in the terrestrial and marine realms. For full details, see Text S1 and Table S2. doi:10.1371/journal.pbio.1001841.t006 PLOS Biology | www.plosbiology.org 9 April 2014 | Volume 12 | Issue 4 | e1001841
- 10. Table 7. The major development needs for the Madingley Model organised by development category. such that cohorts remained intact. This was necessary numerically to keep the number of cohorts manageable. We carried out some targeted simulations to explore the effects of allowing cohorts to split on dispersal, and found that could have quantitative effects, but does not fundamentally alter dynamics (Figure S1). Assump-tions and functional forms about dispersal, and numerical schemes to implement them, are another potentially important area for future research. When the model was applied to a specific grid cell in isolation, dispersal into or out of the grid cell was not modelled. Emergent Properties The properties of individuals and communities that we present below are ‘‘emergent’’; that is, they are not prescribed, but instead emerge through time as a result of the large number of interactions that take place between individual organisms (approximated as cohorts). As a result of these interactions, life histories of individuals are formed over time and can be tracked, and com-munities and ecosystems of individuals self-assemble. Moreover, the dynamics of any one grid cell are affected by the exchange of individuals with other grid cells, which occurs due to dispersal. Thus macroscale predictions (e.g., over the generation length of an individual cohort, across functional groups, or across entire ecosystems) emerge from microscale biological mechanisms. The macroscale predictions differ for ecosystems in different climates, but only because the microscale biology is sensitive to the climate. Similarly, the macroscale predictions differ between the land and sea, but only because microscale biology differs between land and sea. We compared these emergent properties to empirical data. Model Simulations and Comparison to Data We carried out four distinct types of simulations for different assessments of model capabilities (Table 3). Terrestrial grid cells were seeded with two autotroph stocks, deciduous and evergreen, as detailed above, and marine grid cells were seeded with a single phytoplankton stock. Grid cells were seeded with around 1,000 cohorts each, with 112 cohorts in each of nine functional groups in the terrestrial realm and 100 cohorts in each of 10 functional groups in the marine realm. Juvenile and adult body masses of cohorts were drawn at random from a prespecified range (Table 2), and initial abundance was scaled negatively with initial body mass to provide reasonable initial densities (see Text S1 for full details). Detailed numerical analyses were conducted on four focal grid cells (Study 1, Table 3) to investigate ecosystem dynamics over longer time scales. These simulations were used to check for the persistence of key community components (autotrophs, herbivores, carnivores, and omnivores), and to determine the typical time scales for the dynamics to reach some form of equilibrium. These Category Development Need Data 1. Source individual organism-level data with which to constrain ecological processes such as mortality from disease and environmental disturbance, reproductive behaviour, dispersal behaviour, and activity rates in response to environmental or food stress. 2. Gather information on local community structure to evaluate community-level predictions, such as total biomass of functional or trophic groups, whole communities, individual size distributions for entire communities in the terrestrial realm, and biomass fluxes through ecosystems. 3. Collect data detailing ecosystems across space and through time to evaluate emergent ecosystem-level properties—for example, latitudinal or longitudinal transects of biomass and/or abundance, total biomass and/or abundance within a region, and changes in ecosystem structure in response to environmental change through space and/or time. 4. Assemble data on quantified interaction networks for communities with which to compare the individual-level interaction networks predicted by the model. Ecology 1. Include detritivores as a functional group, including the ecological processes that link detritivores to the organic matter inputs from the ecosystem and cycle that processed organic matter back to form inputs for the primary producers of the system, as well as representing detritivore-based food chains. 2. Resolve sub-grid-cell habitat structure and organismal preferences within that structure that will likely lead to patterns of interactions among organisms that violate the well-mixed assumption, for example, by providing refugia for prey: in forests for instance, canopy-dwelling predators encounter canopy-dwelling prey more often than expected, but ground-dwelling prey less often than expected. 3. Incorporate an explicitly resolved, mechanistic model of phytoplankton dynamics with two-way linking between phytoplankton and zooplankton. 4. Incorporate a three-dimensional spatial structure in the oceans with a temporally and spatially varying mixed-layer and deep chlorophyll maxima 5. Represent nonphytoplanktonic coastal NPP (seagrass beds or coral reefs) in order to more realistically capture biodiverse and productive coastal ecosystems. 6. Capture varying organismal ecological stoichiometry to account for biochemical limitations on performance and also to being able to explore biogeochemical cycling through entire ecosystems; useful starting points include ecological stoichiometric [112] and dynamic energy budget [113] concepts. 7. Simulate freshwater ecosystems in addition to terrestrial and marine, and source necessary datasets to constrain ecological parameters and evaluate outputs. 8. Introduce the concept of intelligent behaviour—for example, directed dispersal (e.g., along a gradient of resources), hibernation and stasis strategies, or complex predator–prey and herbivore–plant interactions Methods 1. How does underlying behaviour feed up to mathematical representations of ecological functions? For example, how does the intelligent behaviour of predators and prey affect the Hollings’ functions employed to model this interaction? 2. Analysis of the model framework to identify analytical solutions for emergent properties such as size distributions or trophic structure. 3. Study the implications of the numerical methods employed in the model such as the time step of ecological processes and the cohort approximation. 4. Implement a variable time-scale method wherein smaller, more metabolically rapid organisms have a faster time step [14], which may stabilise the marine realm and will be needed to implement a fully coupled dynamic and mechanistic phytoplankton model. 5. Formally constrain the model against data (data needs are described above) in order to rigorously select the most appropriate assumptions, functional forms, and parameter values. doi:10.1371/journal.pbio.1001841.t007 A Mechanistic General Model of Global Ecosystems PLOS Biology | www.plosbiology.org 10 April 2014 | Volume 12 | Issue 4 | e1001841
- 11. analyses used the same climatological time series per year to remove the effects of interannual environmental variation. For each focal grid cell, we ran 10 model simulations for 1,000 y at a monthly time step. To test the effect of the cohort-merging regime on modelled dynamics, we repeated the simulation ensembles for each focal grid cell with the threshold number of cohorts at which merging is activated set at 500, 1,000, 5,000, and 10,000 cohorts and for a shorter period of 100 y. Additional detailed simulations were carried out for the focal grid cells over a 100-y period to generate highly resolved predictions of emergent ecosystem properties at two levels of biological organisation: individual and ecosystem level (Study 2, Table 3). We compared the properties of individual organisms with empirical data. Importantly, none of these properties were defined in the model as parameters, but rather they emerged as a result of the ecological interactions among individuals. The predicted relationship between body mass and growth rates was compared to estimates for reptiles, mammals, birds, and fish [46–48], and the relationship between body mass and time to reach maturity to estimates for invertebrates, reptiles, mammals, birds, and fish [49– 57] (where necessary body masses were estimated from body lengths using relationships in [58–61]). The predicted relationship between body mass and mortality rates was compared with data for invertebrates, mammals, birds, and fish, taken from a single study [62]. The predicted relationship between body mass and lifetime reproductive success was compared with data for mammals, birds, and a few insect species [63–71]. Of these emergent properties, the growth rate of organisms derives most closely from the functional forms and input parameters. Specif-ically, growth rate could theoretically be a simple sum of food assimilation rates under conditions of saturating prey density minus metabolic costs. To test whether this was the case, we calculated the theoretical growth rate for organisms of a range of body masses under these conditions. We compared our novel predictions of complete ecosystem structure in two grid cells (T1 and M1) (Table 4) to empirical data: the biomass density of large herbivores with an estimate for Uganda [72], and the predicted herbivore to autotroph biomass ratios with average observed ratios for similar ecosystems [73]. We further compared the modelled relationships between body mass and population density with empirical estimates derived from fish assemblages [74,75]. To test the ability of our model to capture broad-scale patterns in the basic trophic structure of ecosystems, we compared our model predictions (Study 3, Table 3) to empirical estimates from the same dataset used to calculate the global average trophic structure ([73]; see above), but this time using specific values for 14 sites for which we could identify the spatial location (Table S3). This dataset is the most geographically wide-ranging dataset on ecosystem structure that we are aware of, including sites in both the terrestrial and marine realms. We also generated model outputs at a global scale (Study 4, Table 3). These were used in two ways: firstly, to investigate the mechanisms giving rise to variation in ecosystem structure by assessing the relationship between trophic structure and produc-tivity in the model along large gradients of autotroph productivity in both terrestrial (along a meridional transect from the low productivity Saharan desert to high productivity Congo Basin tropical forest region) and marine (along a meridional transect from low productivity Antarctic waters to high productivity East Atlantic upwelling zones) realms; and secondly, to make novel predictions of as-yet unmeasured global properties (e.g., latitudinal gradients in total biomass) and to compare to other modelled A Mechanistic General Model of Global Ecosystems estimates of total biomass and density at a global scale [76]. We also compared modelled global average ratios of herbivore to autotroph biomass with the average ratios observed in the same dataset that we used to test the predictions made by individual cells [73]. Finally, we investigated how modelled marine ecosystem structure responded to mechanisms that have been proposed to cause inverted trophic biomass pyramids, such as dispersal [77], turnover rate of autotrophs, and turnover rate of consumers [77– 79]. To do this, we simulated the global marine realm with no dispersal permitted between grid cells (Study 5, Table 3) and the effects of reducing the turnover rate of biomass through the ecosystem (Study 6, Table 3). Results Grid Cell: Dynamics For the 1,000-y simulations (Study 1), model dynamics converged rapidly (,100 y) to dynamic equilibria for all 10 replicates in all four focal grid cells (Figure 2). Autotrophs, herbivores, omnivores, and carnivores persisted in all simulations. The dynamics of total biomass by functional group differed markedly among the four grid cells. Terrestrial grid cells were dominated by autotroph biomass and, among heterotrophic organisms, by herbivores, with lower biomasses of omnivores and carnivores. Marine grid cells, in comparison, had much lower biomasses of autotrophs, and omnivorous and carnivorous organisms were more dominant. Unsurprisingly, the seasonal grid cells in both the terrestrial and marine realms (Figure 2B and 2D) exhibited much greater fluctuations in biomasses within years, particularly for lower trophic levels. The high-productivity marine grid cell exhibited large-amplitude, high-frequency variations in zooplankton abundance. Biomass dynamics were robust to the choice of the threshold number of cohorts at which to activate merging above a threshold of 1,000 cohorts (Figure S2). Grid Cell: Individuals The power-law relationships between body mass and the properties of individual organisms that emerged from the model were generally consistent with empirical data (Figure 3). For growth rates and times taken to reach reproductive maturity, the modelled and empirical values were very similar, although the slope of the relationship between predicted growth rates and body mass was steeper. In absolute terms the predicted growth rates tended to be higher and the predicted times to maturity tended to be lower than those observed in the empirical data (Table S4). Our assumptions about underlying ecological processes, such as handling times and metabolic rates, place a fundamental limit on the growth rate of organisms of a given body mass (i.e., the net growth rate of individuals that are feeding at the maximum rate). If most individuals attained this maximum, then the growth rates would not be emergent, so much as defined by the model assumptions. But this was not the case. The emergent relationship between body mass and growth rate was not a simple function of maximum possible food assimilation and metabolic costs: mod-elled growth rates were typically one-tenth of theoretical maximum model growth rates and showed large variation for any given body mass (Figure S3). This variation resulted from the many other factors that affected growth rate, most notably the abundance and body masses of potential prey and predators competing for the same prey. Predicted mortality rates showed a negative power-law relationship with body mass (Figure 3C), qualitatively consistent with empirical data, although the relationship was generally shallower and absolute rates were higher (Table S4). Finally, PLOS Biology | www.plosbiology.org 11 April 2014 | Volume 12 | Issue 4 | e1001841
- 12. A Mechanistic General Model of Global Ecosystems Figure 2. 1,000-year dynamics for four locations. Medians from ensembles of 10 replicate simulations (lines) and absolute ranges (shaded regions) of biomass densities for autotrophs (dark green lines), herbivores (light green), omnivores (blue), and carnivores (red) within four 1u61u focal grid cells; T1, terrestrial aseasonal (A); T2, terrestrial seasonal (B); M1, marine aseasonal (C); and M2, marine seasonal (D) (Table 4). The temporal dynamics in these metrics emerges from underlying ecological processes that affect a large number of cohorts within each grid cell. Insets zoom in on medians for the last 5 y of the simulations, demonstrating the seasonal variability in each cell. doi:10.1371/journal.pbio.1001841.g002 predicted reproductive rates in the terrestrial realm showed a weak positive power-law relationship with body mass, broadly consistent with empirical estimates (Figure 3D, Table S4), whereas predicted reproductive rates in the marine realm were weakly negative. Predicted reproductive rates were substantially more variable than the empirical data (Figure 3D). Grid Cell: Community For the four focal grid cells, terrestrial ecosystems exhibited a pyramid of biomass across the different trophic levels (Figure 4A), which is widely accepted to be present in terrestrial systems [80]. The predicted herbivore biomass as a proportion of producer biomass (0.98%) was consistent with empirical terrestrial estimates (median value=0.93%) (Table S5) [73]. However, predicted biomass of large-bodied herbivores was four to six times higher than estimated from a field study [72]. Consistent with current opinion and observations [78,81–84], marine ecosystems exhibited an inverted pyramid of biomass structure [73,82], with the highest biomasses in the highest trophic levels (Figure 4C). Marine systems exhibited relatively faster flow rates of productivity from autotrophs to higher trophic levels compared with terrestrial ecosystems—and at rates much higher than those estimated to date (Figure 4A and 4C) [85]. Predicted herbivore biomass as a proportion of producer biomass for the marine grid cells was much higher than in terrestrial ecosystems (63%), and of a similar magnitude to empirical estimates (median value=52%) (Table S5) [73]. Expressed as abundance rather than biomass, and consistent with theoretical expectations [86,87], trophic pyramids were not inverted in either realm: that is, communities contained a greater number of herbivores than carnivores (Figure S4).However, omnivores were more abundant than herbivores, by a factor of 3 in the terrestrial cell and by two orders of magnitude in the marine cell. This was because the average size of omnivores was smaller than the average size of herbivores or carnivores. In both terrestrial and marine grid cells, densities of organisms showed a negative, approximately log-linear relationship with individual body mass (Figure 4B and 4D), the slopes of which fell within observed ranges in fish community assemblages from some sources (Figure S5) [75], although not from others (Table S6) [74]. Geographical Patterns in Ecosystem Structure Across 14 Sites Predicted ratios of heterotroph to autotroph biomass were broadly consistent with empirical estimates in many of the terrestrial and marine locations (Figure 5). For terrestrial ecosystems, the model and empirical data were in closest agreement in the two savannah ecosystems (Figure 5J and N). For the other ecosystem types—desert, tundra, deciduous forest, and tropical forest—there was lower agreement between model and empirical estimates of trophic structure, with modelled heterotroph to autotroph biomass ratios generally greater than empirical estimates, sometimes by orders of magnitude (Figure 5). PLOS Biology | www.plosbiology.org 12 April 2014 | Volume 12 | Issue 4 | e1001841
- 13. A Mechanistic General Model of Global Ecosystems Figure 3. Comparison of emergent life history metrics with empirical data. Empirical (black) and emergent model (grey) relationships between body mass and (A) growth rate, (B) maturity, (C) individual mortality rates, and (D) lifetime reproductive success. These life history metrics are not part of the model definition. Rather, they emerge from underlying ecological processes such as metabolism and feeding (see main text). Life history metrics were sampled from 100-y model runs for the four focal grid cells (Table 4). Individual mortality rates are estimated as the inverse of lifespan, and because the minimum simulated lifespan is one model time step (1 mo), estimated individual mortality rates were bounded at 12. doi:10.1371/journal.pbio.1001841.g003 Modelled ecosystems in the marine realm generally showed closer agreement with empirical estimates than in the terrestrial realm. However, in both Santa Monica Bay, San Francisco (Figure 5A), and the Swartkops estuary in South Africa (Figure 5F), median modelled herbivore to autotroph biomass ratios were three orders of magnitude larger than empirical estimates. Trophic Structure Along Productivity Gradients The structure of both marine and terrestrial ecosystems showed marked changes along a gradient of increasing NPP (Figure 6). Marine ecosystems showed increasing biomass for all three heterotroph types (carnivores, omnivores, and herbivores), and flat then declining and highly variable autotroph standing biomass (Figure 6A). Terrestrial ecosystems also showed a trend of increasing heterotrophic biomass with productivity (Figure 6B). Carnivores increased in biomass with productivity more steeply than for other trophic levels, and were entirely absent from the lowest productivity desert ecosystem. In the most productive terrestrial ecosystems, carnivores typically had higher biomass densities than omnivores. Global Ecosystems Global patterns of total heterotroph biomass, averaged across the final year of the simulation (Figure 7A), were similar to patterns of primary productivity (Figure S6). In the marine realm, our modelled estimate of median heterotroph biomass density was 167,147 kg km22, approximately 7–30 times greater than previ-ous modelled estimates, which range from 5,500–25,000 kg km22 [76,88–90]. However, a recent empirical study into mesopelagic fish biomass suggests that some fish biomass densities are likely to be an order of magnitude higher than these previous estimates [90] and so our prediction is plausible. Global median ratios of herbivore to primary producer biomass estimated by the model were 0.8% for terrestrial and 189% for marine ecosystems, compared to 0.93% and 52% for empirical estimates (Table S5) [73]. Our modelled estimate of median total terrestrial hetero-troph biomass density was 151,089 kg km22, a prediction which, as far as we are aware, has never been made previously. In the marine realm, high heterotroph biomass is predicted in upwelling systems and areas of high annual productivity (e.g., the North Atlantic). In the terrestrial realm, predicted heterotroph biomass was highest in naturally forested areas and lowest in deserts. There was no clear latitudinal gradient of biomass density in either system, but latitudinal variability was substantially greater in the terrestrial realm. At subtropical latitudes in the northern hemisphere in the terrestrial realm, there was a band in which carnivores had higher biomass density than omnivores, whereas elsewhere omnivores had greater biomass density. This switch in the relative dominance of omnivores in the northern hemisphere coincided with a decline in mean herbivore biomass density. No PLOS Biology | www.plosbiology.org 13 April 2014 | Volume 12 | Issue 4 | e1001841
- 14. A Mechanistic General Model of Global Ecosystems Figure 4. Community-level emergent properties. Community-level properties—(A, C) biomass pyramids and (B, D) body mass–density relationships across all cohorts belonging to each trophic level—emergent from the model for an example terrestrial (A, B) and marine (C, D) grid cell (grid cells T1 and M1 from Table 4). Results are from the final year of a 100-y model run. Dark green represents autotrophs, light green herbivores, blue omnivores, and red carnivores. In (A) and (C), standing stocks of biomass are indicated by the widths (after log-transformation) and numbers within the boxes; curved arrows and percent values represent the biomass transferred among or within trophic levels from herbivory and predation, as a proportion of the standing stock of the source of each flow; dashed arrows and percent values represent NPP of autotrophs as a proportion of the autotroph standing stock. doi:10.1371/journal.pbio.1001841.g004 discernible decline in mean herbivore biomass densities was observed at subtropical latitudes in the terrestrial southern hemisphere. Not all grid cells conformed to the pattern of inverted biomass pyramids in the marine realm and noninverted biomass pyramids in the terrestrial realm. Out of all terrestrial cells modelled, 9% were predicted with more omnivore than herbivore biomass and 46% with greater carnivore than omnivore biomass (Figure S7). Conversely in the marine realm, 12% of cells had less herbivore than autotroph biomass, 10% of cells had less omnivore than herbivore biomass, and 0.4% of cells had less carnivore than omnivore biomass (Figure S7). The spatial extent and frequency of cells in the marine realm with noninverted pyramids was significantly higher when dispersal was prevented from occurring (Figures S8 and S9). There was also evidence that noninverted trophic structure was more likely when the turnover rate of phytoplankton was lower and when the rate and efficiency with which matter is transferred through the system were reduced (Figure S10). PLOS Biology | www.plosbiology.org 14 April 2014 | Volume 12 | Issue 4 | e1001841
- 15. A Mechanistic General Model of Global Ecosystems Figure 5. Global heterotroph:autotroph biomass ratios. Comparisons of modelled (open) and empirical (filled) heterotroph to autotroph biomass ratios in marine (A–F) and terrestrial (G–N) environments (Table S3). Green squares are herbivore to autotroph ratios, blue triangles are omnivore to autotroph ratios, and red diamonds are carnivore to autotroph ratios. Modelled ratios are medians from 10 simulations, and vertical lines are 1 standard deviation over these simulations. Empirical ratios are individual estimates or, where more than one estimate was available, the median of these with sample sizes of H (n = 5), K (n = 2), L (n = 2), and N (n = 3), and vertical lines indicate maximum and minimum empirical estimates. Comparison locations are shown on a map of the predicted ratio of herbivore to autotroph biomass constructed from the global simulation (Study 4, Table 3). doi:10.1371/journal.pbio.1001841.g005 Discussion We have shown that it is possible to derive global predictions about the emergent properties of ecosystem structure and function from a GEM based on processes of, and interactions among, individual organisms, without any model-imposed constraints on those properties. Stability of Emergent Dynamics The model reached a dynamic steady state in all grid cells, with the persistence of all trophic levels, which is expected in the absence of perturbation [91]. Real ecosystems are not expected to exhibit such stable dynamics because they are subject to numerous interannual environmental fluctuations and perturbations. These were not incorporated for this study, but could be in the future. PLOS Biology | www.plosbiology.org 15 April 2014 | Volume 12 | Issue 4 | e1001841
- 16. A Mechanistic General Model of Global Ecosystems Figure 6. Ecosystem structure along productivity gradients. Variation in emergent ecosystem structure along productivity gradients in the marine environment (A) from the Southern Ocean to the West African Coast and in the terrestrial realm (B) from the Saharan Desert to the Congolian Forests. Transect locations are presented on the maps set into each panel. Dark green circles correspond to autorotroph biomass, light green squares correspond to herbivore biomass, blue triangles to omnivore biomass, and red diamonds to carnivore biomass. Broad biogeographic regions are roughly distinguished using dashed vertical lines. doi:10.1371/journal.pbio.1001841.g006 The global simulations (which included dispersal) converged to equilibria with similar characteristics to the focal grid cells, although with higher biomass densities. The higher biomass must have been a result of dispersal, as this is the only difference between the focal-cell simulations and may be owing to a rescue effect from neighbouring grid cells. Nonetheless, the similarity of the simulations with and without dispersal provides support for the use of isolated focal grid cells in more detailed studies. One form of instability in the dynamics was the large temporal variation in biomasses in the high-productivity, seasonal marine grid cell. Plankton and zooplankton are known to exhibit marked biomass fluctuations, but the modelled variation was much greater, and has a different temporal signature (chaotic variation within the productive season, whereas real cycles are repeatable year to year). This appears to be an artefact of the long time step used, allowing massive unconstrained changes in biomass over a single time step. Model simulations carried out using a daily time step (only feasible over shorter time periods and for single grid cells due to the computational demand) produced substantially more stable dynamics. However, the mean predicted biomass was PLOS Biology | www.plosbiology.org 16 April 2014 | Volume 12 | Issue 4 | e1001841
- 17. A Mechanistic General Model of Global Ecosystems Figure 7. Emergent global-level ecosystem properties. Properties emergent from the model after a 100-y global (65uN to 65uS) simulation using a grid-cell resolution of two degrees. (A) The spatial distribution of annual mean heterotroph biomass density; breaks in the colour scheme were based on quantiles in the data. (B, C) Latitudinal gradients in biomass density; solid lines represent means for each trophic level, and shading represents the range of values across all longitudes in each latitude band. doi:10.1371/journal.pbio.1001841.g007 similar between simulations using different time steps, suggesting that most of the properties of our results are robust. Nevertheless, future research is needed into numerical and computational methods for more appropriately simulating small organisms in GEMs (see Table 7 and Text S2). Emergent Life Histories and Trophic Structure Many aspects of the life history of individuals emerge from the underlying ecological processes and interactions with other organisms. For example, growth rates are determined by a combination of food assimilation rates and metabolic losses, which themselves depend on the abundance and properties of the other individuals at the location, and are also constrained by the maximum possible rate of assimilation and environmentally determined metabolic rate. Modelled growth rates varied widely among cohorts, between the maximum and minimum theoreti-cally possible rates (Figure S3), but showed good correspondence with observed values (Figure 3A). Predicted mortality rates were much higher than empirically observed rates, especially for larger organisms (Figure 3C). This may reflect a mismatch with the data, as discussed below; in this case, empirical mortality rates were observed in laboratory conditions in the absence of predation mortality. Comparing the empirical data and model predictions at a higher level of resolution, for example within functional groups PLOS Biology | www.plosbiology.org 17 April 2014 | Volume 12 | Issue 4 | e1001841
- 18. or biomes, might help us to better diagnose discrepancies in the future. Growth rates were slightly faster and times to maturity slightly shorter than those from observation. Modelled rates of biomass transfer calculated for the two focal grid cells were higher than empirically observed rates, particularly in the marine realm (Figure 4) [85]. At least in part, this discrepancy may result from a bias in the data toward larger organisms, leading to empirical estimates underestimating real biomass flow rates. Similarly, the negative log-linear relationship between individ-ual body mass and organism density is consistent with ecological theory [92], although uni- [93,94] or multimodal [95,96] relationships have been observed. The modelled slopes were shallower than empirical estimates for a log-linear relationship, which again might indicate that turnover rates in the model were overestimated, causing greater suppression of smaller organism abundance and higher abundance of larger organisms than in real ecosystems. Another difference between the model and data was that the modelled biomass of large-bodied herbivores was several times higher than observations [72]. Modelled ratios of herbivore to autotroph biomass were also higher than empirical estimates in most cases, especially for terrestrial ecosystems. There are three potential explanations for this. The first is that herbivores, like predators, are eating too efficiently in the model, which might result from incorrect functional forms or missing processes. The second explanation is that because the available data are extremely sparse, the data are thus potentially not representative of the system. Thirdly, human impacts might have reduced large herbivore biomass in the empirical data compared to the undisturbed ecosystem assumed in these simulations of the model. The closer match between modelled and empirical trophic structure for marine and savannah ecosystems, compared to forests, might be because these ecosystems conform much better to the assumption that individuals are well mixed. This assumption implies that herbivores can find all plant material and predators can find all prey. In all ecosystems, but most obviously in forests, many leaves are physically out of reach of many herbivores, and many prey are able to find refuge from predation. This may act to slow down biomass turnover in forests in comparison to the ocean and savannas, in a way that cannot be captured by a model that assumes complete mixing within a grid cell. On the other hand, the discrepancy could also be caused by incomplete empirical data. It is easier to estimate whole-ecosystem properties in savannas (where animals tend to be highly visible) and in the ocean (which can be trawled with nets) compared with forests. Alternatively, the terrestrial plant model might be inaccurately capturing the allocation of productivity to structural or nonstruc-tural matter at these specific forest sites. However, this appears less likely, as the allocation function of this model has been rigorously constrained using a global dataset, and evaluation shows the model predicts well for this property [36]. We note, however, that at finer, site-level scales, plant allocation strategies will certainly be more heterogeneous and will certainly be different from the larger scale average predicted by the global model. It is important to note that differences between the marine and terrestrial realms were not imposed on the model as top-down limits on the structure of ecosystems but rather emerged from individual-scale ecology. A necessarily different set of representa-tive functional groups was defined for the marine environment compared to the terrestrial environment, but all functional groups in the model followed the same fundamental ecological functions. The only other encoded differences between marine and terrestrial cohorts were the proportion of total autotroph biomass available for consumption by a given herbivore cohort, the different optimal A Mechanistic General Model of Global Ecosystems prey body sizes for predators, and the assumption that marine ectotherms are not thermally restricted in their capacity to function. The primary cause of the much lower ratio of herbivore biomass to autotroph biomass in the focal terrestrial cells versus in the oceans was the allocation by terrestrial plants of primary productivity to structural tissues, which are inedible to all herbivores in the model (Figure S11). This assumption probably made it more likely that terrestrial cells would exhibit a conventional pyramid of biomass structure. However, the model predicted considerable variation in the shape of the trophic biomass pyramid across terrestrial and marine cells, including an inverted structure in some terrestrial cells and a noninverted structure in some marine cells (Figure S7). Emergent Global Patterns: Model Results and Predictions The modelled global estimates of biomass density represent the first attempt to assess the scaling of ecosystem properties from individuals to communities at a global level, and to apply a general ecological modelling methodology consistently across both the marine and terrestrial realms. Some of these properties have been estimated previously in specific locations, but none have been estimated globally using mechanistic models (although marine animal biomass and biomass densities have been predicted mechanistically [76,88,89]). In addition, we have calculated emergent properties that are, as far as we are aware, unprecedented (Table 8), and we discuss these below. Heterotroph Biomass and NPP. At a global scale, the spatial pattern of heterotroph biomass was broadly consistent with observed NPP [97], which is unsurprising, as NPP is the basal resource in all of the modelled ecosystems. However, the relationship between primary productivity and heterotroph biomass was not simple: a given level of primary productivity could result in a wide range of heterotroph biomass (Figure S6A– D). This variation arises from differences in climate, which lead to differences in biomass allocation to different plant tissues and to variation in animal metabolic rates and levels of activity. The predicted peak in terrestrial heterotroph biomass densities observed in locations with intermediate levels of NPP is also likely to result from these factors; for example, plants in the most productive areas allocate a greater proportion of biomass to structural tissues, whereas plants in intermediate productivity ecosystems such as grasslands have a greater relative allocation to nonstructural tissues. Autotroph biomass was also influenced by herbivory, as demonstrated by removing all heterotrophs from the model and representing mortality of plants through herbivory using a constant loss term (Figure S6E and F). This experiment suggests the impact of herbivory on plants varies significantly across the world, indicating the potential importance of explicitly considering herbivores in carbon cycle models, such as DGVMs, or models of ocean biogeochemistry, which is not done at present. Exploring the impacts of heterotrophs on carbon cycling and predicted carbon dynamics is an important avenue of research for future development of GEMs. Emergent Structure and Productivity. Modelled variation in trophic structure along gradients of productivity supported theoretical expectations that the NPP of systems will determine the length of trophic chains [9,10,98]. In low-productivity terrestrial systems, there is insufficient autotrophic biomass propagating to higher trophic levels to support carnivores, whereas in high-productivity ecosystems, carnivore biomass is greater than omnivore biomass. In the marine realm, autotroph biomass decreased with increasing primary productivity beyond NPP of 40,000 kg km22 y21, inconsistent with expectations from the PLOS Biology | www.plosbiology.org 18 April 2014 | Volume 12 | Issue 4 | e1001841
- 19. Table 8. Novel predictions and datasets needed to evaluate them. Prediction Data to Evaluate trophic release hypothesis (Figure 6B) [11]. The model predicts for marine ecosystems that with increasing primary productivity herbivore biomass increases and carnivore biomass, as a propor-tion of total biomass, decreases. For terrestrial ecosystems, herbivore biomass increased to around 40,000 kg km22 and then decreased, whereas the carnivore biomass proportion decreased only after around 550,000 kg km22. The relationship predicted for marine ecosystems is in agreement with the general findings from available empirical data on changes in trophic structure associated with changes in productivity, derived from freshwater, intertidal, and reef fish communities [99–103]. However, our results indicate that a qualitatively different relationship between trophic structure and productivity appears to exist in the terrestrial realm. There are additional factors that influence modelled community structure along productivity gradients that will require detailed investigation in the future, including (i) seasonality, which will vary among different modelled locations with similar productivity; (ii) climatic differences, which might affect the composition of autotroph biomass in terrestrial ecosystems; and (iii) dispersal regimes. Emergent Latitudinal Patterns of Community Stru-cture. Predictions of latitudinal variation in community struc-ture (as shown in Figure 7B and 7C) give an insight into the mechanistic basis of these patterns at a global scale. On land, there was greater variation in the biomass density of all trophic groups, both latitudinally and longitudinally, compared to in the oceans (Table 8). The greater variation in terrestrial biomass densities was likely driven by greater environmental heterogeneity in the terrestrial realm and the greater range and speed of dispersal processes (e.g., advective dispersal) in the oceans. For example, both temporal [104,105] and spatial variability [106] in environ-mental temperature is higher on land versus the ocean. In the mid to high latitudes of the terrestrial northern hemisphere, omnivorous organisms account for greater biomass than carnivores. However, in equatorial latitudes and extending to 30uS, carnivorous organisms constituted a greater fraction of the total ecosystem biomass than omnivores (Figure 7C and Table 8). The equatorial and low southern hemisphere latitudes correspond to more stable environmental conditions [106] compared with mid to high northern latitudes. Therefore, the model appears, in the terrestrial realm, to be selecting for generalist feeding strategies in more variable environments, while favouring specialism where the environment is more stable. Mechanisms Giving Rise to Inverted Marine Trophic Structure. The model showed that dispersal of organisms plays an important role in the spatial extent and frequency of inversion of marine trophic structure (Figures S8 and S9), which is consistent with the hypothesis that the import of allocthonous organic matter supports relatively higher heterotrophic biomass in oligotrophic freshwater systems, which has been postulated previously but not investigated in detail [77]. Furthermore, we show that noninverted trophic biomass structure is more frequent when the turnover rate of phytoplankton is reduced and when the rate and efficiency of biomass transfer through the ecosystem is lower (Figure S10), in agreement with current theory [77–79]. The generality of inverted trophic pyramids in the marine realm remains unknown, but there are numerous examples of herbivore biomass being larger than producer biomass in ocean environments [73]. Inversion at the top of the trophic pyramid has apparently been observed in some near-pristine reef habitats [84], though this may simply be an overestimation artefact of the visual census approach used [107]. Future Model Development In developing the first global GEM, our strategy was to start with a ‘‘simple’’ model that can be improved later. To keep it simple, we excluded numerous aspects of ecology—some of which are captured by existing models of particular ecosystems [14,15]. Adding this ecology back into our model would, arguably, make it more realistic. Then again, attempting to include all known ecological processes occurring in every ecosystem around the world would not only be completely impractical but would also be excessive for most of the purposes for which a GEM is intended. Thus, we would expect the set of ecological processes represented in GEMs to evolve over time and to depend on the ways in which GEMs come to be used. Moreover, there are several other important ways in which our model could be improved, as outlined in Table 7, and discussed below. Future Model Development: Ecology. The physical envi-ronment is currently represented very simply in the model. For example, in reality, variation in habitat structure within grid cells will alter interactions between organisms. And a fully integrated and explicitly resolved mechanistic model of phytoplankton is required in future iterations of the model, as is representation of nonphytoplanktonic coastal autotrophs (e.g., seagrass beds or coral Median terrestrial total heterotrophic biomass density is predicted to be 151,089 kg km22 and maximum terrestrial heterotrophic biomass densities are found in ecosystems with intermediate levels of NPP (Figure 7A and Figure S6A) Empirical or modelled information on the total biomass of heterotrophic organisms in a sample of terrestrial biomes, from which median terrestrial biomass density could be inferred Median marine total heterotophic biomass density is predicted to be 167,147 kg km22, approximately 7–30 times greater than previous modelled estimates Empirical information on the total biomass of heterotrophic organisms in a sample of marine locations, from which median marine biomass density could be inferred Omnivorous organisms account for greater biomass than carnivores in low to mid productivity terrestrial environments, for example in the Saharan desert—Sahelian savanna transition (Figure 6B), or more widely in the mid to high latitudes in the northern hemisphere (Figure 7C). At equatorial latitudes and extending to 30uS, carnivorous organisms constitute greater biomass than omnivores on average Ecosystem trophic structure or food web structure for low to mid productivity terrestrial environments in equatorial latitudes and mid latitudes in both hemispheres Terrestrial biomass densities vary more than marine biomass densities across latitudes (Figure 7B and C) Observations of total biomass contained in trophic groups at a set of sites within the same latitude band, carried out across a range of latitude bands. For the terrestrial realm, the band between 20u and 30uN has potentially substantial latitudinal variation in total biomass. doi:10.1371/journal.pbio.1001841.t008 A Mechanistic General Model of Global Ecosystems PLOS Biology | www.plosbiology.org 19 April 2014 | Volume 12 | Issue 4 | e1001841
- 20. reefs) and detritivores. The detrital loop in particular is important in ‘‘closing the system.’’ Other ecological processes that should be incorporated in future iterations of the model include ecological stoichiometry; intelligent behaviour, such as directed dispersal, hibernation, and stasis; and complex predator–prey and herbi-vore– plant interactions (Table 7). Future Model Development: Data. Robust data-con-strained parameterisation of the model and rigorous evaluation of our novel but testable outputs was not possible because the necessary data were not generally available. Therefore, another set of developments are needed around the acquisition and collation of data for use in GEM modelling (Table 8 and Table 7), which are reflected by the biodiversity informatics community [108]. Future Model Development: Numerical and Math-ematical Methods. The development of the Madingley Model was enabled by combination of numerical methods that is, far as we are aware, novel (e.g., the cohort approach to trait-driven interactions, combined with cohort merging, randomly ordered updating, the treatment of autotrophs as continuous state variables, and exponential differencing of loss rates within time steps; see Text S2 for further examples). Given the novelty of this modelling paradigm in ecology, at least five areas of development will be required: detailed analysis and understanding of the mathematical representations of ecology, analytical tractability of predicted ecosystem properties, the implications of alternative abstractions and numerical methods used to implement them, the infrastructure to allow flexibility in scale, and the infrastructure to constrain and evaluate the model so that the benefits of additional components or realism can be assessed objectively (Table 7). In addition, it would be interesting to explore the approach referred to as ‘‘parameterization’’ in the biogeosciences modelling commu-nity— that is, to fit phenomenological relationships to the output of GEMs, thus allowing approximate versions of them to be run much more quickly, or within the context of more general ESMs. Future Model Development: Community. The further development of GEMs discussed above will be expedited by a community of researchers improving upon the model presented here or developing alternative GEMs. We call for such a community of ecologists, biologists, mathematicians, and comput-er scientists to form around the GEM concept so that this class of model can be rapidly advanced to better meet the pressing needs of conservationists and policymakers. In this spirit, we have developed our model architecture in such a way that it is relatively easy to alter the representation of ecological processes and have made our model code freely available to the community (www. madingleymodel.org). Use of GEMs Our model is the first step towards the development of a more ecologically refined GEM (and GEMs) that occupies a very different niche to the more specialised modelling approaches that have been used to inform biodiversity policy to date, and is more akin to the global climate models that inform global climate science and policy [8]. Our GEM necessarily made numerous simplifying assumptions in order to capture a broad range of ecological processes and organisms. This nevertheless provides a new approach to answering important outstanding questions in ecology and with which to begin to ask entirely new questions— questions that require an integrated, mechanistic understanding of whole ecosystems; the connections among them; and their response to environmental variation and natural or human perturbations. In the following sections, we briefly discuss how GEMs could be used to inform ecological science and conservation policy. A Mechanistic General Model of Global Ecosystems Use of GEMs: Ecology. GEMs will help in the development of ecological theory. The study of ecology is so broad that most pieces of ecological research necessarily focus on a small subset, whether in terms of scale, taxa, or the processes concerned. The implications of the findings in these disparate research areas for the longer term and larger scale dynamics of whole communities and ecosystems are hard to assess. This has led some ecologists to call for a renewed interest in ‘‘systems ecology,’’ which aims to study important ecological processes within the context of other important ecosystem and earth-system processes to enable a better understanding of the natural environment [109]. Models like ours provide one way to do this: new ecological findings can be used to modify the model, or different competing formulations of ecological theories (e.g., prey density or ratio-dependent predation functions [110]) can be represented in the model and the results assessed against known ecosystem structure. By doing so, the processes of critical importance for ecosystem structure and functioning could be identified and priorities for development of new ecological hypotheses or data-gathering determined. Our preliminary investigations of community trophic structure along productivity gradients and of the mechanisms giving rise to the inversion of marine cells illustrate the potential of GEMs in this regard. Use of GEMs: Conservation. The simulations presented here are not directly relevant to conservation decision-making, as the model currently does not directly include anthropogenic influences. In principle, a model of this kind could be used to better inform the management of the world’s ecosystems, in much the same way that mechanistic ESMs are used to predict and explore scenarios of anthropogenic climate change [7]. Forcing the model with time-varying historic or future projections of environmental variables would provide the kinds of novel and highly relevant outputs that could enable a mechanistic approach to conservation decision-making. By taking a system-level approach, GEMs are uniquely able to simulate the interacting relationships between various simulta-neous human pressures (such as climate change, land use change, and harvesting of wild animals) and various metrics of ecosystem structure and function, exploring the trajectories derived from external scenarios of human pressure. For example, they could predict (1) static measures of ecosystem properties, such as the variation in the functional traits represented in ecosystems, an important measure of biodiversity thought to be related to ecosystem functioning [26]; (2) metrics that are currently used to monitor the state of ecological systems, such as the total abundance of large endotherms as an analogue of the Living Planet Index [111]; (3) metrics relating to focal species, by examining the fate of organisms with similar traits to those species, although important species-specific factors may not be captured that way; and (4) dynamic ecosystem measures, such as stability (the magnitude of temporal variation in ecosystem properties) or resilience (predicted time to recover from a perturbation). A unique advantage of GEM-like models relative to statistical modelling approaches is their capacity to model completely novel perturbation scenarios—that is, perturbations for which there are no data, experiments, or observations. The structure of this type of model also allows for a wide set of anthropogenic perturbations to be considered simultaneously. For example, such models will be able to simulate how whole ecosystems respond to, and feed back upon, the effects of changes in atmospheric carbon dioxide concentrations on plants; altered climate on all organisms and ecological processes; harvesting of animals, land-use change, and harvesting of vegetation; invasive species; and toxic pollutants. The effects of these disparate PLOS Biology | www.plosbiology.org 20 April 2014 | Volume 12 | Issue 4 | e1001841
- 21. perturbations could be measured using a common set of metrics. Considering these impacts together in a GEM should allow for much more holistic understanding, and management, of the world’s ecosystems, which will make GEMs a powerful tool for bodies such as the Intergovernmental Platform on Biodiversity and Ecosystem Services. Conclusions We have developed the first General Ecosystem Model (GEM) that synthesizes fundamental aspects of ecological theory, to model, simulate, and predict how the structure and function of ecosystems at multiple scales emerges from the biology and interactions of individual organisms. Our model matches a broad range of empirical data well, to a first approximation. Where it departs from either observations or expectations, it does so in ways that afford interesting avenues for future ecological research, future model development, and empirical data collection. It also provides a set of novel predictions that can be independently assessed. We anticipate that this will be the beginning of a long-term exploration of GEMs, and we call upon ecologists, biologists, mathematicians, and computer scientists to join in creating a modelling community surrounding GEMs that can catalyse the development of more realistic, sophisticated, yet better understood models of ecosystems worldwide. Our hope is that GEMs will form the basis of new science in ecology and, in particular, science that proves actionable to those charged with conserving the biosphere on which we all depend. Supporting Information Figure S1 Cohort dispersal effects on autotrophic and heterotrophic biomass. The difference between fracturing cohort and whole cohort dispersal expressed as a percentage of the whole cohort dispersal value. Percentage differences were calculated over a 10610 grid of 1u61u marine grid cells extending from 30u to 40uN and 40u to 30uW, using median and annual mean biomasses from an ensemble of 10 simulations for both fracturing cohort and whole cohort dispersal. Negative values therefore indicate lower biomass in the fracturing cohort ensemble median, whereas positive values indicate the opposite. (TIFF) Figure S2 Cohort number effects on long-term means of trophic-level biomass. Medians from the mean over the last 5 y of ensembles of 20 replicate simulations (points) and absolute ranges (error bars) of biomass densities for autotrophs (dark green lines and dark green squares), herbivores (green lines and green circles), omnivores (blue lines and blue triangles), and carnivores (red lines and red diamonds). Ensembles of replicates were run with a threshold of 500, 1,000, 5,000, or 10,000 cohorts per grid cell for terrestrial cell T1 and marine cell M1 (Table 4). (TIFF) Figure S3 Emergent model growth rates compared to theoretical maximum rates. (A) Absolute emergent model growth rate (grey crosses and diamonds) relationship with body mass compared with empirical (black points) and theoretical maximum (red line). (B) The relationship between emergent model growth rate as a fraction of theoretical maximum growth rate (grey open circles) and body mass for each trophic level in terrestrial or marine cells. Modelled emergent individual-level properties are sampled from 100-y model runs for the four focal grid cells (Table 4). (TIFF) A Mechanistic General Model of Global Ecosystems Figure S4 Trophic abundance pyramids. Community-level abundance pyramids across all cohorts belonging to each trophic level emergent from the model for an example of terrestrial and marine grid cell (grid cells T1 and M1 from Table 4). Results are from the final year of a 100-y model run. Light green represents herbivores, blue represents omnivores, and red represents carnivores. Total abundance densities (1,000 s individ-uals/ km2) are indicated by the widths (after log-transformation) and numbers within the boxes. (TIF) Figure S5 Comparison of model predicted with empir-ical normalised body mass spectra (NBS). Frequency distribution of the slope of NBS from [75] with model-derived NBS slope values, calculated following Sprules and Munawar [114], for carnivores (red), omnivores (blue), and herbivores (green). Triangles correspond to slopes for the low productivity, aseasonal marine cell (M1, Table 4) and circles to the high productivity, aseasonal terrestrial cell (T1, Table 4). (TIF) Figure S6 Relationships between predicted biomass densities and NPP. The global relationship between total heterotrophic biomass and NPP split between terrestrial and marine realms (A). The global relationship between the ratio of herbivore to autotroph biomasses and NPP split between terrestrial and marine realms (B). The relationships between different trophic levels and NPP across terrestrial (C) and marine (D) environments. The relationship between autotroph biomass and NPP across terrestrial (E) and marine environments (F) with heterotrophs modelled explicitly ‘‘full’’ and constant proportional autotroph herbivory loss rates of 0.25, 0.5, and 0.75. (TIFF) Figure S7 Frequency distributions of trophic biomass structure. Frequency distributions of log-transformed ratios of trophic-level biomasses in terrestrial grid cells (brown) and marine grid cells (blue), for H:A= herbivore to autotroph, O:H = omni-vore to herbivore, C:H =carnivore to herbivore, and C:O= car-nivore to omnivore biomass ratio. Red dashed lines indicate where the biomass ratio equals 1.0, which means equality of the two trophic-level biomasses. (TIFF) Figure S8 Spatial extent of un-inverted marine trophic structure for the bottom two trophic levels: herbivores and autotrophs. Spatial locations (green points) of un-inverted herbivores to autotroph trophic structure (i.e., where there is less herbivore than autotroph biomass) in (A) a simulation where dispersal was permitted (Study 4, Table 3) and (B) when dispersal is not modelled. (TIFF) Figure S9 Frequency distribution of marine trophic structure in the absence of dispersal. Frequency distribu-tions of log-transformed ratios of trophic-level biomasses in marine grid cells with dispersal (upper set of histograms—Study 4, Table 3) and marine grid cells without any dispersal modelled (lower set of histograms). H:A, herbivore to autotroph; O:H, omnivore to herbivore; C:H, carnivore to herbivore; C:O, carnivore to omnivore biomass ratio. Red dashed lines indicate where the biomass ratio equals 1.0, which means equality of the two trophic-level biomasses. (TIFF) Figure S10 The effects of turnover rates and trophic transfer efficiencies on marine trophic structure. Box PLOS Biology | www.plosbiology.org 21 April 2014 | Volume 12 | Issue 4 | e1001841
- 22. and whisker plots of the predicted ratios of trophic levels (H:A, herbivore to autotroph; O:H, omnivore to herbivore; C:H, carnivore to herbivore; C:O, carnivore to omnivore biomass ratio) for ensembles of 10 replicate simulations with different model assumptions investigating the mechanisms giving rise to inverted marine trophic biomass structure: N, the full model for a single grid cell; H, herbivore assimilation efficiency reduced to 20% (from 60–70% omnivore–herbivore); HP, herbivore and predator assimilation efficiency reduced to 20% (from 60–80% omnivore–carnivore); A, attack rates of herbivores and predators decreased by two orders of magnitude; AHP, combined reduction of attack rates, herbivore assimilation, and predator assimilation as above. Dark bars indicate median values, boxes the interquartile ranges, and whiskers the maximal range. Upper panels correspond to grid cell M1 and lower panels to grid cell M2 (Table 4). (TIFF) Figure S11 Community-level properties for cell T1 with all edible plant matter available for herbivory. Trophic pyramid and size distribution spectra for focal cell T1 with the value of parameter wherb,f equal to 1 for terrestrial herbivores, which means that each terrestrial herbivore cohort experiences 100% of the edible plant matter in the grid cell when it is eating. The release of this parameter does not affect the low herbivore to primary producer ratio for terrestrial communities. Here, the ratio is 1.0%, marginally higher than that calculated for the same location using a value for wherb,f of 10% (Figure 4). (TIFF) Table S1 Environmental data sources. External global environmental data sources used within the model. Units represent those used within the Madingley model, not those of the original source data. a Environmental variables were long-term/multi-decadal average values. (DOCX) Table S2 Model parameters and their values. (DOCX) Table S3 Empirical estimates of trophic-level biomass-es in globally widespread ecosystems in both marine and terrestrial environments. Notes: 1. Consider only the pelagic producers. Assume that dissolved organic carbon (DOC) and suspended particulate organic carbon (POC) are available to the pelagic community. Do not include benthic suspension feeders. Assume micro-zooplankton are herbivores (as defined in our model). For omnivores and carnivores, assume that the proportion of biomass that is supported originally by pelagic primary production is equal to the proportional rate of consumption of pelagically derived foods relative to consumption of foods from all sources. 2. From Table 12.2 (plants taken as above ground vascular + Moss + Algae + Lichens) of Chapin et al [115]. 3. Herbivore biomass taken from [73]. 4. Producer and herbivore biomasses from [73]. 5. Producer biomass of 9,999 g C m-2 comes from Figure 8 of Frangi and Lugo [116]. Montane palm floodplain forest; herbivore biomass taken from [73]. (DOCX) A Mechanistic General Model of Global Ecosystems Table S4 Comparison of emergent individual-level properties from the model with observations. The slopes and intercepts of the relationships between predicted properties and body mass compared to empirical data. The probability that the slope and intercept of the predicted relationship were different from those for the empirical data was calculated as the t statistic of linear models fitted to combined model and empirical data for each emergent property using a categorical factor to indicate a model or empirical datum. The probability that the t statistic for the model including the categorical factor indicates the signifi-cance of the difference. (DOCX) Table S5 Summary statistics of empirical community herbivore and primary producer biomasses. Summary statistics, derived from [73], for those ecosystem types most closely representing the ecosystems within the two grid cells shown in Figure 3. PB, primary producer biomass; HB, herbivore biomass. Median herbivore biomass in temperate and tropical grassland ecosystems is 52.3% of that in communities of marine phyto-plankton, whereas median primary producer biomass is 57 times larger in the terrestrial compared to the marine ecosystem. (DOCX) Table S6 Comparison of abundance–density slopes predicted by the model with observed slopes. Abun-dance– density relationships predicted by the model (for cells T1 and M1, Table 4) compared with observations. Empirical abundance–density relationships were derived from Jennings et al. [74]. The reported total biomass versus body mass relationships were converted to abundance versus body mass relationships, by dividing the total biomass in each mass bin by the central mass of that mass bin, which can be approximated as subtracting 1 from the slope of total biomass against body mass. (DOCX) Text S1 Technical and mathematical details of the model. (DOCX) Text S2 Model time step effects. (DOCX) Acknowledgments We thank L. Joppa for engaging in discussion and ideas that helped us to conceptualize the model and A. Blandon, K. Boughey, and E. Pynegar for compiling empirical data with which to compare the model. Author Contributions The author(s) have made the following declarations about their contributions: Conceived and designed the experiments: MH TN DT SE JH VL MJS JPWS DWP. Performed the experiments: MH TN DT. Analyzed the data: MH TN DT MS DP. Contributed reagents/materials/ analysis tools: MH TN DT MS VL DP. Wrote the paper: MH TN DT SE JH MJS JPWS DWP. 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