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ecological complexity 5 (2008) 140–145
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Ecological community integration increases with added
trophic complexity
Christopher K. Wright *
U.S. Geological Survey Center for Earth Resources Observation and Science, 47914 252nd Street, Sioux Falls, SD 57198-0001, United States
article info
abstract
Article history:
The existence of functional biological organization at the level of multi-species commu-
Received 12 February 2007
nities has long been contested in ecology and evolutionary biology. I found that adding a
Received in revised form
trophic level to simulated ecological communities enhanced their ability to compete at the
5 October 2007
community level, increasing the likelihood of one community forcing all or most species in a
Accepted 25 October 2007
second community to extinction. Community-level identity emerged within systems of
Published on line 20 February 2008
interacting ecological networks, while competitive ability at the community level was
enhanced by intense within-community selection pressure. These results suggest a reas-
Keywords:
sessment of the nature of biological organization above the level of species, indicating that
Ecological organization
the drive toward biological integration, so prominent throughout the history of life, might
Metacommunities
extend to multi-species communities.
# 2007 Elsevier B.V. All rights reserved.
Levels of selection
Lotka-Volterra
Predator-prey
Dynamical systems
1.
Introduction
A fundamental question in ecology is whether communities
of co-existing species are organized by deterministic forces,
like competition and consumption, into functional wholes
possessing emergent properties (Clements, 1936; Odum,
1969; Pimm, 1991), or are simply random assortments of
species with similar environmental requirements (Gleason,
1926; Whittaker, 1962; Hubbell, 2001). Parallel to this
question of holism in ecology is the levels of selection
debate in evolutionary biology (Reeve and Keller, 1999),
where individual selectionists (Williams, 1966) and proponents of selfish gene theory (Dawkins, 1976) have rejected
group selection and the idea of the superorganism (Wilson
and Sober, 1989).
Over a decade ago, Gilpin (1994) found that LotkaVolterra communities of competing species could form
entities capable of competing en masse against other such
entities. Although this finding has been confirmed (Toquenaga, 1997), its potential implications with respect to multispecies ecological organization have not been investigated
further. Here I extend Gilpin’s theoretical result from
competition-only systems to communities containing two
trophic levels.
One might imagine community-level competition occurring after some barrier between two separate communities
is removed. Indeed, Gilpin’s study was motivated by
Vermeij’s (1991) observation that large-scale biotic interchanges tend to be asymmetric (e.g., movement of species
between North America and South America following formation of the Isthmus of Panama), with more
species from one assemblage successfully invading
newly accessible habitat of another assemblage than vice
versa.
* Tel.: +1 605 594 2553; fax: +1 605 594 6529.
E-mail address: [email protected].
1476-945X/$ – see front matter # 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.ecocom.2007.10.004
ecological complexity 5 (2008) 140–145
2.
Methods
With some modification, I repeated Gilpin’s (1994) simulation
experiment, and then added a second trophic level (for ease of
exposition, two trophic-level systems are referred to as
predator-prey communities, but can also be thought of as
communities of primary producers and their consumers, or
plants and herbivores). Two different types of five-species
predator-prey communities were created. The first, what I call
‘naı̈ve communities’, contained four prey species and one
predator species that were mutually compatible with one
another de novo, i.e., no extinction events occurred when their
population trajectories were simulated over time. The second
type of five-species community was assembled via a sequence
of extinction events. These communities began with eight
prey species and two predator species, and only those systems
that collapsed to four prey species and a single predator were
kept. I call these ‘self-organized communities’.
Pairwise community mixing was simulated within source
pools of four different community types (one or two trophic
levels by naı̈ve or self-organized community assembly).
Competitive interactions in the lower trophic level were
specified such that, on average, intraspecific competition was
twice as strong as interspecific competition—assuming that
individuals from the same species, and sharing the same niche,
compete more intensely than different species occupying
similar, but not identical niches. Among predators, direct
intraspecific competition was set to zero, although indirect
competition was modeled implicitly by prey depletion. However, direct interspecific competition between predators was
allowed, representing behaviors where predators interfere with
other species’ access to prey, e.g., through territoriality or intraguild predation. Negative effects of predators on their prey were,
on average, an order-of-magnitude greater than reciprocal,
positive effects of prey on predators, reflecting intrinsic inefficiencies in converting prey individuals into predator offspring.
Following Gilpin (1994), I simulated the dynamics of single
trophic level communities using a normalized version of the
Lotka-Volterra equations:
dx
¼ xðb þ AxÞ;
dt
(1)
where population sizes are normalized by their carrying capacities. All elements of the b vector of intrinsic growth rates,
and all diagonal elements (intraspecific competition coefficients) of the community matrix, A, were set to one. With
these parameters fixed, different competition communities
were created by randomly specifying interspecific competition
coefficients on the off-diagonal elements of A from the uniform interval (1, 0).
In five-species predator-prey communities, one prey species
in x was replaced with a predator. Correspondingly, one
element in b was replaced with a density-independent predator
death rate of 0.1. Predator effects on prey species were
randomly sampled from the uniform interval (1, 0), while
positive effects of the four prey species on predators were
randomly sampled from a smaller uniform interval (0, 0.1).
Predator self-limitation, one diagonal element in A, was set to
zero. When more than one predator species was present (during
141
assembly of self-organized communities, and at the onset of
community mixing) interspecific competition coefficients were
randomly sampled from the uniform interval (1, 0).
In assembling naı̈ve and self-organized communities, I
simulated population trajectories over 104 time steps using a
4th-order Runge-Kutta method. Initial conditions were randomly drawn from a uniform (0, 1) distribution. If a
population’s size dropped below 105, it was set to zero. This
threshold reflected the vulnerability of very small populations
to stochastic events causing extinction. If communities
contained five species after 104 time steps, I checked
analytically whether they had an interior fixed point where
equilibrium population sizes were all greater than zero.
Communities that satisfied this criterion were added to source
pools for community mixing.
Randomly selected pairs of five-species communities were
mixed using an augmented community matrix:
A1;2 ¼
A1
C2
C1
:
A2
(2)
The two C matrices determined the effects of species in one
community on species in the other community, and were
randomly sampled from the same uniform distributions
determining interactions in the original communities. Note
that in Gilpin’s (11) study the C1 and C2 matrices were
symmetric, i.e. C2 ¼ C01 . This guaranteed that any given pair of
species from different communities had identical competitive
effects on one another. Although obviously not a realistic
simplification, Gilpin (1994) argued that balancing interactions
between species from different communities was necessary to
establish that asymmetric outcomes of community mixing
resulted from within-community, not between-community,
properties. I disagreed with this line of reasoning. My question
of interest was the effect of building five-species communities
in four different ways (one or two trophic levels by naı̈ve or
self-organized community assembly) on the outcome of
community competition. This was a within-community
treatment effect that I varied, all the while keeping the
mechanics of community mixing fixed.
Source pools for community mixing contained 20 communities. Within each pool, 2000 mixing trials were conducted,
with a new set of between-community interaction coefficients
randomly selected at the onset of each trial. Initial conditions for
the two communities were the same as their final values at the
end of the assembly process. Community dynamics were
simulated over 104 time steps and final community composition
was classified as symmetric or asymmetric. In asymmetric
outcomes, the post-mixing community contained four or five
species from one community, and zero or one species from the
other community. All other post-mixing combinations of species were classified as symmetric. Entire experiments – assembly
of 20 communities followed by 2000 mixing trials – were
repeated 20 times for each of the four community types (Fig. 1).
3.
Results
Community type had a substantial effect on the frequency of
asymmetric outcomes (Fig. 2, F3,76 = 175.1, P = 4.8E34). In
142
ecological complexity 5 (2008) 140–145
Fig. 1 – Flowchart of steps in community mixing experiments repeated for each of the four community types: naı̈ve
competition, self-organized competition, naı̈ve predator-prey, and self-organized predator-prey.
particular: (i) asymmetric outcomes were more frequent
among self-organized communities than in their naı̈ve
counterparts (P < 0.01); (ii) adding a predator increased
asymmetric outcomes in naı̈ve communities (P < 0.01), but
not to the level of self-organized prey communities (P < 0.01);
(iii) adding a predator increased asymmetric outcomes among
self-organized communities (P < 0.01). By results (ii) and (iii),
added trophic complexity generated an increase in ecological
organization—in the sense that such assembled five-species
communities had an elevated tendency to win or lose as
wholes, or nearly so.
Remarkably, well over one-third of mixing trials between
self-organized, predator-prey communities resulted in one
community dominating the other (Fig. 2). Under a null model
assuming that each species has the same probability of
Fig. 2 – Mean (WS.E.M.) number of asymmetric outcomes by
community type (n = 20 community assembly and mixing
experiments). All values are significantly different at the
P < 0.01 level (Bonferroni-adjusted multiple comparison
test).
extinction (Pextinction = 0.43, the observed extinction rate over
all mixing trials), the probability of these results was vanishingly small (expected value = 130 asymmetric outcomes in
2000 community mixing trials, x2 = 62,926, d.f. = 19,
P < 1.0E307). Among asymmetric outcomes, the winning
community retained all five of its species while forcing all
species from the other community to extinction in an average
of 283 22 (S.E.M.) mixing trials, significantly more instances
(n = 20, t = 8.1, P = 8.4E09) than when naı̈ve predator-prey
communities were mixed (mean number of complete victories
by one community = 86 11).
The process by which pools of naı̈ve and self-organized
communities were created was essentially a form of artificial
selection on the coefficients determining interactions
between species, or the off-diagonal elements of the community matrix in Eq. (1). Among self-organized predator-prey
communities, the distributions of prey competition coefficients, and the effects of predators on prey species, were both
shifted toward weaker interactions relative to naı̈ve communities (Fig. 3). These shifts are consistent with other studies
demonstrating the importance of weak interspecific interactions in promoting community persistence (May, 1972;
McCann et al., 1998; Kokkoris et al., 1999).
Notably, naı̈ve and self-organized predator-prey communities had very different attractors. Jacobian matrices evaluated at the interior fixed point of each self-organized
predator-prey community each had one eigenvalue with a
positive real component, i.e., each community’s fixed point
was a saddle, with both stable and unstable manifolds. By
contrast, all but seven naı̈ve predator-prey communities had
an asymptotically stable interior fixed point.
4.
Discussion
Community integration, or the tendency of Lotka-Volterra
communities to compete against one another as whole
ecological complexity 5 (2008) 140–145
143
Fig. 3 – Distributions of prey competition coefficients and predator effects on prey. Histograms (a) and (c) were assembled
from the 400 naı̈ve predator-prey communities created over the course of this study. Histograms (b) and (d) were compiled
from 400 self-organized predator-prey communities.
entities, is of obvious benefit to species from the winning
community, and allows rare species to persist in the face of
disruption from other communities. But integration also
imposes costs—particularly on dominant species of the losing
community. Community integration increases the ability of
some communities to resist perturbation, while at the same
time making other communities sensitive to wholesale
invasion. Perhaps this dynamic played a role in the globally
observed pattern of asymmetric biotic interchange (Vermeij,
1991). As human activities eliminate barriers separating
communities (e.g., by construction of canals, long-distance
transport of multiple species, etc.) or force separate communities to occupy common habitat (due to habitat destruction or
global warming-induced shifts in species distributions),
asymmetric community competition could potentially generate cascades of species extirpations.
A recurring theme in the history of life is the combination
of previously independent components as a basis for major
evolutionary transitions, e.g., in the origins of chromosomes,
eukaryotes, sexual reproduction, multicellular organisms, and
social groups (Maynard Smith and Szathmáry, 1998). Vermeij
(2006) recently commented, ‘‘Union, cooperation, and integration are so widely advantageous by enhancing power and
competitive ability that selection favoring them should be
strong and common regardless of the hierarchical level at
which unions take place.’’ From this perspective, it would
seem odd if the drive toward biological integration did not
extend to multi-species communities.
One argument that ecological communities are not
functional unions is that they lack a degree of individuality
and separateness from other entities of the same kind
(Maynard Smith and Szathmáry, 1998). But synonymous
with the property of community integration is a type of
community identity. Given a propensity to not mix randomly,
the theoretical communities in this study exhibit a degree of
boundedness. This identity is by no means complete—in
some asymmetric outcomes one species from the losing
community remains or one species from the winning
community goes extinct. Nonetheless, there is an underlying
dynamical attractor that increases in strength as a trophic
level is added or communities are self-organized prior
to mixing.
144
ecological complexity 5 (2008) 140–145
The probability of a randomly constructed 10-species
Lotka-Volterra system having a stable fixed point is low
(May, 1972), and thus mixed communities are expected to
collapse, with the probability of stability increasing with
decreasing dimensionality. However, the mixed communities
that I constructed were only semi-random, containing fivespecies subcommunities known to be bi-stable or asymptotically stable in 5D space. These subcommunities bias the
collapse of higher dimensional systems toward combinations
of species dominated by one community. This type of attractor
– acting on concatenated dynamical systems – has not been
described in the dynamical systems literature, to the best of
my knowledge, and is the source of apparent community
identity. Gilpin’s (1994) original contribution was to show that
community identity emerged spontaneously from competitive
interactions combining elements of both spatial segregation
and mixing. I find that adding additional aspects of biological
reality exaggerates this tendency. Although my predator-prey
model remains a relatively simple caricature of underlying
reality, perhaps this phenomenon is common to more
complicated, realistic models and, more importantly, actually
operates in nature.
The ability of Lotka-Volterra communities to compete en
masse presents a scenario in which, given some initial degree
of spatial segregation, a population of communities, or a
metacommunity (Wilson, 1992), could form—with individual
subcommunities exhibiting differential fitness as conditions
allow them to interact. Within this scenario we have the
essential elements necessary for natural selection to operate
at the community level (Wilson, 1992; Johnson and Boerlisjt,
2002). However, theories of multi-level natural selection
assume a conflict between levels such that selection within
communities favors species that disrupt community-level
function (Wilson and Sober, 1989; Wilson, 1992; Reeve and
Keller, 1999; Johnson and Boerlisjt, 2002). But, in building selforganized communities, I found that the collapse of 10-species
systems resulted in five-species communities that were more
integrated than their naı̈ve counterparts (Fig. 2). Intense
within-community selection was disruptive of larger communities, but the end result was to enhance community-level
function (albeit in smaller communities). Within-community
selection, by increasing community integration, or, conversely, by engendering community identity, set the stage for
between-community selection to occur.
The Lotka-Volterra equations belong to the more general
class of replicator equations (Schuster and Sigmund, 1983;
Hofbauer and Sigmund, 1998), which have been applied in
population genetics (Fisher, 1930), prebiotic chemistry (Eigen
and Schuster, 1979), game theory (Taylor and Jonker, 1978),
and economics (Standish, 2000). This wide-ranging homology
suggests that the Lotka-Volterra equations are a canonical
model for the study of complex systems. In terms of generality, the state variables ‘species’ might be replaced with ‘agents’
(e.g., genes, individuals, business firms, or nation-states) in
the models studied. We then have a mechanism whereby
agents acting solely in their own self-interest might form
higher-level entities with both potential benefits and costs to
individual constituents. The key insight is to treat agents not
as if they are isolated within a single network, but as being
embedded within a matrix of interacting networks, where the
fate of agents is tied to the members of their local network as
they interact with members of a more distant network.
The increase in ecological organization that I attribute to
added trophic complexity is obviously limited to a universe of
five-species Lotka-Volterra communities under a prescribed
set of conditions. Whether demonstration of community-level
competition, in theory, is representative of a real ecological (or
wider-ranging) phenomenon remains to be seen. It is striking,
however, that the novel behavior of the Lotka-Volterra
equations that Gilpin (1994) originally discovered, and I have
expanded upon, has gone unnoticed in such a well-studied
and venerable model. In our models, perhaps we look for that
which we believe possible. The possibility that ecological
communities might form integrated, novel evolutionary
entities deserves serious re-examination.
Acknowledgements
This research was developed while the author was a National
Research Council Postdoctoral Associate at the U.S. Geological
Survey Center for Earth Resources Observation and Science.
The author thanks Michael Gilpin, Guy Hoelzer, Robert May,
and an anonymous reviewer for helpful comments on earlier
drafts of the manuscript.
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