Persistence and flow reliability in simple food webs

Science, 2009

Insights into what stabilizes natural food webs have always been limited by a fundamental dilemma: studies either need to make unwarranted simplifying assumptions, undermining their relevance, or only examine few replicates of small food webs, hampering the robustness of findings. Here we use generalized modeling to study several billion replicates of food webs with nonlinear interactions and up to 50 species. In this way, we show, first, that higher variability in link strengths stabilizes food webs only when webs are relatively small, whereas larger webs are instead destabilized. Second, we reveal a new power law describing how food-web stability scales with the number of species and their connectance. Third, we report two universal rules: food-web stability is enhanced when (i) species at high trophic level feed on multiple prey species and (ii) species at intermediate trophic level are fed upon by multiple predator species. Understanding the dynamic properties of food webs is a problem of both theoretical and practical importance (1-16), especially as concerns about the robustness of natural systems escalate. Further, the discovery of stabilizing factors in food webs can yield much-needed design principles for institutional networks (17). Robert May (1) showed that randomly assembled webs became less robust (measured in terms of their dynamical stability) as their complexity (measured in terms of the number of interacting species and their connectivity) increased. While it has often been pointed out that food webs can persist in non-stationary states, there is growing evidence that May's stability-complexity relationship also holds for non-stationary dynamics (18). Moreover, population cycles or external forcing averages out if food webs are considered on longer timescales, so that time-averaged dynamics can be considered as stationary. However, detailed investigations aiming at a deeper understanding of what makes food webs robust have generally been hampered by computational constraints (e.g., 12). Here, we avoid these constraints through the use of generalized modeling (19,20). For a given class of mathematical models, generalized modeling (GM) identifies para

2014

Why are large, complex ecosystems stable? Both theory and simulations of current models predict the onset of instability with growing size and complexity, so for decades it has been conjectured that ecosystems must have some unidentified structural property exempting them from this outcome. We show that 'trophic coherence' -- a hitherto ignored feature of food webs which current structural models fail to reproduce -- is a better statistical predictor of linear stability than size or complexity. Furthermore, we prove that a maximally coherent network with constant interaction strengths will always be linearly stable. We also propose a simple model which, by correctly capturing the trophic coherence of food webs, accurately reproduces their stability and other basic structural features. Most remarkably, our model shows that stability can increase with size and complexity. This suggests a key to May's Paradox, and a range of opportunities and concerns for biodiversity conservation.

Communications in Nonlinear Science and Numerical Simulation, 2019

New results are collected using the Webworld model which simulates evolutionary food web construction with population dynamics [1]. We show that it supports a link-species relationship of neither constant link-density nor constant connectance, and new properties for the food webs are calculated including clustering coefficients and stability in the sense of community robustness to species deletion. Time-series for more than 40 properties of the taxonomic and trophic webs are determined over the course of individual simulations. Robustness is found to be positively correlated with connectance, but negatively with diversity, and we study the long-term development of model webs including the distribution of extinction events in a simulation with 10 8 speciation events.

Theoretical Population Biology, 1979

arXiv (Cornell University), 2014

A classic measure of ecological stability describes the tendency of a community to return to equilibrium after small perturbation. While many advances show how the network structure of these communities severely constrains such tendencies, few if any of these advances address one of the most fundamental properties of network structure: heterogeneity among nodes with different numbers of links. Here we systematically explore this property of "degree heterogeneity" and find that its effects on stability systematically vary with different types of interspecific interactions. Degree heterogeneity is always destabilizing in ecological networks with both competitive and mutualistic interactions while its effects on networks of predator-prey interactions such as food webs depend on prey contiguity, i.e., the extent to which the species consume an unbroken sequence of prey in community niche space. Increasing degree heterogeneity stabilizes food webs except those with the most contiguity. These findings help explain previously unexplained observations that food webs are highly but not completely contiguous and, more broadly, deepens our understanding of the stability of complex ecological networks with important implications for other types of dynamical systems. Understanding the intricate relationship between the structure and dynamics of complex ecological systems has been one of the key issues in ecology [1-4]. Equilibrium stability of ecological systems, a measure that considers an ecological system stable if it returns to its equilibrium after a small perturbation, has been a central research topic for over four decades [1, 5-15]. Empirical observations suggest that communities with more species are more stable, i.e., a positive diversity-stability relationship [16]. Yet, these intuitive ideas were challenged by

2005

Food webs are one of the most useful, and challenging, objects of study in ecology. These networks of predator-prey interactions, conjured in Darwin's image of a "tangled bank," provide a paradigmatic example of complex adaptive systems. While it is deceptively easy to throw together simplified caricatures of feeding relationships among a few taxa as can be seen in many basic ecology text books, it is much harder to create detailed descriptions that portray a full range of diversity of species in an ecosystem and the complexity of interactions among them ( ). Difficult to sample, difficult to describe, and difficult to model, food webs are nevertheless of central practical and theoretical importance. The interactions between species on different trophic (feeding) levels underlie the flow of energy and biomass in ecosystems and mediate species' responses to natural and unnatural perturbations such as habitat loss. Understanding the ecology and mathematics of food webs, and more broadly, ecological networks, is central to understanding the fate of biodiversity and ecosystems in response to perturbations.

We use a network-theoretic approach to address questions about the evolution of food-web characteristics under fluctuating environments. Our model is a weighted, directed graph with nodes representing populations and edges the interactions between them. The dynamics of the network are driven by stochastic generalized Lotka-Volterra equations. Networks evolve by extinction due to interand intra-specific density effects, followed by probabilistic recolonization and speciation. We use numerical simulations and analytical calculations to understand the effects of different kinds of stochasticity on network evolution. The results provide multiple insights about the relationship between environmental uncertainty and food-web evolution as well as the structural and dynamical properties of emergent food-webs. In particular, we show that demographic and environmental stochasticity can have unpredictable and sometimes counterintuitive effects, that stability and certain topological features can be associated with the environmental conditions in which food-webs assemble and persist, and that foodwebs can achieve stability by selection for specific life history distributions of component populations.

Journal of Theoretical Biology, 2009

To understand the dynamics of natural species communities, a major challenge is to quantify the relationship between their assembly, stability, and underlying food web structure. To this end, two complementary aspects of food web structure can be related to community stability: sign structure, which refers to the distributions of trophic links irrespective of interaction strengths, and interaction strength structure, which refers to the distributions of interaction strengths with or without consideration of sign structure. In this paper, using data from a set of relatively well documented community food webs, I show that natural communities generally exhibit a sign structure that renders their stability sensitive to interaction strengths. Using a Lotka-Volterra type population dynamical model, I then show that in such communities, individual consumer species with high values of a measure of their total biomass acquisition rate, which I term ''weighted generality'', tend to undermine community stability. Thus consumer species' trophic modules (a species and all its resource links) should be ''selected'' through repeated immigrations and extinctions during assembly into configurations that increase the probability of stable coexistence within the constraints of the community's trophic sign structure. The presence of such constraints can be detected by the incidence and strength of certain non-random structural characteristics. These structural signatures of dynamical constraints are readily measurable, and can be used to gauge the importance of interaction-driven dynamical constraints on communities during and after assembly in natural communities.

Journal of the Royal Society, Interface, 2017

A classic measure of ecological stability describes the tendency of a community to return to equilibrium after small perturbations. While many advances show how the network architecture of these communities severely constrains such tendencies, one of the most fundamental properties of network structure, i.e. degree heterogeneity-the variability of the number of links associated with each species, deserves further study. Here we show that the effects of degree heterogeneity on stability vary with different types of interspecific interactions. Degree heterogeneity consistently destabilizes ecological networks with both competitive and mutualistic interactions, while its effects on networks of predator-prey interactions such as food webs depend on prey contiguity, i.e. the extent to which the species consume an unbroken sequence of prey in community niche space. Increasing degree heterogeneity tends to stabilize food webs except those with the highest prey contiguity. These findings he...

2014

Food webs have markedly non-random network structure. Ecologists maintain that this non-random structure is key for stability, since large random ecological networks would invariably be unstable and thus should not be observed empirically. Here we show that a simple yet overlooked feature of natural food webs, the correlation between the effects of consumers on resources and those of resources on consumers, substantially accounts for their stability. Remarkably, random food webs built by preserving just the distribution and correlation of interaction strengths have stability properties similar to those of the corresponding empirical systems. Surprisingly, we find that the effect of topological network structure on stability, which has been the focus of countless studies, is small compared to that of correlation. Hence, any study of the effects of network structure on stability must first take into account the distribution and correlation of interaction strengths.