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Register a new userReconciling cooperation, biodiversity and stability in complex ecological communities
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Empirical observations show that ecological communities can have a huge number of coexisting species, also with few or limited number of resources. These ecosystems are characterized by multiple type of interactions, in particular displaying cooperative behaviors. However, standard modeling of population dynamics based on Lotka-Volterra type of equations predicts that ecosystem stability should decrease as the number of species in the community increases and that cooperative systems are less stable than communities with only competitive and/or exploitative interactions. Here we propose a stochastic model of population dynamics, which includes exploitative interactions as well as cooperative interactions induced by cross-feeding. The model is exactly solved and we obtain results for relevant macro-ecological patterns, such as species abundance distributions and correlation functions. In the large system size limit, any number of species can coexist for a very general class of interaction networks and stability increases as the number of species grows. For pure mutualistic/commensalistic interactions we determine the topological properties of the network that guarantee species coexistence. We also show that the stationary state is globally stable and that inferring species interactions through species abundance correlation analysis may be misleading. Our theoretical approach thus show that appropriate models of cooperation naturally leads to a solution of the long-standing question about complexity-stability paradox and on how highly biodiverse communities can coexist.
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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.
Forty years ago, Robert May questioned a central belief in ecology by proving that sufficiently large or complex ecological networks have probability of persisting close to zero. To prove this point, he analyzed large networks in which species interact at random. However, in natural systems pairs of species have well-defined interactions (e.g., predator-prey, mutualistic or competitive). Here we extend Mays results to these relationships and find remarkable differences between predator-prey interactions, which increase stability, and mutualistic and competitive, which are destabilizing. We provide analytic stability criteria for all cases. These results have broad applicability in ecology. For example, we show that, surprisingly, the probability of stability for predator-prey networks is decreased when we impose realistic food web structure or we introduce a large preponderance of weak interactions. Similarly, stability is negatively impacted by nestedness in bipartite mutualistic networks.
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