Gellner, Gabriel; Kevin McCann and Alan Hastings

Ecologists have long sought to understand how diversity and structure mediate the stability of whole ecosystems. For high-diversity food webs, the interactions between species are typically represented using matrices with randomly chosen interaction strengths. Unfortunately, this procedure tends to produce ecological systems with no underlying equilibrium solution, and so ecological inferences from this approach may be biased by nonbiological outcomes. Using recent computationally efficient methodological advances from metabolic networks, we employ for the first time an inverse approach to diversity–stability research. We compare classical random interaction matrices of realistic food web topology (hereafter the classical model) to feasible, biologically constrained, webs produced using the inverse approach. We show that an energetically constrained feasible model yields a far higher proportion of stable high-diversity webs than the classical random matrix approach. When we examine the energetically constrained interaction strength distributions of these matrix models, we find that although these diverse webs have consistent negative self-regulation, they do not require strong self-regulation to persist. These energetically constrained diverse webs instead show an increasing preponderance of weak interactions that are known to increase local stability. Further examination shows that some of these weak interactions naturally appear to arise in the model food webs from a constraint-generated realistic generalist–specialist trade-off, whereby generalist predators have weaker interactions than more specialized species. Additionally, the inverse technique we present here has enormous promise for understanding the role of the biological structure behind stable high-diversity webs and for linking empirical data to the theory.