Abstract

The stability of ecological systems has been a long-standing focus of ecology. Recently, tools from random matrix theory have identified the main drivers of stability in ecological communities whose network structure is random. However, empirical food webs differ greatly from random graphs. For example, their degree distribution is broader, they contain few trophic cycles, and they are almost interval. Here we derive an approximation for the stability of food webs whose structure is generated by the cascade model, in which ‘larger' species consume ‘smaller' ones. We predict the stability of these food webs with great accuracy, and our approximation also works well for food webs whose structure is determined empirically or by the niche model. We find that intervality and broad degree distributions tend to stabilize food webs, and that average interaction strength has little influence on stability, compared with the effect of variance and correlation.

Highlights

  • The stability of ecological systems has been a long-standing focus of ecology

  • We show numerically that our approximation estimates the stability of these food webs with great accuracy, and that similar results are obtained when we generate food webs starting from empirical data, or when using the niche model[10]

  • We show that intervality and broad degree distributions tend to stabilize food webs, and we highlight a counterintuitive result: research on the relationship between stability and the distribution of interaction strengths has historically focused on average strength[11,12,13,14], we show that its role in determining stability is small, compared with that of variance and correlation

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Summary

Introduction

The stability of ecological systems has been a long-standing focus of ecology. Recently, tools from random matrix theory have identified the main drivers of stability in ecological communities whose network structure is random. In empirical webs the degree distribution, describing the number of partners each species interact with, is much broader[6] than in random graphs; the webs contain only a handful of trophic cycles[7] (in which, for example, species a consumes b, b consumes c and c consumes a), while random graphs with the same number of links would contain many more; empirical webs are almost interval—there is a way to order all species such that consumers tend to prey on consecutive species in the hierarchy[8] To overcome this limitation, we derive an approximation for the stability of food webs whose structure is generated by the cascade model[9], which assumes that species can be ordered such that ‘larger’ species consume ‘smaller’ ones. We show that intervality and broad degree distributions tend to stabilize food webs, and we highlight a counterintuitive result: research on the relationship between stability and the distribution of interaction strengths has historically focused on average strength[11,12,13,14], we show that its role in determining stability is small, compared with that of variance and correlation

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