The stability of large food webs
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 much broader, they contain few or no 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, and whose interaction strengths are sampled from an empirical distribution obtained via body-size scaling theory. 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 show that intervality and broad degree distributions tend to stabilize food webs, and we highlight a counterintuitive result: though research on the relationship between stability and the distribution of interaction strengths has historically focused on average strength, we show that its role in determining stability is small, compared to that of variance and correlation.