Self-regulation and the stability of large ecological networks.

The stability of complex ecological networks depends both on the interactions between species and the direct effects of the species on themselves. These self-effects are known as 'self-regulation' when an increase in a species' abundance decreases its per-capita growth rate. Sources of self-regulation include intraspecific interference, cannibalism, time-scale separation between consumers and their resources, spatial heterogeneity and nonlinear functional responses coupling predators with their prey. The influence of self-regulation on network stability is understudied and in addition, the empirical estimation of self-effects poses a formidable challenge. Here, we show that empirical food web structures cannot be stabilized unless the majority of species exhibit substantially strong self-regulation. We also derive an analytical formula predicting the effect of self-regulation on network stability with high accuracy and show that even for random networks, as well as networks with a cascade structure, stability requires negative self-effects for a large proportion of species. These results suggest that the aforementioned potential mechanisms of self-regulation are probably more important in contributing to the stability of observed ecological networks than was previously thought.