What prevents natural populations from reaching unbounded exponential growth? The two main mechanisms are regulation by other species (starvation when prey are scarce; consumption when predators are abundant), and regulation by conspecifics due to crowding, interference, or intraspecific competition - what is generally known as "self-regulation". Though self-regulation must certainly play a role at very high abundances (due for example to spatial crowding), probing its influence at the population densities observed in natural systems is a formidable challenge from an empirical point of view. This led to theoretical explorations of this question, resulting in two opposing camps: "self-regulationists" maintain that strong self-effects are quite common in nature, affecting maybe as many as half of all species (e.g., Yodzis 1981 Nature, Sterner et al. 1997 Ecology), while the opposing camp posits that only producers and maybe top predators experience non-negligible self-regulation, as championed by Pimm in his influential book "Food Webs" (1982). Here we apply newly published mathematical methods to ask how common self-regulation must be for large ecological networks to be locally stable.
We present a theoretical analysis showing that empirical food web structures cannot be stabilized unless an overwhelming majority of species exhibit substantially strong self-regulation. We support our finding by deriving a general analytical formula predicting the effects of self-regulation on network stability with high accuracy. Using this result, we show that even for random networks, as well as networks with cascade structure, stability requires negative self-effects for almost all species. The implications are far-reaching and pose a strong dilemma to ecologists: either self-regulation is far more prevalent than even self-regulationists have previously thought, or else the idea of locally stable communities needs to be abandoned.