Bounds on Transient Instability for Complex Ecosystems

Transient dynamics in a nonequilibrium superdiffusive reaction-diffusion process: Nonequilibrium random search as a case study

Transient regimes, often difficult to characterize, can be fundamental in establishing final steady states features of reaction-diffusion phenomena. This is particularly true in ecological problems. Here, through both numerical simulations and an analytic approximation, we analyze the transient of a nonequilibrium superdiffusive random search when the targets are created at a certain rate and annihilated upon encounters (a key dynamics, e.g., in biological foraging). The steady state is achieved when the number of targets stabilizes to a constant value. Our results unveil how key features of the steady state are closely associated to the particularities of the initial evolution. The searching efficiency variation in time is also obtained. It presents a rather surprising universal behavior at the asymptotic limit. These analyses shed some light into the general relevance of transients in reaction-diffusion systems.

Degree heterogeneity and stability of ecological networks

A classic measure of ecological stability describes the tendency of a community to return to equilibrium after small perturbations. While many advances show how the network architecture of these communities severely constrains such tendencies, one of the most fundamental properties of network structure, i.e. degree heterogeneity-the variability of the number of links associated with each species, deserves further study. Here we show that the effects of degree heterogeneity on stability vary with different types of interspecific interactions. Degree heterogeneity consistently destabilizes ecological networks with both competitive and mutualistic interactions, while its effects on networks of predator-prey interactions such as food webs depend on prey contiguity, i.e. the extent to which the species consume an unbroken sequence of prey in community niche space. Increasing degree heterogeneity tends to stabilize food webs except those with the highest prey contiguity. These findings help explain why food webs are highly but not completely interval and, more broadly, deepen our understanding of the stability of complex ecological networks.

Correction: Bounds on Transient Instability for Complex Ecosystems

[This corrects the article DOI: 10.1371/journal.pone.0157876.].