Dispersal-induced destabilization of metapopulations and oscillatory Turing patterns in ecological networks

TL;DR

This paper extends Turing's pattern formation theory to ecological networks, revealing that oscillatory dispersal effects can destabilize ecosystems and cause species oscillations or extinctions, which are more common than in chemical systems.

Contribution

It demonstrates that oscillatory Turing instabilities are prevalent in ecological networks, leading to destabilization and species extinction, a phenomenon less observed in chemical systems.

Findings

Oscillatory Turing instability causes heterogeneous oscillations in ecological networks.

Instability is more common in ecological metapopulations than in chemical reactions.

All three-species food webs examined exhibit these instabilities under various conditions.

Abstract

As proposed by Alan Turing in 1952 as a ubiquitous mechanism for nonequilibrium pattern formation, diffusional effects may destabilize uniform distributions of reacting chemical species and lead to both spatially and temporally heterogeneous patterns. While stationary Turing patterns are broadly known, the oscillatory instability, leading to traveling waves in continuous media and also called the wave bifurcation, is rare for chemical systems. Here, we extend the analysis by Turing to general networks and apply it to ecological metapopulations of biological species with dispersal connections between habitats. Remarkably, the oscillatory Turing instability does not lead to wave patterns in networks, but to spontaneous development of heterogeneous oscillations and possible extinction of some species, even though they are absent for isolated populations. Furthermore, our theoretical analysis reveals that this instability is more common in ecological metapopulations than in chemical reactions. Indeed, we find the instabilities for all possible food webs with three predator or prey species, under various assumptions about the mobility of individual species and nonlinear interactions between them. Therefore, we suggest that the oscillatory Turing instability is generic and must play a fundamental role in metapopulation dynamics, providing a common mechanism for dispersal-induced destabilization of ecosystems.