Three-fold way to extinction in populations of cyclically competing species

TL;DR

This paper explores the complex extinction dynamics in cyclically competing species, revealing three distinct extinction mechanisms including coarsening, oscillating traveling waves, and heteroclinic orbits, influenced by mixing and system size.

Contribution

It uncovers the rich, previously unrecognized diversity of extinction pathways in a classic ecological model, extending understanding beyond coarsening to include oscillatory and heteroclinic dynamics.

Findings

Identified three types of extinction dynamics: coarsening, traveling waves, heteroclinic orbits.

Showed the dominance of different mechanisms depends on mixing and system size.

Provided analytical and numerical characterization of extinction scenarios.

Abstract

Species extinction occurs regularly and unavoidably in ecological systems. The time scales for extinction can broadly vary and inform on the ecosystem's stability. We study the spatio-temporal extinction dynamics of a paradigmatic population model where three species exhibit cyclic competition. The cyclic dynamics reflects the non-equilibrium nature of the species interactions. While previous work focusses on the coarsening process as a mechanism that drives the system to extinction, we found that unexpectedly the dynamics to extinction is much richer. We observed three different types of dynamics. In addition to coarsening, in the evolutionary relevant limit of large times, oscillating traveling waves and heteroclinic orbits play a dominant role. The weight of the different processes depends on the degree of mixing and the system size. By analytical arguments and extensive numerical simulations we provide the full characteristics of scenarios leading to extinction in one of the most surprising models of ecology.