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

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