On the metapopulation Dynamics of Autocatalysis: Extinction Transients Related to Ghosts

One of the theoretical approaches to study spatially-extended ecosystems is given by metapopulation models, which consider fragmented populations inhabiting discrete patches linked by migration. Most of the metapopulation models assume exponential growth of the local populations and few works have explored the role of cooperation in fragmented ecosystems. In this letter, we study the dynamics and the bifurcation scenarios of a minimal, two-patch metapopulation Turing-like model given by nonlinear differential equations with an autocatalytic reaction term together with diffusion. We also analyze the extinction transients of the metapopulations focusing on the effect of coupling two local populations undergoing delayed transition phenomena due to ghost saddle remnants. We find that increasing diffusion rates enhance the delaying capacity of the ghosts. We finally propose the saddle remnant as a new class of transient generator mechanism for ecological systems.