Metapopulation oscillations from satiation of predators

LAGUNA FABIANA; JOSE LUIS LANATA; KUPERMAN MARCELO; ABRAMSON GUILLERMO; ADRIAN MONJEAU

trieste

Workshop; School and Workshop on Patterns of Synchrony: Chimera States and Beyond; 2019

We develop a mathematical model of extinction and coexistence in a generic predator?preyecosystem composed of two herbivores in asymmetrical competition and a predator of both. With theaim of representing the satiety of predators when preys are overabundant, we introduce for thepredation behavior a dependence on prey abundance. Speci􀂍cally, predation is modeled as growingproportionally to the presence of herbivores at low densities, and saturating when the totalmetapopulation of prey is su􀂋ciently large. The model predicts the existence of di􀂊erent regimesdepending on the parameters considered: survival of a single species, coexistence of two species andextinction of the third one, and coexistence of the three species. But more interestingly, in someregions of parameters space the solutions oscillate in time, both as a transient phenomenon and aspersistent oscillations of constant amplitude. The phenomenon is not present for the more idealizedlinear predation model, suggesting that it can be the source of real ecosystems oscillations.