Fixation in competing populations: Diffusion and strategies for survival

Abstract

How should dispersal strategies be chosen to increase the likelihood of survival of a species? We obtain the answer for the spatially extended versions of three well-known models of two competing species with unequal diffusivities. Though identical at the mean-field level, the three models exhibit drastically different behavior leading to different optimal strategies for survival, with or without a selective advantage for one species. With conserved total particle number, dispersal has no effect on survival probability. With a fluctuating number, faster dispersal is advantageous if intraspecies competition is present, while moving slower is the optimal strategy for the disadvantaged species if there is no intraspecies competition: it is imperative to include fluctuations to properly formulate survival strategies.