Non-uniform dispersal of logistic population models with free boundaries in a spatially heterogeneous environment

Abstract

In many cases, the movement of species within a region depends on the availability of food and other resources necessary for their survival. Starvation-driven diffusion (SDD) is a non-uniform dispersal strategy that increases the motility of biological organisms in unfavorable environments, i.e., a species moves more frequently in search of food if resources are insufficient [4]. In this study, the proposed model represents the dispersion of an invasive species undergoing SDD, where the free boundary represents the expanding front. We observed that the spreading-vanishing dichotomy, which holds in the linear dispersal model, also holds in the model undergoing SDD. In the case that spreading of species occurs, it is shown that the asymptotic spreading speed of the moving front is uniquely determined in relation to the semi-wave speed. Moreover, our results are compared with the results of the linear dispersal model to investigate the advantages of this strategic dispersal with respect to survival in new environments, i.e., the conditions that allowed the species undergoing SDD to spread and the random diffusers to vanish are monitored.