Persistence of the weaker species in a non-homogeneous competitive system: exact result through a quantum mechanical analogy

Abstract

We have studied an ecological system of two species, which we denote strong and weak, respectively, that compete for a single food resource. This system is modelled as a three component reaction-diffusion process. In the presence of a solitary pulse of increased resources, the weaker competitor can diffuse toward this surplus, gaining a competitive advantage and hence persisting in contraposition with the classical Lotka-Volterra result. An exact analytical solution has been found through a quantum mechanical analogy. A stability analysis of this solution against changes in different parameters has been carried out.