Self-localized states in species competition

Abstract

We study the conditions under which species competition, as described by competitive Lotka- Volterra models in a homogeneous niche space, can support localized states, i.e. patches of species with enhanced population surrounded by species with smaller densities. Using some approximations we show analytically and numerically that for strong enough self-interaction, such states exist and are stable, representing self-enhanced populations arising from the interactions, and not by any preferred niche location or better fitness. These structures can be thought as portions of stable periodic density patterns (which are also supported by the system), inserted in the background of homogeneous density of species.