Survival of the Scarcer in Space

Abstract

The dynamics leading to extinction or coexistence of competing species is of great interest in ecology and related fields. Recently a model of intra- and interspecific competition between two species was proposed by Gabel et al. [Phys. Rev. E 87 (2013) 010101], in which the scarcer species (i.e., with smaller stationary population size) can be more resistant to extinction when it holds a competitive advantage; the latter study considered populations without spatial variation. Here we verify this phenomenon in populations distributed in space. We extend the model of Gabel et al. to a d-dimensional lattice, and study its population dynamics both analytically and numerically. Survival of the scarcer in space is verified for situations in which the more competitive species is closer to the threshold for extinction than is the less competitive species, when considered in isolation. The conditions for survival of the scarcer species, as obtained applying renormalization group analysis and Monte Carlo simulation, differ in detail from those found in the spatially homogeneous case. Simulations highlight the speed of invasion waves in determining the survival times of the competing species.Comment: 19 pages, 11 figures. In Journal of Statistical Mechanics 201