Survival of the Scarcer in Space

TL;DR

This paper investigates how a less abundant but competitively advantaged species can survive in spatially distributed populations, extending previous models to include spatial dynamics and analyzing conditions for survival.

Contribution

It extends the non-spatial competition model to spatially structured populations and analyzes the conditions for the survival of the scarcer species using analytical and numerical methods.

Findings

Survival of the scarcer species verified in spatial models.

Spatial dynamics influence survival thresholds and invasion speeds.

Conditions differ from non-spatial models, highlighting the importance of 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.