  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.
