Survival of the scarcer

Abstract

We investigate extinction dynamics in the paradigmatic model of two competing species $A$ and $B$ that reproduce ($A\ensuremath{\rightarrow}2A$, $B\ensuremath{\rightarrow}2B$), self-regulate by annihilation ($2A\ensuremath{\rightarrow}0$, $2B\ensuremath{\rightarrow}0$), and compete ($A+B\ensuremath{\rightarrow}A$, $A+B\ensuremath{\rightarrow}B$). For a finite system that is in the well-mixed limit, a quasistationary state arises which describes coexistence of the two species. Because of discrete noise, both species eventually become extinct in time that is exponentially long in the quasistationary population size. For a sizable range of asymmetries in the growth and competition rates, the paradoxical situation arises in which the numerically disadvantaged species according to the deterministic rate equations survives much longer.