Fixation in Fluctuating Populations

Abstract

We investigate the dynamics of the voter model in which the population itself changes endogenously via the birth-death process. There are two species of voters, labeled A and B, and the population of each species can grow or shrink by the birth-death process at equal rates $b$. Individuals of opposite species also undergo voter model dynamics in which an AB pair can equiprobably become AA or BB with rate $v$---neutral evolution. In the limit $b/v\to \infty$, the distribution of consensus times varies as $t^{-3}$ and the probability that the population size equals $n$ at the moment of consensus varies as $n^{-3}$. As the birth/death rate $b$ is increased, fixation occurs more more quickly; that is, population fluctuations promote consensus.

15 pages, 6 figures, IOP format. Version 2: minor changes in response to referee comments. For publication in JSTAT. Version 3: Various minor errors fixed

References in corpus (3)

• Evolution of a Fluctuating Population in a Randomly Switching Environment
• Species coexistence in a neutral dynamics with environmental noise
• Growth-induced breaking and unbreaking of ergodicity in fully-connected spin systems