Fixation in fluctuating populations

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 -> infinity, 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.