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arXiv · 1901.08229

Fixation in Fluctuating Populations

Deepak Bhat·Jordi Piñero·S. Redner
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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.

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Deepak Bhat, Jordi Piñero, S. Redner. 2019-01-24. Fixation in Fluctuating Populations. https://doi.org/10.1088/1742-5468/ab1ddd

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