We study an eco-evolutionary dynamics in finite populations of two haploid asexually reproducing allelic types. We focus on the quasi-neutral case when individual types differ only in their intrinsic birth and death rates but have the same expected lifetime reproductive output. We assume that the population size can fluctuate stochastically. We solve the Kolmogorov forward equation in the population whose size fluctuates only minimally and show that the fixation probability is decreasing with the increasing turnover rate. We also show that when the mutant's turnover is small enough, selection favors the mutant replacing residents. Similarly, when the turnover is high enough, selection opposes the replacement. This basic result has previously been demonstrated numerically for the contact process and shown analytically for the Moran process; the current paper extends this analysis to provide an analytical proof for the contact process. We also demonstrate numerically that our results extend for general fluctuating populations and beyond the quasi-neutral case.
Keywords: Birth–death process; Contact process; Death-birth process; Eco-evolutionary dynamics; Moran process; Stochastic fluctuation.
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