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Stochastic viability in an island model with partial dispersal : Approximation by a diffusion process in the limit of a large number of islands | | Dhaker Kroumi
; Sabin Lessard
; | | Date: |
1 Nov 2023 | | Abstract: | In this paper, we study a finite population undergoing discrete, nonoverlapping generations, that is structured into $D$ demes, each containing $N$ individuals of two possible types, $A$ and $B$, whose viability coefficients, $s_A$ and $s_B$, respectively, vary randomly from one generation to the next. We assume that the means, variances and covariance of the viability coefficients are inversely proportional to the number of demes $D$, while higher-order moments are negligible in comparison to $1/D$. We use a discrete-time Markov chain with two time scales to model the evolutionary process, and we demonstrate that as the number of demes $D$ approaches infinity, the accelerated Markov chain converges to a diffusion process for any deme size $Ngeq 2$. This diffusion process allows us to evaluate the fixation probability of type $A$ following its introduction as a single mutant in a population that was fixed for type $B$. We explore the impact of increasing the variability in the viability coefficients on this fixation probability. At least when $N$ is large enough, it is shown that increasing this variability for type $B$ or decreasing it for type $A$ leads to an increase in the fixation probability of a single $A$. The effect of the population-scaled variances, $sigma^2_A$ and $sigma^2_B$, can even cancel the effects of the population-scaled means, $mu_A$ and $mu_B$. We also show that the fixation probability of a single $A$ increases as the deme-scaled migration rate increases. Moreover, this probability is higher for type $A$ than for type $B$ if the population-scaled geometric mean is higher for type $A$ than for type $B$, which means that $mu_A-sigma_A^2/2>mu_B-sigma_B^2/2$. | | Source: | arXiv, 2311.00275 | | Services: | Forum | Review | PDF | Favorites | |
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