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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 viabilitycoefficients, $s_A$ and $s_B$, respectively, vary randomly from one generationto the next. We assume that the means, variances and covariance of theviability coefficients are inversely proportional to the number of demes $D$,while higher-order moments are negligible in comparison to $1/D$. We use adiscrete-time Markov chain with two time scales to model the evolutionaryprocess, and we demonstrate that as the number of demes $D$ approachesinfinity, the accelerated Markov chain converges to a diffusion process for anydeme size $N\geq 2$. This diffusion process allows us to evaluate the fixationprobability of type $A$ following its introduction as a single mutant in apopulation that was fixed for type $B$. We explore the impact of increasing thevariability in the viability coefficients on this fixation probability. Atleast when $N$ is large enough, it is shown that increasing this variabilityfor type $B$ or decreasing it for type $A$ leads to an increase in the fixationprobability of a single $A$. The effect of the population-scaled variances,$\sigma^2_A$ and $\sigma^2_B$, can even cancel the effects of thepopulation-scaled means, $\mu_A$ and $\mu_B$. We also show that the fixationprobability of a single $A$ increases as the deme-scaled migration rateincreases. 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 $\mu_A-\sigma_A^2/2>\mu_B-\sigma_B^2/2$.

Stochastic viability in an island model with partial dispersal : Approximation by a diffusion process in the limit of a large number of islands