  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 $N\geq 2$. 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 $\mu_A-\sigma_A^2/2>\mu_B-\sigma_B^2/2$.
