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Classical stochastic demography predicts that environmental stochasticityreduces population growth rates and, thereby, can increase extinction risk. Incontrast, the SAS-CFF model demonstrates that environmental stochasticity canpromote genetic diversity. Extending the SAS-CFF to account for demography, Iexamine the simultaneous effects of environmental stochasticity on geneticdiversity and population persistence. Consistent with Gillespie's analysis, ifthe log-fitness function is concave and allelic responses to the environmentare not perfectly correlated, then per-capita growth rates of rare alleles arepositive and genetic diversity is maintained in the sense of stochasticpersistence i.e. allelic frequencies tend to stay away from zero almost-surelyand in probability. Alternatively, if the log-fitness function is convex, thenper-capita growth rates of rare alleles are negative and an alleleasymptotically fixates with probability one. If the population's low-density,per-capita growth rate is positive, then the population persists in the senseof stochastic persistence, else it goes asymptotically extinct with probabilityone. In contrast to per-capita growth rates of rare alleles, the population'sper-capita growth rate is a decreasing function of the concavity of thelog-fitness function. Moreover, when the log-fitness function is concave,allelic diversity increases the population's per-capita growth rate whiledecreasing the per-capita growth rate of rare alleles, and environmentalstochasticity increases the per-capita growth rate of rare alleles butdecreases the population's per-capita growth rate. Collectively, these results(i) highlight how mechanisms promoting population persistence may be at oddswith mechanisms promoting genetic diversity, and (ii) provide conditions underwhich population persistence relies on existing standing genetic variation.

When do factors promoting balanced selection also promote population persistence? A demographic perspective on Gillespie's SAS-CFF model