Classical stochastic demography predicts that environmental stochasticity reduces population growth rates and, thereby, can increase extinction risk. In contrast, in a 1978 Theoretical Population Biology paper, Gillespie demonstrated with his stochastic additive scale and concave fitness function (SAS-CFF) model that environmental stochasticity can promote genetic diversity. Extending the SAS-CFF to account for demography, I examine the simultaneous effects of environmental stochasticity on genetic diversity and population persistence. Explicit expressions for the per-capita growth rates of rare alleles and the population at low-density are derived. Consistent with Gillespie's analysis, if the log-fitness function is concave and allelic responses to the environment are not perfectly correlated, then per-capita growth rates of rare alleles are positive and genetic diversity is maintained in the sense of stochastic persistence i.e. allelic frequencies tend to stay away from zero almost-surely and in probability. Alternatively, if the log-fitness function is convex, then per-capita growth rates of rare alleles are negative and an allele asymptotically fixates with probability one. If the population's low-density, per-capita growth rate is positive, then the population persists in the sense of stochastic persistence, else it goes asymptotically extinct with probability one. In contrast to per-capita growth rates of rare alleles, the population's per-capita growth rate is a decreasing function of the concavity of the log-fitness function. Moreover, when the log-fitness function is concave, allelic diversity increases the population's per-capita growth rate while decreasing the per-capita growth rate of rare alleles; when the log-fitness function is convex, environmental stochasticity decreases the per-capita growth rate of rare alleles, but increases the population's per-capita growth rate. Collectively, these results (i) highlight how mechanisms promoting population persistence may be at odds with mechanisms promoting genetic diversity, and (ii) provide conditions under which population persistence relies on existing standing genetic variation.

中文翻译：

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什么时候促进遗传多样性的因素也促进了种群的持久性？Gillespie 的 SAS-CFF 模型的人口统计视角。

经典随机人口学预测环境随机性会降低人口增长率，从而增加灭绝风险。相比之下，在 1978 年的理论种群生物学论文中，Gillespie 用他的随机加性尺度和凹适应度函数 (SAS-CFF) 模型证明了环境随机性可以促进遗传多样性。将 SAS-CFF 扩展到人口统计学，我研究了环境随机性对遗传多样性和种群持久性的同时影响。导出了稀有等位基因的人均增长率和低密度人口的显式表达式。与 Gillespie 的分析一致，如果 log-fitness 函数是凹的，并且对环境的等位基因反应不完全相关，那么稀有等位基因的人均增长率是正的，并且遗传多样性在随机持久性的意义上保持不变，即等位基因频率几乎肯定地和概率地趋向于远离零。或者，如果对数拟合函数是凸的，则稀有等位基因的人均增长率为负，并且等位基因以概率 1 渐近固定。如果人口的低密度人均增长率为正，则人口在随机持续性的意义上持续存在，否则它会以概率 1 渐近灭绝。与稀有等位基因的人均增长率相反，人口的人均增长率是对数拟合函数的凹度的减函数。此外，当 log-fitness 函数是凹函数时，等位基因多样性增加了人口的人均增长率，同时降低了稀有等位基因的人均增长率；当对数拟合函数为凸时，环境随机性会降低稀有等位基因的人均增长率，但会提高人口的人均增长率。总的来说，这些结果（i）强调了促进种群持久性的机制可能与促进遗传多样性的机制不一致，并且（ii）提供了种群持久性依赖于现有遗传变异的条件。