We investigate the evolutionary rescue of a microbial population in a gradually deteriorating environment, through a combination of analytical calculations and stochastic simulations. We consider a population destined for extinction in the absence of mutants, which can only survive if mutants sufficiently adapted to the new environment arise and fix. We show that mutants that appear later during the environment deterioration have a higher probability to fix. The rescue probability of the population increases with a sigmoidal shape when the product of the carrying capacity and of the mutation probability increases. Furthermore, we find that rescue becomes more likely for smaller population sizes and/or mutation probabilities if the environment degradation is slower, which illustrates the key impact of the rapidity of environment degradation on the fate of a population. We also show that our main conclusions are robust across various types of adaptive mutants, including specialist and generalist ones, as well as mutants modeling antimicrobial resistance evolution. We further express the average time of appearance of the mutants that do rescue the population and the average extinction time of those that do not. Our methods can be applied to other situations with continuously variable fitnesses and population sizes, and our analytical predictions are valid in the weak-to-moderate mutation regime.

中文翻译：

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适应或灭亡：逐渐恶化的环境中的进化救援。

我们通过分析计算和随机模拟相结合，研究在逐渐恶化的环境中微生物种群的进化拯救。我们认为在没有突变体的情况下注定要灭绝的种群，只有在突变体充分适应新环境的出现和修复时才能生存。我们发现，在环境恶化过程中较晚出现的突变体有更高的修复概率。当承载能力与突变概率的乘积增大时，种群的获救概率呈S形增大。此外，我们发现，如果环境退化较慢，则较小的种群规模和/或突变概率更有可能获得救援，这说明了环境退化的速度对种群命运的关键影响。我们还表明，我们的主要结论在各种类型的适应性突变体中都是稳健的，包括专业突变体和通才突变体，以及模拟抗菌素耐药性进化的突变体。我们进一步表达了拯救种群的突变体的平均出现时间和那些没有拯救种群的突变体的平均灭绝时间。我们的方法可以应用于适应度和种群规模连续变化的其他情况，并且我们的分析预测在弱到中度突变机制中是有效的。