波动环境下有限种群通过 bet-hedging（风险对冲）实现的进化适应
Evolutionary adaptation through bet-hedging in finite populations under fluctuating environments
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中文总结 AI 辅助
本文通过随机模型揭示波动环境下有限种群的进化规律，发现环境变异性可促进表型风险对冲，进化会平衡生长与灭绝目标，种群规模决定最优策略，大种群趋增长最大化、小种群趋韧性策略。
中文摘要 AI 辅助
自然种群在波动环境与有限资源下进化，但这些因素如何共同塑造适应仍不明确。本文引入随机切换环境中种群生死过程的极简随机模型，个体继承决定世代间表型分布的表型策略。首先证实环境变异性可促进表型多样性（风险对冲），且最大化平均增长率的策略通常与最小化灭绝风险的策略不同；随后证明进化驱动种群向平衡这些冲突目标的策略发展。此外，种群规模调控进化结果：大种群收敛到增长率最大化策略，小种群则进化为更具韧性的策略。最后，本文提供简单近似启发式方法捕捉这些结果，阐明生长、灭绝与突变间的相互作用。
英文摘要
Natural populations evolve under fluctuating environments and limited resources, yet it is unclear how these factors jointly shape adaptation. Here, we introduce a minimal stochastic model of a population undergoing a birth-death process in a randomly switching environment, where individuals inherit phenotypic strategies that determine the distribution of phenotypes across generations. First, we confirm that environmental variability can favor phenotypic diversity (bet-hedging), and that the strategy maximizing the average growth rate generally differs from the one minimizing extinction risk. We then demonstrate that evolution drives populations toward strategies that balance these competing objectives. Furthermore, we show that population size modulates this evolutionary outcome: large populations converge to the growth-maximizing strategy, whereas smaller ones evolve toward more resilient strategies. Finally, we provide a simple heuristic approximation that captures these results, clarifying the interplay between growth, extinction, and mutation.
