Okabe Takuya, Yoshimura Jin
Graduate School of Integrated Science and Technology, Shizuoka University, 3-5-1 Johoku, Hamamatsu 432-8561, Japan.
Department of International Health, Institute of Tropical Medicine, Nagasaki University, 1-14 Bunkyōmachi, Nagasaki 852-8521, Japan.
PNAS Nexus. 2022 Oct 7;1(5):pgac228. doi: 10.1093/pnasnexus/pgac228. eCollection 2022 Nov.
The trade-off between short-term success and long-term sustainability is a common subject of great importance both in the biological evolution of organisms and in the economic activities of human beings. In evolutionary biology, bet-hedging theories have described it as the trade-off between the (within-generation) arithmetic mean fitness and the (between-generation) geometric mean fitness of a genotype. Accordingly, bet-hedging strategies observed in various organisms are regarded as optimizing the geometric mean fitness. To increase the geometric mean fitness signifies to suppress the between-generation variance in the mean fitness. Thus, this view is consistent with mean-variance portfolio analysis in which the standard deviation of a portfolio is regarded as a measure of risk. In the present study, we provide yet another measure of long-term sustainability, which is based on minimization of the probability of extinction/bankruptcy that randomly varying population/asset size after a long time becomes less than a certain small value. We present results for representative examples to show that the present criterion gives a qualitatively similar but quantitatively different prediction from the traditional ones. In particular, we emphasize that maximizing survival probability (i.e. minimizing extinction probability) is equivalent neither to maximizing geometric mean fitness nor to minimizing variance in mean fitness, while these three are consistently related to each other.
短期成功与长期可持续性之间的权衡，是生物进化以及人类经济活动中极为重要的常见主题。在进化生物学中，下注策略理论将其描述为一个基因型的（代内）算术平均适合度与（代间）几何平均适合度之间的权衡。相应地，在各种生物体中观察到的下注策略被视为对几何平均适合度的优化。增加几何平均适合度意味着抑制平均适合度的代间方差。因此，这种观点与均值 - 方差投资组合分析一致，在该分析中，投资组合的标准差被视为风险度量。在本研究中，我们提供了另一种长期可持续性的度量方法，它基于将长时间随机变化的种群/资产规模小于某个小值时的灭绝/破产概率最小化。我们给出了代表性示例的结果，以表明当前标准与传统标准给出的预测在定性上相似但在定量上不同。特别是，我们强调最大化生存概率（即最小化灭绝概率）既不等同于最大化几何平均适合度，也不等同于最小化平均适合度的方差，尽管这三者相互之间存在一致的关联。
