Gomulkiewicz Richard, Krone Stephen M, Remien Christopher H
School of Biological Sciences Washington State University Pullman WA USA.
Department of Mathematics University of Idaho Moscow ID USA.
Evol Appl. 2017 Mar 17;10(5):471-484. doi: 10.1111/eva.12467. eCollection 2017 Jun.
Many populations are doomed to extinction, but little is known about how evolution contributes to their longevity. We address this by modeling an asexual population consisting of genotypes whose abundances change independently according to a system of continuous branching diffusions. Each genotype is characterized by its initial abundance, growth rate, and reproductive variance. The latter two components determine the genotype's "risk function" which describes its per capita probability of extinction at any time. We derive the probability distribution of extinction times for a polymorphic population, which can be expressed in terms of genotypic risk functions. We use this to explore how spontaneous mutation, abrupt environmental change, or population supplementation and removal affect the time to extinction. Results suggest that evolution based on new mutations does little to alter the time to extinction. Abrupt environmental changes that affect all genotypes can have more substantial impact, but, curiously, a beneficial change does more to extend the lifetime of thriving than threatened populations of the same initial abundance. Our results can be used to design policies that meet specific conservation goals or management strategies that speed the elimination of agricultural pests or human pathogens.
许多种群注定要灭绝，但对于进化如何影响它们的存续时间却知之甚少。我们通过对一个无性繁殖种群进行建模来解决这个问题，该种群由基因型组成，其丰度根据连续分支扩散系统独立变化。每个基因型由其初始丰度、增长率和繁殖方差来表征。后两个组成部分决定了基因型的“风险函数”，该函数描述了其在任何时候的人均灭绝概率。我们推导出了多态种群灭绝时间的概率分布，它可以用基因型风险函数来表示。我们用这个来探索自发突变、突然的环境变化或种群补充与移除如何影响灭绝时间。结果表明，基于新突变的进化对改变灭绝时间作用不大。影响所有基因型的突然环境变化可能有更显著的影响，但奇怪的是，一个有益的变化对繁荣种群寿命的延长作用比对具有相同初始丰度的受威胁种群更大。我们的结果可用于设计实现特定保护目标的政策或加速消灭农业害虫或人类病原体的管理策略。
