Centre for Conservation Biology, Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway.
Genetics. 2009 Oct;183(2):629-37. doi: 10.1534/genetics.109.105841. Epub 2009 Jul 20.
Fluctuations in age structure caused by environmental stochasticity create autocorrelation and transient fluctuations in both population size and allele frequency, which complicate demographic and evolutionary analyses. Following a suggestion of Fisher, we show that weighting individuals of different age by their reproductive value serves as a filter, removing temporal autocorrelation in population demography and evolution due to stochastic age structure. Assuming weak selection, random mating, and a stationary distribution of environments with no autocorrelation, we derive a diffusion approximation for evolution of the reproductive value weighted allele frequency. The expected evolution obeys an adaptive topography defined by the long-run growth rate of the population. The expected fitness of a genotype is its Malthusian fitness in the average environment minus the covariance of its growth rate with that of the population. Simulations of the age-structured model verify the accuracy of the diffusion approximation. We develop statistical methods for measuring the expected selection on the reproductive value weighted allele frequency in a fluctuating age-structured population.
由环境随机因素引起的年龄结构波动会导致种群数量和等位基因频率产生自相关性和瞬时波动，这使得人口统计学和进化分析变得复杂。根据 Fisher 的建议，我们表明，通过繁殖价值对不同年龄的个体进行加权，可以作为一种过滤器，消除由于随机年龄结构而导致的种群动态和进化中的时间自相关性。在假设弱选择、随机交配和环境分布稳定且无自相关的情况下，我们推导出了一个繁殖价值加权等位基因频率进化的扩散近似。预期的进化遵循由种群长期增长率定义的适应地形。基因型的预期适合度是其在平均环境下的马尔萨斯适合度减去其增长率与种群增长率的协方差。对年龄结构模型的模拟验证了扩散近似的准确性。我们开发了统计方法，用于测量在波动的年龄结构种群中，对繁殖价值加权等位基因频率的预期选择。
