Engen Steinar, Lande Russell, Saether Bernt-Erik
Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim.
Genetics. 2005 Jun;170(2):941-54. doi: 10.1534/genetics.104.028233. Epub 2005 Apr 16.
Previous theories on the effective size of age-structured populations assumed a constant environment and, usually, a constant population size and age structure. We derive formulas for the variance effective size of populations subject to fluctuations in age structure and total population size produced by a combination of demographic and environmental stochasticity. Haploid and monoecious or dioecious diploid populations are analyzed. Recent results from stochastic demography are employed to derive a two-dimensional diffusion approximation for the joint dynamics of the total population size, N, and the frequency of a selectively neutral allele, p. The infinitesimal variance for p, multiplied by the generation time, yields an expression for the effective population size per generation. This depends on the current value of N, the generation time, demographic stochasticity, and genetic stochasticity due to Mendelian segregation, but is independent of environmental stochasticity. A formula for the effective population size over longer time intervals incorporates deterministic growth and environmental stochasticity to account for changes in N.
以往关于年龄结构种群有效大小的理论假定环境恒定，且通常种群大小和年龄结构也恒定。我们推导出了因人口统计学和环境随机性共同作用而导致年龄结构和总人口大小波动的种群方差有效大小的公式。分析了单倍体以及雌雄同株或雌雄异株的二倍体种群。利用随机人口统计学的最新结果，得出了总人口大小(N)和选择性中性等位基因频率(p)联合动态的二维扩散近似。(p)的无穷小方差乘以世代时间，得出了每代有效种群大小的表达式。这取决于(N)的当前值、世代时间、人口统计学随机性以及孟德尔分离导致的遗传随机性，但与环境随机性无关。较长时间间隔内有效种群大小的公式纳入了确定性增长和环境随机性，以考虑(N)的变化。
