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Modelling evolutionary processes in small populations: not as ideal as you think

机译:对小群体中的进化过程进行建模: 不如你想象的那么理想

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摘要

Evolutionary processes are routinely modeled using ‘ideal’ Wright–Fisher populations of constant size N in which each individual has an equal expectation of reproductive success. In a hypothetical ideal population, variance in reproductive success (Vk) is binomial and effective population size (Ne) = N. However, in any actual implementation of the Wright– Fisher model (e.g., in a computer), Vk is a random variable and it’s realized value in any given replicate generation (Vk*) only rarely equals the binomial variance. Realized effective size (Ne*) thus also varies randomly in modeled ideal populations, and the consequences of this have not been adequately explored in the literature. Analytical and numerical results show that random variation in Vk*and Ne*can seriously distort analyses that evaluate precision or otherwise depend on the assumption that is constant. We derive analytical expressions for Var(Vk) [4(2N – 1)(N – 1)/N3] and Var(Ne) [N(N – 1)/(2N – 1) ≈ N/2] in modeled ideal populations and show that, for a genetic metric G = f(Ne), Var(^G) has two components: VarGene (due to variance across replicate samples of genes, given a specific Ne*) and VarDemo (due to variance in Ne*). Var(^G) is higher than it would be with constant Ne= N, as implicitly assumed by many standard models. We illustrate this with empirical examples based on F (standardized variance of allele frequency) and r2 (a measure of linkage disequilibrium). Results demonstrate that in computer models that track multilocus genotypes, methods of replication and data analysis can strongly affect consequences of variation in Ne*. These effects are more important when sampling error is small (large numbers of individuals, loci and alleles) and with relatively small populations (frequently modeled by those interested in conservation).
机译:进化过程通常使用恒定大小N的“理想” Wright-Fisher种群建模,其中每个个体对繁殖成功的期望均等。在假设的理想人群中,生殖成功(Vk)的方差是二项式,有效人群大小(Ne)=N。但是,在Wright-Fisher模型的任何实际实现中(例如,在计算机中),Vk都是随机变量它在任何给定的复制代(Vk *)中的实现值很少等于二项式方差。因此,在模拟的理想人群中,实现的有效大小(Ne *)也随机变化,并且其结果尚未在文献中得到充分探讨。分析和数值结果表明,Vk *和Ne *的随机变化会严重扭曲评估精度的分析,否则将取决于恒定的假设。我们在模型理想中推导了Var(Vk)[4(2N – 1)(N – 1)/ N3]和Var(Ne)[N(N – 1)/(2N – 1)≈N / 2]的解析表达式。并显示,对于遗传度量G = f(Ne),Var(^ G)具有两个成分:VarGene(由于基因重复样本之间的差异,给定特定的Ne *)和VarDemo(由于Ne的差异*)。正如许多标准模型所隐含的那样,Var(^ G)比常数Ne = N时要高。我们用基于F(等位基因频率的标准方差)和r2(连锁不平衡的量度)的经验示例对此进行说明。结果表明,在追踪多基因座基因型的计算机模型中,复制和数据分析的方法会严重影响Ne *变异的后果。当采样误差较小(大量的个体,基因座和等位基因)且种群相对较小(通常由对保护感兴趣的人建模)时,这些影响更为重要。

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