Engen Steinar, Lande Russell, Saether Bernt-Erik
Centre for Conservation Biology, Department of Mathematical Sciences, Norwegian University of Science and Technology, N-7491 Trondheim, Norway.
Genet Res (Camb). 2009 Feb;91(1):73-82. doi: 10.1017/S0016672308000013.
We compute an accurate approximation to the probability of fixation for a beneficial mutation in a population fluctuating with a stationary distribution of population size. The population dynamics are described by the theta-logistic model with environmental variance, assuming that the population size is large enough to ignore demographic variance. We show that stochastic fluctuations of population size reduce the probability of fixation. However, it is not the magnitude of the population fluctuations per se that creates this reduction. Only the environmental variance has a substantial effect on the probability of fixation. The strength of density dependence (or expected return time to equilibrium) and the functional form of density-regulation, given by the parameter theta in the theta-logistic model, have little effect on the fixation probability. Effective population size based on harmonic mean population size will therefore underestimate the expected fixation rate of beneficial mutations in fluctuating populations.
我们计算了在种群大小呈平稳分布波动的情况下，有益突变固定概率的精确近似值。种群动态由具有环境方差的θ-逻辑斯谛模型描述，假设种群大小足够大，可以忽略人口统计学方差。我们表明，种群大小的随机波动会降低固定概率。然而，造成这种降低的并非种群波动本身的幅度。只有环境方差对固定概率有实质性影响。由θ-逻辑斯谛模型中的参数θ给出的密度依赖性强度（或预期平衡恢复时间）以及密度调节的函数形式，对固定概率影响很小。因此，基于调和平均种群大小的有效种群大小会低估波动种群中有益突变的预期固定率。
