Limits to the Rate of Adaptive Substitution in Sexual Populations

In large populations, many beneficial mutations may be simultaneously available and may compete with one another, slowing adaptation. By finding the probability of fixation of a favorable allele in a simple model of a haploid sexual population, we find limits to the rate of adaptive substitution, , that depend on simple parameter combinations. When variance in fitness is low and linkage is loose, the baseline rate of substitution is , where is the population size, is the rate of beneficial mutations per genome, and is their mean selective advantage. Heritable variance in log fitness due to unlinked loci reduces by under polygamy and under monogamy. With a linear genetic map of length Morgans, interference is yet stronger. We use a scaling argument to show that the density of adaptive substitutions depends on , , , and only through the baseline density: . Under the approximation that the interference due to different sweeps adds up, we show that , implying that interference prevents the rate of adaptive substitution from exceeding one per centimorgan per 200 generations. Simulations and numerical calculations confirm the scaling argument and confirm the additive approximation for ; for higher , the rate of adaptation grows above , but only very slowly. We also consider the effect of sweeps on neutral diversity and show that, while even occasional sweeps can greatly reduce neutral diversity, this effect saturates as sweeps become more common—diversity can be maintained even in populations experiencing very strong interference. Our results indicate that for some organisms the rate of adaptive substitution may be primarily recombination-limited, depending only weakly on the mutation supply and the strength of selection.在大种群中，诸多有益突变可能同时出现并彼此竞争，进而延缓适应性演化进程。通过在单倍体有性种群（haploid sexual population）的简化模型中求解有利等位基因固定（fixation）的概率，我们得到了适应性替换速率$Lambda$的上限，该上限依赖于一组简单的参数组合。当适合度方差较低且连锁关系疏松时，基准替换速率为$Lambda_0=2Nmu s$，其中$N$为种群规模，$mu$为每个基因组的有益突变率，$s$为其平均选择优势（selective advantage）。由非连锁位点导致的对数适合度遗传方差，在多配偶制下会使$Lambda$降低至原基准值的$1/(1+Nssigma_phi^2)$，在单配偶制下则降低至$1/(1+Nssigma_phi^2/2)$。当遗传图谱为长度$L$摩尔根（Morgans）的线性图谱时，遗传干涉（interference）的影响会更强。我们通过尺度缩放论证表明，适应性替换的密度仅通过基准密度依赖于$N、mu、s$与$L$：$ ho_{adaptive}=Lambda_0/L$。在不同选择性扫荡（selective sweeps）引发的遗传干涉可叠加的近似条件下，我们推导出$Lambdaapproxfrac{log(2Ns)}{2 au}$，这意味着遗传干涉会使适应性替换速率无法超过每200代每厘摩（centimorgan）1次。模拟与数值计算验证了该尺度缩放论证，并证实了当$Nssigma_phi^2ll1$时的加性近似；当$Nssigma_phi^2$取值更高时，适应性演化速率会高于$Lambda_0$，但增长幅度极小。我们还探讨了选择性扫荡对中性多样性（neutral diversity）的影响，结果表明：即便偶发的选择性扫荡也可大幅降低中性遗传多样性，但随着扫荡事件愈发频繁，该效应会趋于饱和——即便在遗传干涉极强的种群中，中性多样性仍可得以维持。我们的研究结果显示，对于部分生物而言，适应性替换速率可能主要受重组限制，仅微弱依赖于突变供给能力与选择作用强度。