Nagylaki T
Genetics. 1976 Jul;83(3 PT.2):583-600.
Assuming age-independent fertilities and mortalities and random mating, continuous-time models for a monoecious population are investigated for weak selection. A single locus with multiple alleles and two alleles at each of two loci are considered. A slow-selection analysis of diallelic and multiallelic two-locus models with discrete nonoverlapping generations is also presented. The selective differences may be functions of genotypic frequencies, but their rate of change due to their explicit dependence on time (if any) must be at most of the second order in s, (i.e., O(s2), where s is the intensity of natural selection. Then, after several generations have elapsed, in the continuous time models the time-derivative of the deviations from Hardy-Weinberg proportions is of O(s2), and in the two-locus models the rate of change of the linkage disequilibrium is of O(s2). It follows that, if the rate of change of the genotypic fitnesses is smaller than second order in s (i.e., o(s2)), then to O(s2) the rate of change of the mean fitness of the population is equal to the genic variance. For a fixed value of s, however, no matter how small, the genic variance may occasionally be smaller in absolute value than the (possibly negative) lower order terms in the change in fitness, and hence the mean fitness may decrease. This happens if the allelic frequencies are changing extremely slowly, and hence occurs often very close to equilibrium. Some new expressions are derived for the change in mean fitness. It is shown that, with an error of O(s), the genotypic frequencies evolve as if the population were in Hardy-Weinberg proportions and linkage equilibrium. Thus, at least for the deterministic behaviour of one and two loci, deviations from random combination appear to have very little evolutionary significance.
假设生育率和死亡率与年龄无关且随机交配，针对弱选择情况研究了雌雄同体种群的连续时间模型。考虑了一个具有多个等位基因的单基因座以及两个基因座上各有两个等位基因的情况。还给出了具有离散非重叠世代的双等位基因和多等位基因双基因座模型的慢选择分析。选择差异可能是基因型频率的函数，但其由于对时间的明确依赖（如果有）而导致的变化率在选择强度(s)下至多为二阶（即(O(s^2))，其中(s)是自然选择强度）。那么，经过几代之后，在连续时间模型中，偏离哈迪 - 温伯格比例的偏差的时间导数为(O(s^2))，在双基因座模型中，连锁不平衡的变化率为(O(s^2))。由此可知，如果基因型适合度的变化率在(s)下小于二阶（即(o(s^2))），那么到(O(s^2))阶，种群平均适合度的变化率等于基因方差。然而，对于固定的(s)值，无论多小，基因方差在绝对值上偶尔可能小于适合度变化中较低阶（可能为负）的项，因此平均适合度可能会降低。当等位基因频率变化极其缓慢时就会发生这种情况，因此这种情况经常发生在非常接近平衡的时候。推导出了一些关于平均适合度变化的新表达式。结果表明，误差为(O(s))时，基因型频率的演化就好像种群处于哈迪 - 温伯格比例和连锁平衡状态。因此，至少对于一个和两个基因座的确定性行为而言，偏离随机组合似乎几乎没有进化意义。
