Lessard S
Département de mathématiques et de statistique, Université de Montréal, Succursale Centre-Ville, Montréal, Québec, H3C 3J7, Canada.
Theor Popul Biol. 1997 Oct;52(2):119-36. doi: 10.1006/tpbi.1997.1324.
W. J. Ewens, following G. R. Price, has stressed that Fisher's fundamental theorem of natural selection about the increase in mean fitness is of general validity without any restrictive assumptions on the mating system, the fitness parameters, or the numbers of loci and alleles involved, but that it concerns only a partial change in mean fitness. This partial change is obtained by replacing the actual genotypic fitnesses by the corresponding additive genetic values and by keeping these values fixed in the change of the mean with respect to changes in genotype frequencies. We propose an alternate interpretation for this partial change which uses partial changes in genotype frequencies directly consequent on changes in gene frequencies, the fitness parameters being kept constant. We argue that this interpretation agrees more closely with Fisher's own explanations. Moreover, this approach leads to a decomposition for the total change in mean fitness which explains, unifies, and extends previous decompositions. We consider a wide range of models, from discrete-time selection models with nonoverlapping generations to continuous-time models with overlapping generations and age effects on viability and fecundity, which is the original framework for Fisher's fundamental theorem.
继G. R. 普赖斯之后，W. J. 尤恩斯强调，费希尔关于平均适合度增加的自然选择基本定理具有普遍有效性，对交配系统、适合度参数或所涉及的基因座和等位基因数量没有任何限制性假设，但它仅涉及平均适合度的部分变化。这种部分变化是通过用相应的加性遗传值替换实际基因型适合度，并在平均适合度随基因型频率变化而变化时保持这些值不变而获得的。我们对这种部分变化提出了另一种解释，该解释直接利用基因频率变化导致的基因型频率的部分变化，同时保持适合度参数不变。我们认为这种解释与费希尔自己的解释更为一致。此外，这种方法导致了平均适合度总变化的分解，它解释、统一并扩展了先前的分解。我们考虑了广泛的模型，从具有不重叠世代的离散时间选择模型到具有重叠世代以及生存力和繁殖力年龄效应的连续时间模型，这是费希尔基本定理的原始框架。
