Crow J F
Ann Hum Genet. 1979 Jan;42(3):355-70. doi: 10.1111/j.1469-1809.1979.tb00669.x.
Fisher's system of reproductive value weighting, whereby each age group is assigned a weight purported to measure its contribution to the ancestry of future generations, was suggested by him as a way of ironing out irregularities in the change of population numbers when the age structure is not in equilibrium. This has been extended to Mendelian populations for two models. In Model I, the reproductive value of each genotype is computed from a table of age-specific survival and reproduction rates, and the genic values are computed by averaging these genotypic values. The total reproductive value of an allele and of the population always increase at a rate equal to the reproductive value-weighted average fitness regardless of age structure. This has the disadvantage that the total reproductive value is not equal to the census numbers, when age-stability has been reached. In Model II, this difficulty is surmounted, but the formula is no longer exact. The reproductive value of an allele for a specific age x is measured from the average death and reproductive rates of individuals of age x carrying that allele. An expression is given for the rate of change of reproductive value of an allele or of the population. In many circumstances this changes nearly uniformly, regardless of irregularities of age structure, and goes over to the census numbers as age stability is approached. The special difficulties in populations with separate sexes are discussed and a formula for rate of change of mean reproductive value, analogous to Fisher's Fundamental Theorem of Natural Selection, is given.
费希尔的生殖价值加权系统，即给每个年龄组赋予一个权重，旨在衡量其对后代祖先的贡献，他提出这是一种在年龄结构不均衡时消除种群数量变化中不规则性的方法。这已被扩展到孟德尔种群的两种模型。在模型I中，每个基因型的生殖价值是根据特定年龄的生存和繁殖率表计算出来的，而基因值则通过对这些基因型值求平均来计算。无论年龄结构如何，一个等位基因和种群的总生殖价值总是以等于生殖价值加权平均适合度的速率增加。这有一个缺点，即当达到年龄稳定时，总生殖价值不等于普查数量。在模型II中，这个困难被克服了，但公式不再精确。对于特定年龄x的一个等位基因的生殖价值，是根据携带该等位基因的年龄为x的个体的平均死亡率和繁殖率来衡量的。给出了一个等位基因或种群生殖价值变化率的表达式。在许多情况下，无论年龄结构是否不规则，这一变化几乎是均匀的，并且随着接近年龄稳定，会趋近于普查数量。讨论了具有不同性别的种群中的特殊困难，并给出了一个类似于费希尔自然选择基本定理的平均生殖价值变化率公式。
