A simple completion of Fisher’s fundamental theorem of natural selection,Ecology and Evolution

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A simple completion of Fisher’s fundamental theorem of natural selection
Ecology and Evolution ( IF 2.3 ) Pub Date : 2020-12-27 , DOI: 10.1002/ece3.6918
Alan Grafen ₁

Affiliation

Fisher's fundamental theorem of natural selection shows that the part of the rate of change of mean fitness that is due to natural selection equals the additive genetic variance in fitness. Fisher embedded this result in a model of total fitness, adding terms for deterioration of the environment and density dependence. Here, a quantitative genetic version of this neglected model is derived that relaxes its assumptions that the additive genetic variance in fitness and the rate of deterioration of the environment do not change over time, allows population size to vary, and includes an input of mutational variance. The resulting formula for total rate of change in mean fitness contains two terms more than Fisher's original, representing the effects of stabilizing selection, on the one hand, and of mutational variance, on the other, making clear for the first time that the fundamental theorem deals only with natural selection that is directional (as opposed to stabilizing) on the underlying traits. In this model, the total (rather than just the additive) genetic variance increases mean fitness. The unstructured population allows an explanation of Fisher's concept of fitness as simply birth rate minus mortality rate, and building up to the definition in structured populations.

中文翻译：

费雪自然选择基本定理的简单补全

费希尔自然选择基本定理表明，自然选择导致的平均适应度变化率部分等于适应度的加性遗传方差。费舍尔将这一结果嵌入到总体适应度模型中，添加了环境恶化和密度依赖性的项。在这里，推导了这个被忽视模型的定量遗传版本，它放宽了其假设，即适应度的加性遗传方差和环境恶化率不随时间变化，允许种群规模变化，并包括突变方差的输入。由此产生的平均适应度总变化率公式比费舍尔原来的公式多了两项，一方面代表稳定选择的影响，另一方面代表突变方差的影响，首次明确了基本定理仅涉及对潜在特征有方向性（而不是稳定）的自然选择。在此模型中，总遗传方差（而不仅仅是加性）增加了平均适应度。非结构化人口可以将费舍尔的健康概念解释为简单的出生率减去死亡率，并建立在结构化人口中的定义。

更新日期：2021-01-22

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