The left hand side of the Fundamental Theorem of Natural Selection. (7th November 2018)

• Record Type: Journal Article
• Authors: Grafen, Alan
• Is Part Of: Journal of theoretical biology. Volume 456(2018)
• Page Start: 175
• Page End: 189
• Publication Date: 2018-11-07
• Subjects: Biological fitness -- Natural selection -- Partial change in mean fitness -- Additive genetic component -- Formal Darwinism; Biology -- Periodicals; Biological Science Disciplines -- Periodicals; Biology -- Periodicals; Biologie -- Périodiques; Theoretische biologie; Biology; Periodicals; 571.05
• DOI: 10.1016/j.jtbi.2018.07.022
• Languages: English
• ISSNs: 0022-5193

Abstract

Highlights: The fundamental theorem of natural selection is understandable and important. The left hand side is the additive genetic component of the change in mean fitness. Fitness must be defined following Grafen's (2015) explanation ofFisher (1930) . The left hand side is shown to represent effectively the action of natural selection. Examples are given for linear and non-linear traits, density dependence and a game. Abstract: The fundamental theorem of natural selection is explained here in very simple terms, suitable for students. The biological significance of the left hand side – the rate of change in mean fitness due to changes in gene frequencies, which is also described as the rate of change due to natural selection – has been regarded since 1972 as problematic, but here a simple graph is used to show that Fisher's poor explanation was of a robust and simple intuition. Simple numerical examples show the theorem at work with fixed genotypic fitness under two different mating systems, with bland density dependence, and also with fitnesses determined by an evolutionary game. The content of the theorem has long been taken for granted by whole-organism evolutionary biologists, though in an imprecise way, even while mathematical population geneticists have been, in sequence, wrongly proving it false, wrongly proving it requires more assumptions than Fisher admitted, and accepting the truth of the theorem as Fisher proved it, but doubting its biological significance. An important emphasis on the instantaneous nature of natural selection, and of its measurement, emerges from the argument. Price's disappointments with the content of the theorem are directly confronted. The new explanation allows us to recognise the central place the theorem already occupies in evolutionary biology, and to begin to incorporate more fully the insights embedded in it.