The left hand side of the Fundamental Theorem of Natural Selection.

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.