Fundamental Theorem of Natural Selection

This communication gives a simple derivation for an appropriate corresponding expression for the discrete-generation model and points out when Fisher's theorem still applies and when it does not.

Abstract

FISHER1 in 1930 stated his "fundamental theorem of natural selection" in the form: "The rate of increase in fitness of any organism at any time is equal to its genetic variance in fitness at that time." Later, Fisher2 restated his theorem more clearly: "The rate of increase in the average fitness of a population is equal to the genetic variance of fitness of that population". The "genetic variance" in the foregoing statements is the linear or additive component of the fitness variance in current literature. Fisher obtained his result on the basis of a continuous time model with logarithmic fitness. This communication gives a simple derivation for an appropriate corresponding expression for the discrete-generation model and points out when Fisher's theorem still applies and when it does not.