Fisher's Fundamental Theorem of Natural Selection

Fisher's fundamental theorem of natural selection states that the rate of increase in the mean fitness of a population due to natural selection equals the additive genetic variance in fitness at that time. Ronald Fisher presented it in his 1930 book The Genetical Theory of Natural Selection.

In its simple form, it says that the more genetic variation there is in fitness, the faster selection can raise the average fitness. A population with no variation in fitness cannot respond to selection. The theorem resembles a law of physics, and Fisher compared it to the second law of thermodynamics, suggesting that the population's fitness behaves in the way entropy does.

Fisher's own wording was brief, and for decades the theorem was read as saying that mean fitness always increases. George Price showed in 1972 that Fisher had in mind only the part of the change that is due to selection acting on gene frequencies, not changes in the environment or from mutation and dominance. This corrected form is accepted, but the theorem's importance for real populations is still discussed.

It is a relative of the breeder's equation, which also predicts the response to selection from heritability, and it is a core result of population genetics and the modern synthesis. Fisher's work can be compared with the shifting balance theory of Sewall Wright. The theorem uses concepts like allele frequency change, and it illustrates how natural selection can be treated mathematically.

• Ronald Fisher — its author
• Fitness (Biology) — the quantity it concerns
• Breeder's Equation — a related prediction of selection response