Price equation

In the theory of evolution and natural selection, the Price equation (also known as Price's equation or Price's theorem) describes how a trait or gene changes in frequency over time. The equation uses a covariance between a trait and fitness to give a mathematical description of evolution and natural selection. It provides a way to understand the effects that gene transmission and natural selection have on the proportion of genes within each new generation of a population. The Price equation was derived by George R. Price, working in London to re-derive W.D. Hamilton's work on kin selection. The Price equation also has applications in economics. Examples of the Price equation can be found here: Price equation examples.

The Price equation shows that a change in the average amount z of a trait in a population from one generation to the next (Δz) is determined by the covariance between the amounts z_i of the trait for subpopulations i and the fitnesses w_i of the subpopulations, together with the expected change in the amount of the trait value due to fitness, namely E(w_i Δz_i):

Here w is the average fitness over the population, and E and cov represent the population mean and covariance respectively.

The covariance term captures the effects of natural selection; if the covariance between fitness (w_i) and the trait value (z_i) is positive then the trait value is predicted to increase on average over population i. If the covariance is negative then the trait is deleterious and is predicted to decrease in frequency.

The second term (E(w_i Δz_i)) represents factors other than direct selection that can affect trait evolution. This term can encompass genetic drift, mutation bias, or meiotic drive. Additionally, this term can encompass the effects of multi-level selection or group selection.

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