page_title: Price equation
section_title: Statement
hierarchical_section_title: Price equation / Statement
caption_attribution_description: English: A trait under positive selection. The blue dashed line shows the current mean population trait value, the red dashed line shows the mean population trait value in the next generation. Because high trait values are associated with higher fitness the the mean trait value increases due to selection.
context_page_description: In the theory of evolution and natural selection, the Price equation describes how a trait or allele 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 frequency of alleles 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. Examples of the Price equation have been constructed for various evolutionary cases. The Price equation also has applications in economics.
context_section_description: The Price equation shows that a change in the average amount  of a trait in a population from one generation to the next () is determined by the covariance between the amounts  of the trait for  subpopulation  and the fitnesses  of the subpopulations, together with the expected change in the amount of the trait value due to fitness, namely : 
  Here  is the average fitness over the population, and  and  represent the population mean and covariance respectively. 'Fitness'  is the ratio of the average number of offspring for the whole population per the number of adult individuals in the population, and  is that same ratio only for subpopulation .
  The covariance term captures the effects of natural selection; if the covariance between fitness () and the trait value () is positive then the trait value is predicted to increase on average over population . If the covariance is negative then the trait is deleterious and is predicted to decrease in frequency.
  The second term, , 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.
  Price (1972) referred to this as the "environment change" term, and denoted both terms using partial derivative notation (∂NS and ∂EC). This concept of environment includes interspecies and ecological effects. Price describes this as follows:
  Fisher adopted the somewhat unusual point of view of regarding dominance and epistasis as being environment effects. For example, he writes (1941): ‘A change in the proportion of any pair of genes itself constitutes a change in the environment in which individuals of the species find themselves.’ Hence he regarded the natural selection effect on M as being limited to the additive or linear effects of changes in gene frequencies, while everything else – dominance, epistasis, population pressure, climate, and interactions with other species – he regarded as a matter of the environment.
  — G.R. Price (1972), Fisher's fundamental theorem made clear
caption: Example for a trait under positive selection
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