W.D. Hamilton in the context of "Evolution of sex"

George Robert Price (October 16, 1922 – January 6, 1975) was an American population geneticist. Price is often noted for his formulation of the Price equation in 1967.

Originally a physical chemist and later a science journalist, he moved to London in 1967, where he worked in theoretical biology at the Galton Laboratory, making three important contributions: first, rederiving W.D. Hamilton's work on kin selection with the new Price equation that vindicated group selection; second, introducing (with John Maynard Smith) the concept of the evolutionarily stable strategy (ESS), a central concept in game theory; and third, formalizing Fisher's fundamental theorem of natural selection.

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 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. For example Collins and Gardner use the Price equation to partition the total change in toxin resistance in microbial communities into evolutionary change, ecological change and physiological change. Ellner et al. use the Price equation to disentangle "ecological impacts of evolution vs. non-heritable trait change", using examples from data on birds, fish and zooplankton. The Price equation also has applications in economics.

Kin selection is a process whereby natural selection favours a trait due to its positive effects on the reproductive success of an organism's relatives, even when at a cost to the organism's own survival and reproduction. Kin selection can lead to the evolution of altruistic behaviour. It is related to inclusive fitness, which combines the number of offspring produced with the number an individual can ensure the production of by supporting others (weighted by the relatedness between individuals). A broader definition of kin selection includes selection acting on interactions between individuals who share a gene of interest even if the gene is not shared due to common ancestry.

Charles Darwin discussed the concept of kin selection in his 1859 book, On the Origin of Species, where he reflected on the puzzle of sterile social insects, such as honey bees, which leave reproduction to their mothers, arguing that a selection benefit to related organisms (the same "stock") would allow the evolution of a trait that confers the benefit but destroys an individual at the same time. J.B.S. Haldane in 1955 briefly alluded to the principle in limited circumstances (Haldane famously joked that he would willingly die for two brothers or eight cousins), and R.A. Fisher mentioned a similar principle even more briefly in 1930. However, it was not until 1964 that W.D. Hamilton generalised the concept and developed it mathematically (resulting in Hamilton's rule) that it began to be widely accepted. The mathematical treatment was made more elegant in 1970 due to advances made by George R. Price. The term "kin selection" was first used by John Maynard Smith in 1964.