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George Price (1922–1975)

Price derived the most general mathematical description of natural selection. The Price equation (1970) expresses evolutionary change as a function of the covariance between a trait and fitness — it partitions the total change into components attributable to selection and to transmission, and it applies to any selection process at any level: genes, organisms, groups, cultural variants, scientific theories. The equation is not a model of any particular biological system; it is a mathematical identity — true by construction for any population undergoing selection — and its generality has made it the foundational tool for multilevel selection theory. Price also co-developed the concept of the evolutionarily stable strategy (ESS) with John Maynard Smith, establishing the field of evolutionary game theory. His career was extraordinary and brief: a physical chemist with no formal training in biology, he produced his major results in a five-year burst of work at University College London before dying by suicide in 1975, impoverished and living in a squat.

Life

Born 6 January 1922 in New York City. His father was an electrician. Educated at Stuyvesant High School and the University of Chicago (BS in chemistry, 1943; PhD in chemistry, 1946). Worked on the Manhattan Project at Argonne National Laboratory during the war. After the war, held positions in chemistry, science journalism, and computing — including work at IBM on early computer-aided design and on medical research at the University of Minnesota.

Price had no connection to evolutionary biology until 1967, when — living in London on savings, having left the United States after a thyroid operation and a period of personal crisis — he read Hamilton’s 1964 papers on inclusive fitness and became convinced that he could contribute to the mathematics of selection. He walked into the Galton Laboratory at University College London and began working on what became the Price equation. Cedric Smith, head of the Galton Laboratory, recognised the quality of Price’s work and gave him an honorary appointment.

The productive period was approximately 1968–73. During this time Price derived the equation, collaborated with Maynard Smith on the ESS concept, corresponded extensively with Hamilton (who later described Price as having “the most remarkable mind” he had encountered), and developed the multilevel selection formulation that D. S. Wilson and others would later build on. The influence ran both ways: Price’s covariance formulation gave Hamilton a far more general derivation of his own kin-selection result than the 1964 papers had provided, and Hamilton adopted the Price equation to re-derive and extend inclusive fitness theory. That Hamilton — who had produced the foundational result — found Price’s framework superior to his own is much of why he rated Price so highly.

In 1970, Price underwent a religious conversion — to a fervent Christianity — that increasingly dominated his life. He gave away his possessions, devoted himself to helping homeless people in London, and deteriorated financially and physically. He died by suicide on 6 January 1975, in a squat in Euston, on his fifty-third birthday. The intellectual-biographical arc — that the man who produced the formal mathematics of the evolution of altruism then turned to living a radically self-emptying altruism — has been a persistent theme in the literature on Price. Oren Harman’s biography The Price of Altruism (2010) develops the arc in detail.

The Price equation

The covariance approach to selection was not entirely without precedent: Alan Robertson’s 1966 “secondary theorem of natural selection” had expressed the response to selection as the covariance between breeding value and fitness. Price’s equation generalises Robertson’s result — it applies to any trait, any fitness measure, any population structure — and does so in a framework that makes the multilevel partition natural. Robertson’s theorem is a special case; the Price equation is the general identity.

“Selection and Covariance” (Nature, 1970). The equation:

Δz̄ = Cov(w, z) / w̄

where Δz̄ is the change in the population mean of a trait z, w is individual fitness, and w̄ is mean fitness. The equation states that the change in the mean value of a trait under selection is proportional to the covariance between the trait and fitness: traits positively correlated with fitness increase; traits negatively correlated with fitness decrease.

Generality. The equation is not a model — it does not assume any particular genetics, any particular population structure, or any particular mechanism. It is a mathematical identity that holds for any population in which entities vary in a trait and in their contribution to the next generation. Its scope extends beyond biology: any selection process (including cultural selection, economic competition, or the differential adoption of scientific theories) can be described by the Price equation.

Multilevel selection. The Price equation can be expanded to partition selection into within-group and between-group components. This is the mathematical foundation of the multilevel selection framework that D. S. Wilson developed in the 1970s and 1980s. If groups vary in the frequency of a trait, and groups with more of the trait contribute more to the next generation, then between-group selection favours the trait — even if within-group selection opposes it. The outcome depends on the relative magnitudes of the two components. The Price equation makes this partition exact and provides the framework within which the group-selection debate can be stated with mathematical precision.

The full Price equation (1972). Price’s second paper, “Extension of Covariance Selection Mathematics” (Annals of Human Genetics), extended the equation to include a transmission term — changes in trait value between parent and offspring that are not due to selection (mutation, developmental noise, cultural transmission). The full equation separates selection (covariance between trait and fitness) from transmission (expected change in trait conditional on ancestry). The extension made the equation applicable to any heritable variation, including cultural and epigenetic variation.

Evolutionary game theory

Price’s collaboration with Maynard Smith produced the concept of the evolutionarily stable strategy (ESS) — a strategy that, if adopted by most members of a population, cannot be invaded by a rare mutant playing a different strategy. The concept was published in Maynard Smith and Price, “The Logic of Animal Conflict” (Nature, 1973), and became the foundation of evolutionary game theory.

The collaboration was productive but the credit distribution has been discussed. Maynard Smith developed the ESS concept further in his 1982 book Evolution and the Theory of Games; Price’s contributions to the foundational work are acknowledged in the 1973 paper but were overshadowed by Maynard Smith’s subsequent programme. Hamilton, who knew both men’s contributions intimately, argued that Price’s mathematical contribution was underrecognised.

Where Price stops

The Price equation is a mathematical identity, not a causal model. It tells you that the change in a trait is the covariance between the trait and fitness, but it does not tell you why the covariance exists — what causal mechanism produces the correlation between trait value and reproductive success. The equation describes the bookkeeping of selection without specifying the ecology, the genetics, or the developmental biology that makes selection happen. This is simultaneously its power (it applies to everything) and its limitation (it explains nothing specific). Whether the Price equation is the deepest statement about selection or a tautology dressed in mathematics is debated: Steven Frank has defended its causal content; Samir Okasha’s Evolution and the Levels of Selection (2006) treats it as the right formal framework for the levels-of-selection debate while acknowledging the bookkeeping concern.

The multilevel partition — decomposing selection into within-group and between-group components — depends on how groups are defined. Different groupings produce different partitions, and the Price equation does not specify which grouping is the right one. The question of which groups are biologically real (as opposed to arbitrary statistical constructs) is the empirical question that the mathematics frames but does not answer.

Key works

See also: Hamilton · Maynard Smith · Wilson (D.S.) · Sober · Darwinism