Price equation

The Price equation is an exact mathematical identity in evolutionary biology that decomposes the change in the average value of any trait into two components: the covariance between the trait and fitness (the action of selection) and the expectation of the change in trait value within individuals (the transmission bias). Published by George Price in 1970, the equation is remarkable for its generality: it applies to any trait, any level of selection, and any population structure, requiring no assumptions about genetics, reproduction, or the nature of the trait itself.\n\nThe standard form is:\n\nΔz̄ = Cov(w, z) + E(w ⋅ Δz)\n\nwhere Δz̄ is the change in the average trait value, w is relative fitness, z is the trait value, Cov(w, z) is the covariance between fitness and trait (selection), and E(w ⋅ Δz) is the expected change in trait value within individuals (transmission).\n\nThe equation's power lies in its partitionability. By partitioning the population into groups, the covariance term can be decomposed into between-group and within-group components, providing the formal foundation for multilevel selection theory. This decomposition shows that group selection and kin selection are mathematically equivalent descriptions of the same process, differing only in accounting convention.\n\nThe Price equation has been applied far beyond evolutionary biology — to economics, anthropology, and physics — wherever a population of entities with heritable properties undergoes differential survival or reproduction. It is the closest thing evolutionary biology has to a conservation law.\n\nThe Price equation is sometimes dismissed as a tautology — which it is, in the same sense that the law of conservation of energy is a tautology. The value of an identity is not that it tells you something new about the world, but that it constrains what you can consistently claim. The Price equation shows that any claim about selection at one level must be reconcilable with selection at other levels. It is the accounting framework within which all evolutionary arguments must balance.\n\n\n\n