The Price equation as a bridge between animal breeding and evolutionary biology.

The genetic response to selection is central to both evolutionary biology and animal and plant breeding. While Price's theorem (PT) is well-known in evolutionary biology, most breeders are unaware of it. Rather than using PT, breeders express response to selection as the product of the intensity of selection (i), the accuracy of selection (ρ) and the additive genetic standard deviation (σA); R = iρσA. In contrast to the univariate 'breeder's equation', this expression holds for multivariate selection on Gaussian traits. Here, I relate R = iρσA to PT, and present a generalized version, R = iwρA,wσA, valid irrespective of the trait distribution. Next, I consider genotype-environment covariance in relation to the breeder's equation and PT, showing that the breeder's equation may remain valid depending on whether the genotype-environment covariance works across generations. Finally, I consider the response to selection in the prevalence of an endemic infectious disease, as an example of an emergent trait. The result shows that disease prevalence has much greater heritable variation than currently believed. The example also illustrates that the indirect genetic effect approach moves elements of response to selection from the second to the first term of PT, so that changes acting via the social environment come within the reach of quantitative genetics. This article is part of the theme issue 'Fifty years of the Price equation'.