Fundamental Theorems of Evolution

2017/02/28 by David C. Queller · 150 citations
Agricultural and Biological Sciences · Biochemistry, Genetics and Molecular Biology · Mathematics · Social Sciences · #Applied mathematics #Artificial intelligence #Biology #Computer science #Econometrics #Epistemology #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #Evolutionary biology #Fixed-point theorem #Focus (optics) #Fundamental theorem #Mathematical economics #Mathematics #Natural selection #Physics #Plant and animal studies #Price equation #Pure mathematics #Scope (computer science) #Selection (genetic algorithm) #Set (abstract data type) #Simplicity #Social evolution

paper · doi:10.1086/690937

published in The American Naturalist 189(4), 345-353 (University of Chicago Press)

openalex publication_date 2017/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Evolutionary biology is undergirded by an extensive and impressive set of mathematical models. Yet only one result, Fisher's theorem about selection and fitness, is generally accorded the status of a fundamental theorem. I argue that although its fundamental status is justified by its simplicity and scope, there are additional results that seem similarly fundamental. I suggest that the most fundamental theorem of evolution is the Price equation, both because of its simplicity and broad scope and because it can be used to derive four other familiar results that are similarly fundamental: Fisher's average-excess equation, Robertson's secondary theorem of natural selection, the breeder's equation, and Fisher's fundamental theorem. These derivations clarify both the relationships behind these results and their assumptions. Slightly less fundamental results include those for multivariate evolution and social selection. A key feature of fundamental theorems is that they have great simplicity and scope, which are often achieved by sacrificing perfect accuracy. Quantitative genetics has been more productive of fundamental theorems than population genetics, probably because its empirical focus on unknown genotypes freed it from the tyranny of detail and allowed it to focus on general issues.

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