2021/07/12 by John C. Baez · 1 voice · 11 citations
Arts and Humanities · Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Social Sciences · #Artificial intelligence #Computer science #Discrete mathematics #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #Fixed-point theorem #Fundamental theorem #Geography #Mathematical economics #Mathematics #Natural (archaeology) #Natural selection #Philosophy and History of Science #Selection (genetic algorithm) #cs.IT #math.IT #msc:37N25 #msc:53B12 #q-bio.PE
paper · pdf · doi:10.3390/e23111436
published in Entropy 23(11), 1436 (Multidisciplinary Digital Publishing Institute) · 6 pages
arxiv published 2021/07/12 · arxiv created 2021/10/06 · openalex publication_date 2021/10/30 · arxiv updated 2021/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Suppose we have n different types of self-replicating entity, with the population Pi of the ith type changing at a rate equal to Pi times the fitness fi of that type. Suppose the fitness fi is any continuous function of all the populations P1,…,Pn. Let pi be the fraction of replicators that are of the ith type. Then p=(p1,…,pn) is a time-dependent probability distribution, and we prove that its speed as measured by the Fisher information metric equals the variance in fitness. In rough terms, this says that the speed at which information is updated through natural selection equals the variance in fitness. This result can be seen as a modified version of Fisher’s fundamental theorem of natural selection. We compare it to Fisher’s original result as interpreted by Price, Ewens and Edwards.