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Title: The fundamental theorem of natural selection
Authors: Baez, John C. 
Keywords: Fisher information metric
Lotka–Volterra equation
Natural selection
Population biology
Replicator equation
Issue Date: 30-Oct-2021
Publisher: MDPI
Citation: Baez, John C. (2021-10-30). The fundamental theorem of natural selection. Entropy 23 (11) : 1436. ScholarBank@NUS Repository.
Rights: Attribution 4.0 International
Abstract: 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. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.
Source Title: Entropy
ISSN: 1099-4300
DOI: 10.3390/e23111436
Rights: Attribution 4.0 International
Appears in Collections:Staff Publications

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