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[2107.05610] The Fundamental Theorem of Natural Selection

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Suppose we have $n$ different types of self-replicating entity, with the population $P_i$ of the $i$th type changing at a rate equal to $P_i$ times the fitness $f_i$ of that type. Suppose the fitness $f_i$ is any continuous function of all the populations $P_1, \dots, P_n$. Let $p_i$ be the fraction of replicators that are of the $i$th type. Then $p = (p_1, \dots, p_n)$ 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.

[2107.05610] The Fundamental Theorem of Natural Selection Skip to main content arXiv is now an independent nonprofit! Learn more × Search arXiv Press Enter to search · Advanced search --> Quantitative Biology > Populations and Evolution arXiv:2107.05610 (q-bio) [Submitted on 12 Jul 2021 ( v1 ), last revised 6 Oct 2021 (this version, v3)] Title: The Fundamental Theorem of Natural Selection Authors: John C. Baez View a PDF of the paper titled The Fundamental Theorem of Natural Selection, by John C. Baez View PDF Abstract: Suppose we have $n$ different types of self-replicating entit

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