The fundamental theorem of natural selection in Ewens' sense. (Case of many loci)
type: Item
instance of: scholarly article
title: The fundamental theorem of natural selection in Ewens' sense. (Case of many loci)
zbMATH Open document ID: 0840.92015
author: Anne-Marie Castilloux
author: Sabin Lessard
published in: Theoretical Population Biology
publication date: 1996-07-01T00:00:00Z
review text: Fisher's Fundamental Theorem of Natural Selection (FTNS) states that ``the rate of increase in fitness of any organism at any time is equal to its genetic variance in fitness at that time'' but ``the rigour of the demonstration requires that the terms employed should be used strictly as defined''. \textit{W. J. Ewens} [ibid. 36, No. 2, 167-180 (1989; Zbl 0702.92012)]\ claims that the FTNS should not be limited to continuous-time models and interprets the FTNS in the case of discrete nonoverlapping generations as follows: a partial change in the mean fitness of a population is exactly equal to the ratio of the additive genetic variance in fitness over the mean fitness. The partial change in the mean fitness is obtained by replacing the exact genotypic values of fitness by the associated additive genotypic values and by keeping these values constant from one generation to the next. Some of the main arguments in support of Ewens' interpretation include the following: the FTNS should be exact and it should hold without any assumption of random mating. A further contribution of Ewens (1989) is to show that the FTNS in its new interpretation holds in the case of fitness determined at many loci. But, in Eq. (26) therein, which characterizes the additive (average) allelic effects on fitness in this case, a term was inadvertently omitted. This equation is corrected in a follow-up paper of \textit{W. J. Ewens} [ibid. 42, No. 3, 333-346 (1992; Zbl 0768.92018)]. But a term is still missing in this corrected equation. We give the complete equation characterizing the additive allelic effects on fitness determined at many loci without the assumption of random mating. Then we confirm that the FTNS in Ewens' (1989) sense is fully valid in this general case. This is pertinent since ``the new interpretation leans heavily on the concept of the average effect of an allele'' (Ewens, 1992).
Mathematics Subject Classification ID: 92D15
zbMATH DE Number: 854732
zbMATH Keywords: Fisher's fundamental theorem of natural selection
zbMATH Keywords: mean fitness
zbMATH Keywords: additive geonotypic values
zbMATH Keywords: additive allelic effects
MaRDI profile type: Publication
full work available at URL: tpbi.1995.1031
OpenAlex ID: W1973341286
Wikidata QID: Q52322848
DOI: 10.1006/TPBI.1995.1031
description: scientific article; zbMATH DE number 854732