Abstract
Mean fitness is not always maximized under natural selection. In particular, in two locus models, recombination and epistasis may combine to prevent the operation of a maximizing priciple for mean fitness. If inversion phenomena are considered, however, there exist fully polymorphic equilibria which maximize the mean fitness and moreover the initial progress of an inversion can proceed if and only if it gives rise to an increase in mean fitness. While not applicable to all models, the principle of mean fitness maximization is still useful heuristically.
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Literature
Atkinson, F. V., G. A. Watterson and P. A. P. Moran. 1960. “A Matrix Inequality.”Quart. J. Math. Oxford, (2)11, 137–140.
Bodmer, W. F. and P. A. Parsons. 1962. “Linkage and Recombination in Evolution.”Adv. Genet.,11, 1–100.
Deakin, M. A. B. 1968. “Interaction of Selection and Recombination.”Aust. J. Biol. Sci.,21, 55–59.
— 1972. “A Model for Inversion Polymorphism.”J. Theor. Biol.,35, 191–212.
Deakin, M. A. B. In Press. “The Effect of Epistasis in the Standard Two-Locus Model.”Aust. J. Biol. Sci. (to appear).
Dobzhansky, T. 1951.Genetics and the Origin of Species (3rd Edition). New York: Columbia University Press.
Ewens, W. J. 1969. “With Additive Fitnesses, the Mean Fitness Increases.”Nature,221, 1076.
Fisher, R. A. 1930.The Genetical Theory of Natural Selection. Oxford: Clarendon Press.
Hardin, G. 1960. “The Competitive Exclusion Principle.”Science,131, 1292–1297.
Kimura, M. 1956. “A Model of a Genetic System Which Leads to Closer Linkage by Natural Selection.”Evolution,10, 278–287.
— 1958. “On the Change of Population Fitness by Natural Selection.”Heredity,12, 145–167.
— 1965. “Attainment of Quasi-Linkage Equilibrium when Gene Frequencies are Changing by Natural Selection.”Genetics,52, 875–890.
— 1966. “Two Loci Polymorphism as a Stationary Point.”Ann. Rep. Nat. Inst. Genet. Japan,17, 65–67.
Kingman, J. F. C. 1961. “On an Inequality in Partial Averages.”Quart. J. Math. Oxford, (2)12, 78–80.
Lewontin, R. C. and K.-I. Kojima. 1960. “The Evolutionary Dynamics of Complex Polymorphisms.”Evolution,14, 458–472.
Moran, P. A. P. 1964. “On the Nonexistence of Adaptive Topographies.”Ann. Human Genet.,27, 383–393.
Mulholland, H. P. and C. A. B. Smith. 1959. “An Inequality Arising in Genetical Theory.”Am. Math. Monthly,66, 673–683.
Nei, M. 1967. “Modification of Linkage Intensity by Natural Selection.”Genetics,57, 625–641.
Rashevsky, N. 1960.Mathematical Biophysics: Physico-Mathematical Foundations of Biology. (3rd Edn) Vol. II. New York: Dover.
Rosen, R. 1967.Optimality Principles in Biology. London: Butterworths.
Scheuer, P. A. G. and S. P. H. Mandel. 1959. “An Inequality in Population Genetics.”Heredity,13, 519–524.
Wright, S. 1932. “The Roles of Mutation, Inbreeding and Selection in Evolution.”Proc. Sixth Int. Cong. Genet., 356–366.
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Deakin, M.A.B. On the status of mean fitness maximization as a governing principle in evolution. Bltn Mathcal Biology 35, 43–50 (1973). https://doi.org/10.1007/BF02558792
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DOI: https://doi.org/10.1007/BF02558792