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1930 The fundamental theorem of natural selection
CHAPTER FIVE
1930 The fundamental theorem of natural selection The concept Sir Ronald Fisher (1930) showed that natural selection at a single locus will increase the mean fitness of the population and that increase will be proportional to the additive genetic variance for fitness. He called this result “The Fundamental Theorem of Natural Selection”. This theorem has been invoked to suggest that natural selection will always result in a population being better adapted to its environment.
The explanation Fisher is credited with many substantial accomplishments in population genetics and statistics. His 1918 paper (Fisher, 1918) is credited with showing how Mendelian genetic systems could explain phenotypic correlation between relatives. This work united the disparate groups of Mendelian and Biometrician branches of genetics (Provine, 1971). However, his book that was first published in 1930 (Fisher, 1930) sought to give a larger view of population genetics and evolution. Indeed, the latter third of the book is devoted to human genetics (which I will briefly touch on later). One of Fisher’s most important results was his demonstration that natural selection would increase the mean fitness of the population at a rate proportional to the additive genetic variance. Fisher’s discussion and proof of this is somewhat opaque and I will outline here a much more direct proof from Crow (1986). The most detailed analysis of the properties of selection at a single locus were worked out by Kingman (1961). Imagine a single locus with two alleles, A1 and A2, at frequencies p1 and p2 respectively. The fitnesses of the three genotypes, A1A1, A1A2, and A2A2 are w11, w12, and w22 respectively. Then the population mean fitness, w, is, p1w1 þ p2w2, where w1 is p1w11 þ p2w12 and w2 is p1w12 þ p2w22.
Conceptual Breakthroughs in Evolutionary Ecology ISBN: 978-0-12-816013-8 https://doi.org/10.1016/B978-0-12-816013-8.00005-3
© 2020 Elsevier Inc. All rights reserved.
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j
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Conceptual Breakthroughs in Evolutionary Ecology
Then after one generation of selection the standardized change in mean fitness, Dw w , is. 2 2 Dw 2 p1 ðw1 wÞ þ p2 ðw2 wÞ V ðwÞ z z 2 2 w w w where V(w) is the additive variance in fitness. The importance of this theorem was that it gave justification for evolutionary biologists to claim that evolution would provide maximal adaptation. I discuss the limitations of this claim in more detail in Chapter 26. Fisher was a major participant in the early development of theoretical population genetics and evolution. He clearly had lofty expectations and thought that biology could use mathematics with the same skill as physicists. In the preface to his book Fisher (1930) longs for the time when “.there is built up a tradition of mathematical work devoted to biological problems, comparable to the researches upon which a mathematical physicist can draw in the resolution of special difficulties”. While these hopes of Fisher have not been realized, the first seven chapters of “The genetical theory of natural selection” are all high-quality, important contributions to evolutionary theory. In contrast, the last five chapters on human genetics and the decay of human civilization are today shocking in their racial, elitist tone. Fisher seemed to feel that social classes of people in modern society was a reflection of their genetic traits. Fisher was deeply concerned that higher status people in western civilization were not having as many children as people from the lower social classes. Fisher summarizes this point of view (Fisher, 1930, pg. 221e222) “. success in human endeavor is inseparable from the maintenance or attainment of social status; wherever, then, the socially lower occupations are more fertile, we must face the paradox that the biologically successful members of our society are to be found principally among its social failures, and equally that classes of persons who are prosperous and socially successful are, on the whole, the biological failures, the unfit of the struggle for existence, doomed more or less speedily, according to their social distinction, to be eradicated from the human stock.” Fisher’s inability to recognize the non-genetic, environmental contribution to “social status” is somewhat surprising given that Fisher was by all other measures a brilliant man.
1930 The fundamental theorem of natural selection
13
Impact: 10 The fundamental theorem of natural section has had a lasting and important impact on research in evolutionary ecology and is thus given this high rating.
References Crow, J.F., 1986. Basic Concepts in Population, Quantitative, and Evolutionary Genetics. W. H. Freeman, New York. Fisher, R.A., 1918. The correlation between relatives on the supposition of Mendelian inheritance. Trans. R. Soc. Edinb. 52, 399e433. Fisher, R.A., 1930. The Genetical Theory of Natural Selection. Oxford University Press. Kingman, J.F.C., 1961. A mathematical problem in population genetics. Math. Proc. Camb. Philos. Soc. 57, 574e582. Provine, W.B., 1971. The Origins of Theoretical Population Genetics. University of Chicago Press.
1930 The fundamental theorem of natural selection The concept Sir Ronald Fisher (1930) showed that natural selection at a single locus will increase the mean fitness of the population and that increase will be proportional to the additive genetic variance for fitness. He called this result “The Fundamental Theorem of Natural Selection”. This theorem has been invoked to suggest that natural selection will always result in a population being better adapted to its environment.
The explanation Fisher is credited with many substantial accomplishments in population genetics and statistics. His 1918 paper (Fisher, 1918) is credited with showing how Mendelian genetic systems could explain phenotypic correlation between relatives. This work united the disparate groups of Mendelian and Biometrician branches of genetics (Provine, 1971). However, his book that was first published in 1930 (Fisher, 1930) sought to give a larger view of population genetics and evolution. Indeed, the latter third of the book is devoted to human genetics (which I will briefly touch on later). One of Fisher’s most important results was his demonstration that natural selection would increase the mean fitness of the population at a rate proportional to the additive genetic variance. Fisher’s discussion and proof of this is somewhat opaque and I will outline here a much more direct proof from Crow (1986). The most detailed analysis of the properties of selection at a single locus were worked out by Kingman (1961). Imagine a single locus with two alleles, A1 and A2, at frequencies p1 and p2 respectively. The fitnesses of the three genotypes, A1A1, A1A2, and A2A2 are w11, w12, and w22 respectively. Then the population mean fitness, w, is, p1w1 þ p2w2, where w1 is p1w11 þ p2w12 and w2 is p1w12 þ p2w22.
Conceptual Breakthroughs in Evolutionary Ecology ISBN: 978-0-12-816013-8 https://doi.org/10.1016/B978-0-12-816013-8.00005-3
© 2020 Elsevier Inc. All rights reserved.
11
j
12
Conceptual Breakthroughs in Evolutionary Ecology
Then after one generation of selection the standardized change in mean fitness, Dw w , is. 2 2 Dw 2 p1 ðw1 wÞ þ p2 ðw2 wÞ V ðwÞ z z 2 2 w w w where V(w) is the additive variance in fitness. The importance of this theorem was that it gave justification for evolutionary biologists to claim that evolution would provide maximal adaptation. I discuss the limitations of this claim in more detail in Chapter 26. Fisher was a major participant in the early development of theoretical population genetics and evolution. He clearly had lofty expectations and thought that biology could use mathematics with the same skill as physicists. In the preface to his book Fisher (1930) longs for the time when “.there is built up a tradition of mathematical work devoted to biological problems, comparable to the researches upon which a mathematical physicist can draw in the resolution of special difficulties”. While these hopes of Fisher have not been realized, the first seven chapters of “The genetical theory of natural selection” are all high-quality, important contributions to evolutionary theory. In contrast, the last five chapters on human genetics and the decay of human civilization are today shocking in their racial, elitist tone. Fisher seemed to feel that social classes of people in modern society was a reflection of their genetic traits. Fisher was deeply concerned that higher status people in western civilization were not having as many children as people from the lower social classes. Fisher summarizes this point of view (Fisher, 1930, pg. 221e222) “. success in human endeavor is inseparable from the maintenance or attainment of social status; wherever, then, the socially lower occupations are more fertile, we must face the paradox that the biologically successful members of our society are to be found principally among its social failures, and equally that classes of persons who are prosperous and socially successful are, on the whole, the biological failures, the unfit of the struggle for existence, doomed more or less speedily, according to their social distinction, to be eradicated from the human stock.” Fisher’s inability to recognize the non-genetic, environmental contribution to “social status” is somewhat surprising given that Fisher was by all other measures a brilliant man.
1930 The fundamental theorem of natural selection
13
Impact: 10 The fundamental theorem of natural section has had a lasting and important impact on research in evolutionary ecology and is thus given this high rating.
References Crow, J.F., 1986. Basic Concepts in Population, Quantitative, and Evolutionary Genetics. W. H. Freeman, New York. Fisher, R.A., 1918. The correlation between relatives on the supposition of Mendelian inheritance. Trans. R. Soc. Edinb. 52, 399e433. Fisher, R.A., 1930. The Genetical Theory of Natural Selection. Oxford University Press. Kingman, J.F.C., 1961. A mathematical problem in population genetics. Math. Proc. Camb. Philos. Soc. 57, 574e582. Provine, W.B., 1971. The Origins of Theoretical Population Genetics. University of Chicago Press.