What Changes Has Mathematics Made to the Darwinian Theory?
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Mathematics has played a key role in validating the Darwinian theory of evolution by natural selection. Perhaps most importantly it shows that the variation needed for evolution by natural selection is conserved under the Mendelian evolutionary system. It then quantifies the rate at which favorable new genetic types are incorporated into a population by natural selection. Analyses at the whole genome level (the current active area of genetical research) are possible only by the use of mathematics, particularly the use of matrix theory. Finally, it is only by a mathematical analysis, using stochastic process theory, that the effects of random changes in gene frequencies, unavoidable because of the finite size of any population, can be assessed.
KeywordsSelection variation evolution Mendelism genetics correlation
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- 1.C. Darwin, On the Origin of Species by Means of Natural Selection or the Preservation of Favoured Races in the Struggle for Life. John Murray, London, 1859.Google Scholar
- 2.G. Mendel, Versuche ¨uber Pflanzenhybriden. (Experiments relating to plant hybridization). Verh. Naturforsch. Ver. Br¨unn 4 (1866), 3–17.Google Scholar
- 4.W. Weinberg, ¨ Uber den Nachweis der Vererbung beim Menschen. (On the detection of heredity in man). Jahreshelfts. Ver. Vaterl. Naturf.W¨urttemb. 64 (1908), 368–382.Google Scholar
- 5.J.B.S. Haldane, The Causes of Evolution. Longmans Green, London, 1932.Google Scholar
- 7.K. Pearson and A. Lee, On the laws of inheritance in man. I. Inheritance of physical characters. Biometrika 2 (1903), 357–462.Google Scholar
- 8.R.A. Fisher, The correlation between relatives on the supposition of Mendelian inheritance. Trans. of the Roy. Soc. of Edinburgh 52 (1918), 399–433.Google Scholar
- 9.G. Mal´ecot, Les Math´ematiques de l’H´er´edit´e. Masson, Paris, 1948.Google Scholar
- 10.R.A. Fisher, The Genetical Theory of Natural Selection. Clarendon Press, Oxford, 1930.Google Scholar
- 13.T. Nagylaki, Selection in One- and Two-Locus Systems. Springer, Berlin, 1977.Google Scholar
- 14.T. Nagylaki, Theoretical Population Genetics. Springer-Verlag, Berlin, 1992.Google Scholar
- 18.Y.M. Svirezhev and V.P. Passekov, Fundamentals of Mathematical Evolutionary Genetics. Kluwer, Dordrecht, 1990.Google Scholar
- 19.R.A. Fisher, On the dominance ratio. Proc. Roy. Soc. Edin. 42 (1922), 321–341.Google Scholar
- 20.S. Wright, Evolution in mendelian populations. Genetics 16 (1931), 97–159.Google Scholar