The diffusion of genes (1937)
In 1937 Ronald Fisher and three Russian mathematicians, Kolmogorov, Petrovsky and Piskunov, independently studied a partial differential equation for the geographic spread of an advantageous gene. They showed that the gene frequency behaved like a wave travelling at a well-defined speed depending on the gene’s advantage and on a diffusion coefficient. Their works were the starting point for the theory of reaction–diffusion equations.
KeywordsDiffusion Equation USSR Academy Advantageous Gene Mendelian Genetic Favourable Gene
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- 2.Kolmogorov, A.N., Petrovskii, I.G., Piskunov, N.S.: A study of the diffusion equation with increase in the amount of substance, and its application to a biological problem. Bull. Moscow Univ. Math. Mech. 1:6, 1–26 (1937) Reprinted in: V.M. Tikhomirov (ed.) Selected Works of A. N. Kolmogorov, vol. 1, p. 242–270. Kluwer, Dordrecht (1991). Also in: I. G. Petrowsky Selected Works, Part II, pp. 106–132. Gordon and Breach, Amsterdam (1996). books.google.com
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