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.


Diffusion Equation USSR Academy Advantageous Gene Mendelian Genetic Favourable Gene 
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Further reading

  1. 1.
    Fisher, R.A.: The wave of advance of advantageous genes. Ann. Eugen. 7, 355–369 (1937). Google Scholar
  2. 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).
  3. 3.
    Oleinik, O.A.: I.G. Petrowsky and modern mathematics. In: I. G. Petrowsky Selected Works, Part I, pp. 4–30. Gordon and Breach, Amsterdam (1996). Google Scholar
  4. 4.
    Pearson, K.: Mathematical Contributions to the Theory of Evolution, XV, A Mathematical Theory of Random Migration. Dulau, London (1906). Google Scholar
  5. 5.
    Rosenfeld, B.A.: Reminiscences of Soviet Mathematicians. In: Zdravkovska, S., Duren, P.L. (eds.) Golden Years of Moscow Mathematics, 2nd edn., pp. 75–100. American Mathematical Society (2007).
  6. 6.
    Shiryaev, A.N. (ed.): Selected Works of A. N. Kolmogorov, vol. 2. Kluwer, Dordrecht (1992). Google Scholar
  7. 7.
    Shiryaev, A.N.: Andrei Nikolaevich Kolmogorov (April 25, 1903 to October 20, 1987). In: Kolmogorov in Perspective, pp. 1–88. American Mathematical Society (2000).

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© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.IRD (Institut de Recherche pour le Développement)BondyFrance

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