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Abstract

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.

Keywords

Diffusion Equation USSR Academy Advantageous Gene Mendelian Genetic Favourable Gene 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Further reading

  1. 1.
    Fisher, R.A.: The wave of advance of advantageous genes. Ann. Eugen. 7, 355–369 (1937). digital.library.adelaide.edu.au 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). books.google.com
  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). books.google.com Google Scholar
  4. 4.
    Pearson, K.: Mathematical Contributions to the Theory of Evolution, XV, A Mathematical Theory of Random Migration. Dulau, London (1906). www.archive.org 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). books.google.com
  6. 6.
    Shiryaev, A.N. (ed.): Selected Works of A. N. Kolmogorov, vol. 2. Kluwer, Dordrecht (1992). books.google.com 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). books.google.com

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

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

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