Mathematics, genetics and evolution

Warren J. Ewens

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Quant. Biol. ›› 2013, Vol. 1 ›› Issue (1) : 9-31. DOI: 10.1007/s40484-013-0003-5
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Mathematics, genetics and evolution

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Abstract

The importance of mathematics and statistics in genetics is well known. Perhaps less well known is the importance of these subjects in evolution. The main problem that Darwin saw in his theory of evolution by natural selection was solved by some simple mathematics. It is also not a coincidence that the re-writing of the Darwinian theory in Mendelian terms was carried largely by mathematical methods. In this article I discuss these historical matters and then consider more recent work showing how mathematical and statistical methods have been central to current genetical and evolutionary research.

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Warren J. Ewens. Mathematics, genetics and evolution. Quant. Biol., 2013, 1(1): 9‒31 https://doi.org/10.1007/s40484-013-0003-5

References

[1]
Darwin, C.(1859) On the Origin of Species by Means of Natural Selection or the Preservation of Favoured Races in the Struggle for Life. London: John Murray.
[2]
Mendel, G.(1866) Versuche über pflanzenhybriden (Experiments relating to plant hybridization). Verh. Naturforsch. Ver. Brunn, 4, 3-17.
[3]
Hardy, G. H. (1908) Mendelian proportions in a mixed population. Science, 28, 49-50.
CrossRef Pubmed Google scholar
[4]
Weinberg, W. (1908) Über den Nachweis der Vererbung beim Menschen. (On the detection of heredity in man). Jahreshelfts. Ver. Vaterl. Naturf. Württemb., 64, 368-382.
[5]
Fisher, R. A. (1930) The Genetical Theory of Natural Selection. Oxford: Clarendon Press.
[6]
Malécot, G.(1948) Les Mathématiques de l’Hérédité. Paris: Masson.
[7]
Kingman, J. F. C.(1961) A mathematical problem in population genetics. Proc. Camb. Philol. Soc., 57, 574-582.
CrossRef Google scholar
[8]
Wright,S. (1931) Evolution in Mendelian populations. Genetics, 16, 97-159.
Pubmed
[9]
Ewens,W. J. (2004) Mathematical Population Genetics. New York: Springer.
[10]
Kimura, M. (1971) Theoretical foundation of population genetics at the molecular level. Theor. Popul. Biol., 2, 174-208. 5162686
CrossRef Google scholar
[11]
Ewens, W. J. and Kirby, K. (1975) The eigenvalues of the neutral alleles process. Theor. Popul. Biol., 7, 212-220.
CrossRef Pubmed Google scholar
[12]
Ewens, W. J. (1972) The sampling theory of selectively neutral alleles. Theor. Popul. Biol., 3, 87-112.
CrossRef Pubmed Google scholar
[13]
Kimura, M. (1969) The number of heterozygous nucleotide sites maintained in a finite population due to steady flux of mutations. Genetics, 61, 893-903.
Pubmed
[14]
Watterson, G. A. (1975) On the number of segregating sites in genetical models without recombination. Theor. Popul. Biol., 7, 256-276.
CrossRef Pubmed Google scholar
[15]
Tavaré, S. (2004) Ancestral inference in population genetics. In Cantoni, O., Tavaré S. and Zeitouni, O. (eds.), École d’Été de Probabilités de Saint-Flour XXXI-2001. Berlin: Springer-Verlag, 1-188.
[16]
Watterson, G. A. (1977) Heterosis or neutrality? Genetics, 85, 789-814.
Pubmed
[17]
Ewens, W. J. (1974) A note on the sampling theory for infinite alleles and infinite sites models. Theor. Popul. Biol., 6, 143-148.
CrossRef Pubmed Google scholar
[18]
Tajima, F. (1989) Statistical method for testing the neutral mutation hypothesis by DNA polymorphism. Genetics, 123, 585-595.
Pubmed
[19]
Hein, J., Schierup, M. H. and Wiuf, C. (2005) Gene Genealogies, Variation and Evolution. Oxford: Oxford University Press.
[20]
Wakeley, J. (2009) Coalescent Theory. Greenwood Village, Colorado: Roberts and Company.
[21]
Marjoram, P. and Joyce, P. (2009) Practical implications of coalescent theory. In Lenwood, L. S. and Ramakrishnan N. (eds.), Problem Solving Handbook in Computational Biology and Bioinformatics. New York: Springer.
[22]
Nordborg, M. (2001) Coalescent theory. In Balding, D. J., Bishop M. J. and Cannings, C. (eds.), Handbook of Statistical Genetics. Chichester, UK: Wiley.
[23]
Kingman, J. F. C. (1982) The coalescent. Stoch. Proc. Appl., 13, 235-248.
CrossRef Google scholar
[24]
Kingman, J. F. C. (1982) On the genealogy of large populations. J. Appl. Probab., 19, 27-43.
CrossRef Google scholar
[25]
Kelly, F. P. (1977) Exact results for the Moran neutral allele model. J. Appl. Probab., 14, 197-201.
[26]
Donnelly, P. J. and Tavaré, S. (1986) The ages of alleles and a coalescent. Adv. Appl. Probab., 18, 1-19.
CrossRef Google scholar
[27]
Donnelly, P. J. (1986) Partition structures, Polya urns, the Ewens sampling formula, and the ages of alleles. Theor. Popul. Biol., 30, 271-288.
CrossRef Pubmed Google scholar
[28]
Watterson, G. A. and Guess, H. A. (1977) Is the most frequent allele the oldest? Theor. Popul. Biol., 11, 141-160.
CrossRef Pubmed Google scholar
[29]
Kingman, J. F. C. (1975) Random discrete distributions. J. R. Stat. Soc. [Ser. A], 37, 1-22.
[30]
Watterson, G. A. (1976) The stationary distribution of the infinitely-many neutral alleles model. J. Appl. Probab., 13, 639-651.
CrossRef Google scholar
[31]
Crow, J. F. (1972) The dilemma of nearly neutral mutations. How important are they for evolution and human welfare? J. Hered., 63, 306-316.
Pubmed
[32]
Griffiths, R. C. (1980) Unpublished notes.
[33]
Engen, S. (1975) A note on the geometric series as a species frequency model. Biometrika, 62, 697-699.
CrossRef Google scholar
[34]
McCloskey, J. W. (1965) A model for the distribution of individuals by species in an environment. Unpublished PhD. thesis. Michigan State University.
[35]
Tavaré, S. (2004) Ancestral inference in population genetics. In Picard J. (ed.), Êcole d’Êté de Probabilités de Saint-Fleur XXX1-2001, 1-188, Berlin: Springer-Verlag.
[36]
Durrett, R. (2008) Probability Models for DNA Sequence Evolution. Berlin: Springer-Verlag.
[37]
Etheridge, A. (2011) Some Mathematical Models from Population Genetics. Berlin: Springer-Verlag

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