Mathematics, genetics and evolution

Quantitative Biology

Volumn 1, Issue 1, 2013, Pages 9-31

  Ewens, Warren J ^a  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

Additive Genetic Variance; Allele Model; Allelic Type; Natural Selection; Random Mating

Indexed keywords

EID: 84893171487     PISSN: 20954689     EISSN: 20954697     Source Type: Journal    
DOI: 10.1007/s40484-013-0003-5     Document Type: Review

References (37)

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.
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.
8. Wright, S. (1931) Evolution in Mendelian populations. Genetics, 16, 97–159.
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.
11. Ewens, W. J. and Kirby, K. (1975) The eigenvalues of the neutral alleles process. Theor. Popul. Biol., 7, 212–220.
12. Ewens, W. J. (1972) The sampling theory of selectively neutral alleles. Theor. Popul. Biol., 3, 87–112.
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.
14. Watterson, G. A. (1975) On the number of segregating sites in genetical models without recombination. Theor. Popul. Biol., 7, 256–276.
15. Tavaré, S. (1984) Lines of descent and genealogical processes, and their applications in population genetic models. Theoret. Pop. Biol., 26, 119–164.
16. Watterson, G. A. (1977) Heterosis or neutrality? Genetics, 85, 789–814.
17. Ewens, W. J. (1974) A note on the sampling theory for infinite alleles and infinite sites models. Theor. Popul. Biol., 6, 143–148.
18. Tajima, F. (1989) Statistical method for testing the neutral mutation hypothesis by DNA polymorphism. Genetics, 123, 585–595.
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.
24. Kingman, J. F. C. (1982) On the genealogy of large populations. J. Appl. Probab., 19, 27–43.
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.
27. Donnelly, P. J. (1986) Partition structures, Polya urns, the Ewens sampling formula, and the ages of alleles. Theor. Popul. Biol., 30, 271–288.
28. Watterson, G. A. and Guess, H. A. (1977) Is the most frequent allele the oldest? Theor. Popul. Biol., 11, 141–160.
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 infinitelymany neutral alleles model. J. Appl. Probab., 13, 639–651.
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.
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.
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.