Singular solutions of the diffusion equation of population genetics

Journal of Theoretical Biology

Volumn 247, Issue 4, 2007, Pages 849-858

  McKane, A J ^a   Waxman, D ^b  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

^b UNIVERSITY OF SUSSEX   (United Kingdom)

Author keywords

Diffusion analysis; Genetic drift; Theory

Indexed keywords

GENE EXPRESSION; GENETIC DRIFT; MIGRATION; MUTATION; POPULATION GENETICS; PROBABILITY; SELECTION;

ARTICLE; DYNAMICS; GENE FREQUENCY; GENE LOSS; GENE MUTATION; GENETIC DRIFT; MATHEMATICAL MODEL; POPULATION GENETICS; PRIORITY JOURNAL; THEORETICAL MODEL;

ANIMALS; GENETIC DRIFT; GENETICS, POPULATION; MODELS, GENETIC; PROBABILITY; VARIATION (GENETICS);

EID: 34447512608     PISSN: 00225193     EISSN: 10958541     Source Type: Journal    
DOI: 10.1016/j.jtbi.2007.04.016     Document Type: Article

References (19)

1. Abramowitz M., and Stegun I. Handbook of Mathematical Functions (1965), Dover, New York
2. Barton G. Elements of Green's Functions and Propagation, Potentials, Diffusion, and Waves (1989), Clarendon Press, Oxford
3. Crow, J.F., Kimura, M., 1956. Some genetic problems in natural populations. In: Neyman, J. (Ed.), Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, vol. 4, University of California Press, Berkeley, pp. 1-22.
4. Crow J.F., and Kimura M. An Introduction to Population Genetics Theory (1970), Harper & Row, New York
5. Dirac P.A.M. Quantum Mechanics. fourth ed. (1958), Oxford University Press, Oxford
6. Ewens W.J. Mathematical Population Genetics (1979), Springer, Berlin
7. Feller W. The parabolic differential equations and the associated semi-group of transformations. Ann. Math. 55 (1952) 468-519
8. Feller W. Diffusion processes in one dimension. Trans. Am. Math. Soc. 77 (1954) 1-31
9. Fisher R.A. On the dominance ratio. Proc. R. Soc. Edinburgh 42 (1922) 321-431
10. Fisher R.A. The Genetical Theory of Natural Selection (1930), Clarendon Press, Oxford
11. Gale J.S. Theoretical Population Genetics (1990), Unwin Hyman, London
12. Gardiner C.W. Handbook of Stochastic Methods. third ed. (2004), Springer, Berlin
13. Kimura M. Stochastic processes and distribution of gene frequencies under natural selection. Cold Spring Harbour Symp. Quant. Biol. 20 (1955) 33-53
14. Kimura M. Solution of a process of random genetic drift with a continuous model. Proc. Natl Acad. Sci. 41 (1955) 141-150
15. Lighthill M.J. Introduction to Fourier Analysis and Generalised Functions (1958), Cambridge University Press, Cambridge
16. Maruyama T. Stochastic Problems in Population Genetics (1977), Springer, Berlin
17. Voronka R., and Keller J.B. Asymptotic analysis of stochastic models in population genetics. Math. Biosci. 25 (1975) 331-362
18. Wright S. Evolution in Mendelian populations. Genetics 16 (1931) 97-159
19. Wright S. The differential equation of the distribution of gene frequencies. Proc. Natl Acad. Sci. USA 31 (1945) 382-389