The frequency spectrum of a mutation, and its age, in a general diffusion model

Theoretical Population Biology

Volumn 64, Issue 2, 2003, Pages 241-251

  Griffiths, R C ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

Age of a mutation; Coalescent process; Diffusion process; Frequency spectrum; Population genetics

Indexed keywords

FREQUENCY ANALYSIS; MUTATION; POPULATION DYNAMICS; PROBABILITY;

EID: 0345274562     PISSN: 00405809     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0040-5809(03)00075-3     Document Type: Article

References (36)

1. Barbour A.D., Ethier S.N., Griffiths R.C. A transition function expansion for a diffusion model with selection. Ann. Appl. Probab. 10:2000;123-162.
2. Barton, N.H., Etheridge, A.M., Strum, A.K., 2003. Coalescence in a random background. Ann. Appl. Prob., to appear.
3. Bustamante C.D., Wakeley J., Hartl D.L. Directional selection and the site-frequency spectrum. Genetics. 159:2001;1779-1788.
4. Donnelly P., Kurtz T.G. A countable representation of the Fleming-Viot measure-valued diffusion. Ann. Appl. Probab. 24:1996;698-742.
5. Ethier S.N., Griffiths R.C. The transition function of a Fleming-Viot process. Ann. Probab. 21:1993;1571-1590.
6. Ewens W.J. Mathematical Population Genetics. Biomathematics. Vol. 9:1979;Springer, Heidelberg.
7. Fu Y.-X. Statistical properties of segregating sites. Theor. Popul. Biol. 48:1995;172-197.
8. Gradshteyn I.S., Ryzhik I.M. Table of Integrals, Series and Products. 1980;Academic Press, London.
9. Griffiths R.C. Lines of descent in the diffusion approximation of neutral Wright-Fisher models. Theor. Popul. Biol. 17:1980;37-50.
10. Griffiths R.C., Tavaré S. Sampling theory for neutral alleles in a varying environment. Proc. R. Soc. London Ser. B. 344:1994;403-410.
11. Griffiths R.C., Tavaré S. The age of a mutation in a general coalescent tree. Stochastic Models. 14:1998;273-295.
12. Griffiths, R.C., Tavaré, S., 2003. The genealogy of a neutral mutation. In: Green, P., Hjort, N., Richardson, S. (Eds.), Highly Structured Stochastics Systems. Oxford University Press, Oxford.
13. Kaplan N.L., Darden T., Hudson R.R. The coalescent process in models with selection. Genetics. 120:1988;819-829.
14. Karlin S., Taylor H.M. A Second Course in Stochastic Processes. 1981;Academic Press, London.
15. Kimura M., Ohta T. The age of a neutral mutant persisting in a finite population. Genetics. 75:1973;199-212.
16. Kingman J.F.C. The coalescent. Stochastic Processes Appl. 13:1982;235-248.
17. Krone S., Neuhauser C. Ancestral processes with selection. Theor. Popul. Biol. 51:1997;210-237.
18. Maruyama T. The age of an allele in a finite population. Genet. Res. 23:1974;137-143.
19. Maruyama T., Fuerst P. Analyses of the age of genes and the first arrival times in a finite population. Genetics. 105:1983;1041-1059.
20. Maruyama T., Kimura M. A note on the speed of gene frequency changes in reverse directions in a finite population. Evolution. 28:1974;161-163.
21. Nagasawa M., Maruyama T. An application of time reversal of Markov processes to a problem of population genetics. Adv. Appl. Probab. 11:1979;457-478.
22. Neuhauser C., Krone S. The genealogy of samples in models with selection. Genetics. 154:1997;519-534.
23. Patterson, N., 2003. How old is the most recent common ancestor of two copies of an allele? In preparation.
24. Petkovsek M., Wilf H.S., Zeilberger D. A=B :1996;A.K. Peters, Ltd. Wellesley, MA.
25. Sawyer S. On the past history of an allele now known to have frequency. p J. Appl. Probab. 14:1977;439-450.
26. Sawyer S.A., Hartl D.L. Population genetics of polymorphism and divergence. Genetics. 132:1992;1161-1176.
27. Slatkin M. The age of alleles. Slatkin M., Veuille M. Modern Developments in Theoretical Population Genetics. 2002;233-260 Oxford University Press, Oxford.
28. Slatkin M.W., Hudson R.R. Pairwise comparisons of mitochondrial DNA sequences in stable and exponentially growing populations. Genetics. 129:1991;555-562.
29. Stephens M. Times on trees and the age of an allele. Theor. Popul. Biol. 57:2000;109-119.
30. Tavaré S. Line-of-descent and genealogical processes, and their application in population genetics models. Theor. Popul. Biol. 26:1984;119-164.
31. van Herwaarden O.A., van der Wal N.J. Extinction time and age of an allele in a large finite population. Theor. Popul. Biol. 61:2002;311-318.
32. Watterson G.A. Reversibility and the age of an allele I. Moran's infinitely many neutral alleles model. Theor. Popul. Biol. 10:1976;239-253.
33. Watterson G.A. Reversibility and the age of an allele II. Two allele models with selection and mutation. Theor. Popul. Biol. 12:1977;179-196.
34. Watterson G.A. Motoo Kimura's use of diffusion theory in population genetics. Theor. Popul. Biol. 49:1996;154-188.
35. Wiuf C. On the genealogy of a sample of neutral rare alleles. Theor. Popul. Biol. 58:2000;61-75.
36. Wiuf C., Donnelly P. Conditional genealogies and the age of a neutral mutant. Theor. Popul. Biol. 56:1999;183-201.