The common ancestor process for a wright-fisher diffusion

Electronic Journal of Probability

Volumn 12, Issue , 2007, Pages 808-847

  Taylor, Jesse E ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

Common ancestor process; Diffusion process; Genetic drift; Selection; Structured coalescent; Substitution rates

Indexed keywords

EID: 34249891061     PISSN: None     EISSN: 10836489     Source Type: Journal    
DOI: 10.1214/EJP.v12-418     Document Type: Article

References (51)

1. H. Akashi. Inferring Weak Selection from Patterns of Polymorphism and Divergence at Silent Sites in Drosophila DNA. Genetics, 139:1067-1076, 1995.
2. E. Baake and H.-O. Georgii. Mutation, selection, and ancestry in branching models: a variational approach. J. Math. Biol., 54:257-303, 2007.
3. N. H. Barton and A. M. Etheridge. The Effect of Selection on Genealogies. Genetics, 166:1115-1131, 2004.
4. N. H. Barton, A. M. Etheridge, and A. K. Sturm. Coalescence in a Random Background. Ann. Appl. Prob., 14:754-785, 2004.
5. N.H. Barton and S. P. Otto. Evolution of Recombination Due to Random Drift. Genetics, 169:2353-2370, 2005.
6. G. Birkhoff and G.-C. Rota. Ordinary differential equations. Wiley, New York, 1989.
7. C. D. Bustamante, J. Wakeley, S. Sawyer, and D. L. Hartl. Directional Selection and the Site-Frequency Spectrum. Genetics, 159:1779-1788, 2001.
8. J. L. Cherry and J. Wakeley. A Diffusion Approximation for Selection and Drift in a Subdivided Population. Genetics, 163:421-428, 2003.
9. G. Coop and R.C. Griffiths. Ancestral inference on gene trees under selection. Theor. Pop. Biol., 66:219-232, 2004.
10. P. Donnelly and T. G. Kurtz. A Countable Representation of the Fleming-Viot MeasureValued Diffusion. Ann. Prob., 24:698-742, 1996.
11. P. Donnelly and T. G. Kurtz. Genealogical Processes for Fleming-Viot Models with Selection and Recombination. Ann. Appl. Prob., 9:1091-1148, 1999.
12. A. M. Etheridge. Evolution in Fluctuating Populations. In A. Bovier, F. Dunlop, F. den Hollander, A. van Enter, and J. Dalibard, editors, Mathematical Statistical Physics, volume 83, pages 489-545. Les Houches, Elsevier, 2005.
13. S. N. Ethier and T. G. Kurtz. Markov Processes: Characterization and Convergence. John Wiley & Sons, New York, N.Y., 1986.
14. W. J. Ewens. Mathematical Population Genetics. Biomathematics, Vol 9. Springer, New York, 2 edition, 2004.
15. P. Fearnhead. The Common Ancestor at a Nonneutral Locus. J. Appl. Prob., 39:38-54, 2002.
16. S. Gavrilets. Perspective: Models of speciation: What have we learned in 40 years? Evolution, 57:2197-2215, 2003.
17. H.-O. Georgii and E. Baake. Supercritical Multitype Branching Processes: The Ancestral Types of Typical Individuals. Adv. Appl. Prob., 35:1090-1110, 2003.
18. J. H. Gillespie. The Causes of Molecular Evolution. Oxford University Press, Oxford, 1991.
19. J. H. Gillespie. Population Genetics: A Concise Guide. Johns Hopkins University Press, Baltimore, 2004.
20. R. C. Griffiths and P. Marjoram. An ancestral recombination graph. In P. Donnelly and S. Tavare, editors, Progress in Population Genetics and Human Evolution, pages 257-270. Springer-Verlag, 1997.
21. P. Jagers. General branching processes as Markov fields. Stoch. Proc. Appl., 32:183-242, 1989.
22. P. Jagers. Stabilities and instabilities in population dynamics. J. Appl. Prob., 29:770-780, 1992.
23. N. L. Kaplan, T. Darden, and R. R. Hudson. The coalescent process in models with selection. Genetics, 120:819-829, 1988.
24. I. Karatzas and S. E. Shreve. Brownian Motion and Stochastic Calculus. Springer, New York, 1991.
25. M. Kimura. Diffusion Models in Population Genetics. J. Appl. Prob., 1:177-232, 1964.
26. F. A. Kondrashov and E. V. Koonin. A common framework for understanding the origin of genetic dominance and evolutionary fates of gene duplications. Trends Genet., 20:287-291, 2004.
27. R. D. Koyous, C. L. Althaus, and S. Bonhoeffer. Stochastic or deterministic: what is the effective population size of HIV-1? Trends Microbiol., 14:507-511, 2006.
28. S. M. Krone and C. Neuhauser. Ancestral processes with selection. Theor. Pop. Biol., 51:210-237, 1997.
29. R. Lande. Natural Selection and Random Genetic Drift in Phenotypic Evolution. Evolution, 30:314-334, 1976.
30. Z. Li, T. Shiga, and L. Yao. A Reversibility Problem for Fleming-Viot Processes. Elect. Comm. in Probab, 4:65-76, 1999.
31. M. Lynch and J. S. Conery. The Origins of Genome Complexity. Science, 302:1401-1404, 2003.
32. G. McVean and J. Vieira. Inferring parameters of mutation, selection and demography from patterns of synonymous site evolution in Drosophila. Genetics, 157:245-257, 2001.
33. E. Nelson. The Adjoint Markoff Process. Duke Math. J., 25:671-690, 1958.
34. C. Neuhauser. The ancestral graph and gene genealogy under frequency-dependent selection. Theor. Pop. Biol., 56:203-214, 1999.
35. R. Nielsen and Z. Yang. Likelihood models for detecting positively selected amino acid sites and applications to the HIV-1 envelope gene. Genetics, 148:929-936, 1998.
36. M. Frank Norman. Ergodicity of Diffusion and Temporal Uniformity of Diffusion Approximation. J. Appl. Prob., 14:399-404, 1977.
37. R. B. O'Hara. Comparing the effects of genetic drift and fluctuating selection on genotype frequency changes in the scarlet tiger moth. Proc. Roy. Soc. Lond. B, 272:211-217, 2005.
38. S. P. Otto and M. C. Whitlock. The Probability of Fixation in Populations of Changing Size. Genetics, 146:723-733, 1997.
39. N. Patterson, D. J. Richter, S. Gnerre, E. S. Lander, and D. Reich. Genetic evidence for complex speciation of humans and chimpanzees. Nature, 441:1103-1108, 2006.
40. A. Poon and L. Chao. Drift Increases the Advantage of Sex in RNA Bacteriophage $6. Genetics, 166, 2004.
41. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery. Numerical Recipes in C. The Art of Scientific Computing. Cambridge University Press, Cambridge, 1992.
42. G. R. Price. Selection and Covariance. Nature, 227:520-521, 1970.
43. A. Richman. Evolution of balanced genetic polymorphism. Mol. Ecol., 9:1953-963, 2000.
44. D. Roze and F. Rousset. Selection and Drift in Subdidived Populations: A Straightforward Method for Deriving Diffusion Approximations and Applications Involving Dominance, Self-ing and Local Extinctions. Genetics, 165:2153-2166, 2004.
45. S. A. Sawyer and D. L. Hartl. Population Genetics of Polymorphism and Divergence. Genetics, 132:1161-1176, 1992.
46. T. Shiga. Diffusion processes in population genetics. J. Math. Kyoto Univ., 21:133-151, 1981.
47. M. Stephens and P. Donnelly. Ancestral inference in population genetics models with selection. Austral. & New Zealand J. Stat., 45:395-423, 2003.
48. M. C. Whitlock. Fixation of New Alleles and the Extinction of Small Populations: Drift Load, Beneficial Alleles, and Sexual Selection. Evol., 54:1855-1861, 2000.
49. S. Williamson, A. Fledel-Alon, and C. D. Bustamante. Population Genetics of Polymorphism and Divergence for Diploid Selection Models With Arbitrary Dominance. Genetics, 168:463-475, 2004.
50. Z. Yang. Among-site rate variation and its impact on phylogenetic analyses. Trends Ecol. Evol., 11:367-372, 1996.
51. A. Zharkikh. Estimation of Evolutionary Distances Between Nucleotide Sequences. J. Mol. Evol., 39:315-329, 1994.