Duality, ancestral and diffusion processes in models with selection

Theoretical Population Biology

Volumn 75, Issue 2-3, 2009, Pages 164-175

  Mano, Shuhei ^a,b,c  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b NAGOYA CITY UNIVERSITY   (Japan)

^c JAPAN SCIENCE AND TECHNOLOGY AGENCY   (Japan)

Author keywords

Ancestral process; Ancestral selection graph; Birth and death process; Coalescent model; Diffusion model

Indexed keywords

ALLELE; BIRTH RATE; CONFERENCE PROCEEDING; CONVERGENT EVOLUTION; NATURAL SELECTION; POPULATION GENETICS; STATISTICAL DISTRIBUTION; STOCHASTICITY;

ALLELE; ARTICLE; GENE FREQUENCY; GENETIC SELECTION; THEORETICAL MODEL;

ALLELES; GENE FREQUENCY; MODELS, THEORETICAL; SELECTION (GENETICS);

EID: 64549138426     PISSN: 00405809     EISSN: 10960325     Source Type: Journal    
DOI: 10.1016/j.tpb.2009.01.007     Document Type: Article

References (22)

1. Athreya S.R., and Swart J.M. Branching-coalescing particle systems. Probab. Theory Related Fields 131 (2005) 376-414
2. In: Erdélyi A. (Ed). Tables of Integral Transforms, vol. II (1954), McGraw-Hill, New York
3. Ethier S.N., and Griffiths R.C. On the two-locus sampling distribution. J. Math. Biol. 29 (1990) 131-159
4. Ethier S.N., and Kurtz T.G. Markov Processes: Characterization and Convergence (1986), Jonh Wiley & Sons, New York
5. Ewens W.J. Conditional diffusion process in population genetics. Theor. Popul. Biol. 4 (1973) 21-30
6. Fearnhead P. The common ancestor at a nonneutral locus. J. Appl. Probab. 39 (2002) 38-54
7. Flammer C. Spheroidal Wave Functions (1957), Stanford University Press, Stanford
8. Gantmacher F.R. Matrix Theory, vol. II (1959), Chelsea, New York
9. Griffiths R.C. Exact sampling distributions from the infinite neutral allele model. Adv. Appl. Probab. 11 (1979) 326-354
10. Griffiths R.C. The two-locus ancestral graph. In: Basawa I.V., and Taylor R.L. (Eds). Selected Proceedings of the Symposium on Applied Probability, Sheffield, 1989. IMS Lecture Notes-Monograph Series vol. 18 (1991), Institute of Mathematical Statistics 100-117
11. Karlin S., and Taylor H.M. A First Course in Stochastic Processes. 2nd ed. (1975), Academic Press, San Diego
12. Kimura M. Stochastic process and distribution of gene frequencies under natural selection. Cold Spring Harbor Symposia on Quantitative Biology 20 (1955) 33-53
13. Kimura M. Some problems of stochastic processes in genetics. Ann. Math. Stat. 28 (1957) 882-901
14. Kimura M., and Ohta T. The average number of generations until fixation of a mutant gene in a finite population. Genetics 61 (1969) 763-771
15. Kingman J.F.C. The coalescent. Stochastic Process. Appl. 13 (1982) 235-248
16. Kingman J.F.C. On the genealogy of large populations. J. Appl. Probab. 19 (1982) 27-43
17. Krone S.M., and Neuhauser C. Ancestral process with selection. Theor. Popul. Biol. 51 (1997) 210-237
18. Maruyama T. The average number and the variance of generations at particular gene frequency in the course of fixation of a mutant gene in a finite population. Genet. Res. Camb. 19 (1972) 109-113
19. Maruyama T., and Kimura M. A note on the speed of gene frequency changes in reverse directions in a finite population. Evolution 28 (1974) 161-163
20. Shiga T. Diffusion processes in population genetics. J. Math. Kyoto Univ. 21 (1981) 133-151
21. Stratton J.A., Morse P.M., Chu L.J., and Hunter R.A. Elliptic Cylinder and Spheroidal Wave Functions (1941), John Wiley and Sons, New York
22. Tavaré S. Line-of-descent and genealogical processes, and their applications in population genetics. Theor. Popul. Biol. 26 (1984) 119-164