The process of most recent common ancestors in an evolving coalescent

Stochastic Processes and their Applications

Volumn 116, Issue 12, 2006, Pages 1836-1859

  Pfaffelhuber, P ^a   Wakolbinger, A ^b  

^a UNIVERSITY OF MUNICH   (Germany)

^b GOETHE UNIVERSITY   (Germany)

Author keywords

Kingman's coalescent; Look down process; Most recent common ancestor

Indexed keywords

DIFFUSION; LIVING SYSTEMS STUDIES; MATHEMATICAL MODELS; PROBLEM SOLVING;

KINGMAN'S COALESCENT; LOOK-DOWN PROCESSES;

RANDOM PROCESSES;

EID: 33750626089     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spa.2006.04.015     Document Type: Article

References (17)

1. Burke P.J. The output of a queueing system. Oper. Res. 4 6 (1956) 699-704
2. Donnelly P., and Kurtz T.G. A countable representation of the Fleming Viot measurable diffusion. Ann. Probab. 24 2 (1996) 698-742
3. Donnelly P., and Kurtz T.G. Particle representations for measure-valued population models. Ann. Probab. 27 1 (1999) 166-205
4. P. Donnelly, T.G. Kurtz, The Eve process, Manuscript (personal communication)
5. Griffiths R.C. Lines of descent in the diffusion approximation of neutral Fisher-Wright models. Theory Pop. Biol. 17 (1980) 37-50
6. Griffiths R.C., and Tavaré S. The genealogy of a neutral mutation. In: Green P.J., Hjort N.L., and Richardson S. (Eds). Highly Structured Stochastic Systems (2003), Oxford University Press 393-413
7. Johnson N.L., and Kotz S. Urn Models and their Applications (1977), John Wiley & Sons
8. Kimura M. Theoretical foundation of population genetics at the molecular level. Theory Pop. Biol. 2 2 (1971) 174-208
9. Kingman J.F.C. The coalescent. Stochastic Process. Appl. 13 3 (1982) 235-248
10. Kurtz T.G. Martingale problems for conditional distributions of Markov processes. Electron. J. Probab. 3 9 (1998) 1-29
11. Littler R.A. Loss of variability at one locus in a finite population. Math. Biosci. 25 (1975) 151-163
12. Rauch E.M., and Bar-Yam Y. Theory predicts the uneven distribution of genetic diversity within species. Nature 431 (2004) 449-452
13. Saunders I.W., Tavaré S., and Watterson G.A. On the genealogy of nested subsamples from a haploid population. Adv. Appl. Probab. 16 (1984) 471-491
14. Tajima F. Relationship between DNA polymorphism and fixation time. Genetics 125 (1990) 447-454
15. J. Wakeley, Coalescent theory. An Introduction. Roberts & Company Publishers, Greenwood Village, 2005, and Scion Publishing Ltd (in press)
16. Watterson G.A. Mutant substitutions at linked nucleotide sites. Adv. Appl. Prob. 14 (1982) 166-205
17. Watterson G.A. Substitution times for mutant nucleotides. J. Appl. Probab. 19A (1982) 59-70