The time back to the most recent common ancestor in exchangeable population models

Advances in Applied Probability

Volumn 36, Issue 1, 2004, Pages 78-97

  Mohle M ^a  

^a UNIVERSITY OF TÜBINGEN   (Germany)

Author keywords

Absorption time; Ancestral process; Coalescent; Exchangeability; Moran model; Most recent common ancestor; Wright Fisher model

Indexed keywords

ABSORPTION TIME; ANCESTRAL PROCESS; COALESCENT; EXCHANGEABILITY; MORAN MODEL; MOST RECENT COMMON ANCESTORS; WRIGHT-FISHER MODEL;

APPROXIMATION THEORY; ASYMPTOTIC STABILITY; CONVERGENCE OF NUMERICAL METHODS; MATHEMATICAL MODELS; SET THEORY; THEOREM PROVING;

POPULATION STATISTICS;

EID: 12144291122     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1239/aap/1077134465     Document Type: Article

References (19)

1. CANNINGS, C. (1974). The latent roots of certain Markov chains arising in genetics: a new approach. I. Haploid models. Adv. Appl. Prob. 6, 260-290.
2. CANNINGS, C. (1975). The latent roots of certain Markov chains arising in genetics: a new approach. II. Further haploid models. Adv. Appl. Prob. 7, 264-282
3. CHANG, J. T. (1999). Recent common ancestors of all present-day individuals. Adv. Appl. Prob. 31, 1002-1026.
4. CROW, J. F. AND KIMURA, M. (1970). An Introduction to Population Genetics Theory. Harper and Row, New York.
5. EWENS, W. J. (1979). Mathematical Population Genetics. Springer, Berlin.
6. GLADSTIEN, K. (1976). Loss of alleles in a haploid population with varying environment. Theoret. Pop. Biol. 10, 383-394.
7. GLADSTIEN, K. (1977). Haploid populations subject to varying environment: the characteristic values and the rate of loss of alleles. SIAM J. Appl. Math. 32, 778-783.
8. GLADSTIEN, K. (1978). The characteristic values and vectors for a class of stochastic matrices arising in genetics. SIAM J. Appl. Math. 34, 630-642.
9. JOHNSON, N. L. AND KOTZ, S. (1969). Distributions in Statistics: Discrete Distributions. Houghton Mifflin, Boston, MA.
10. KINGMAN, J. F. C. (1982). Exchangeability and the evolution of large populations. In Exchangeability in Probability and Statistics, eds G. Koch and F. Spizzichino, North-Holland, Amsterdam, pp. 97-112.
11. KINGMAN, J. F. C. (1982). On the genealogy of large populations. In Essays in Statistical Science (J. Appl. Prob. Spec. Vol. 19A), eds J. Gani and E. J. Hannan, Applied Probability Trust, Sheffield, pp. 27-43.
12. KINGMAN, J. F. C. (1982). The coalescent. Stock. Process. Appl. 13, 235-248.
13. MÖHLE, M. (1998). Robustness results for the coalescent. J. Appl. Prob. 35, 438-447.
14. MÖHLE, M. (1999). The concept of duality and applications to Markov processes arising in neutral population genetics models. Bernoulli 5, 761-777.
15. MÖHLE, M. (2000). Total variation distances and rates of convergence for ancestral coalescent processes in exchangeable population models. Adv. Appl. Prob. 32, 983-993.
16. MÖHLE, M. AND SAGITOV, S. (2001). A classification of coalescent processes for haploid exchangeable population models. Ann. Prob. 29, 1547-1562.
17. Ross, S. M. (2002). Probability Models for Computer Science. Academic Press, San Diego, CA.
18. SAGITOV, S. (2003). Convergence to the coalescent with simultaneous multiple mergers. J. Appl. Prob. 40, 839-854.
19. WALSH, B. (2001). Estimating the time to the most recent common ancestor for the Y chromosome or mitochondrial DNA for a pair of individuals. Genetics 158, 897-912.