Skip to main content Accessibility help
×
Home

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

  • M. Möhle (a1)

Abstract

A class of haploid population models with population size N, nonoverlapping generations and exchangeable offspring distribution is considered. Based on an analysis of the discrete ancestral process, we present solutions, algorithms and strong upper bounds for the expected time back to the most recent common ancestor which hold for arbitrary sample size n ∈ {1,…,N}. New insights into the asymptotic behaviour of the expected time back to the most recent common ancestor for large population size are presented relating the results to coalescent theory.

Copyright

Corresponding author

Postal address: Mathematisches Institut, Eberhard Karls Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany. Email address: martin.moehle@uni-tuebingen.de

References

Hide All
[1] Cannings, C. (1974). The latent roots of certain Markov chains arising in genetics: a new approach. I. Haploid models. 6, 260290.
[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, 264282.
[3] Chang, J. T. (1999). Recent common ancestors of all present-day individuals. Adv. Appl. Prob. 31, 10021026.
[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, 383394.
[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, 778783.
[8] Gladstien, K. (1978). The characteristic values and vectors for a class of stochastic matrices arising in genetics. SIAM J. Appl. Math. 34, 630642.
[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 Koch, G. and Spizzichino, F., North-Holland, Amsterdam, pp. 97112.
[11] Kingman, J. F. C. (1982). On the genealogy of large populations. In Essays in Statistical Science (J. Appl. Prob. Spec. Vol. 19A), eds Gani, J. and Hannan, E. J., Applied Probability Trust, Sheffield, pp. 2743.
[12] Kingman, J. F. C. (1982). The coalescent. Stoch. Process. Appl. 13, 235248.
[13] Möhle, M., (1998). Robustness results for the coalescent. J. Appl. Prob. 35, 438447.
[14] Möhle, M., (1999). The concept of duality and applications to Markov processes arising in neutral population genetics models. Bernoulli 5, 761777.
[15] Möhle, M., (2000). Total variation distances and rates of convergence for ancestral coalescent processes in exchangeable population models. Adv. Appl. Prob. 32, 983993.
[16] Möhle, M. and Sagitov, S. (2001). A classification of coalescent processes for haploid exchangeable population models. Ann. Prob. 29, 15471562.
[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, 839854.
[19] Walsh, B. (2001). Estimating the time to the most recent common ancestor for the Y chromosome or mito-chon-drial DNA for a pair of individuals. Genetics 158, 897912.

Keywords

MSC classification

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

  • M. Möhle (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed