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Recent common ancestors of all present-day individuals

  • Joseph T. Chang (a1)

Previous study of the time to a common ancestor of all present-day individuals has focused on models in which each individual has just one parent in the previous generation. For example, ‘mitochondrial Eve’ is the most recent common ancestor (MRCA) when ancestry is defined only through maternal lines. In the standard Wright-Fisher model with population size n, the expected number of generations to the MRCA is about 2n, and the standard deviation of this time is also of order n. Here we study a two-parent analog of the Wright-Fisher model that defines ancestry using both parents. In this model, if the population size n is large, the number of generations, 𝒯 n , back to a MRCA has a distribution that is concentrated around lgn (where lg denotes base-2 logarithm), in the sense that the ratio 𝒯 n (lgn) converges in probability to 1 as n→∞. Also, continuing to trace back further into the past, at about 1.77 lgn generations before the present, all partial ancestry of the current population ends, in the following sense: with high probability for large n, in each generation at least 1.77lgn generations before the present, all individuals who have any descendants among the present-day individuals are actually ancestors of all present-day individuals.

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Postal address: Statistics Department, Yale University, Box 208290, New Haven, CT 06520, USA. Email address:
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[1] Athreya, K. B. and Ney, P. (1972). Branching Processes. Springer, New York.
[2] Ayala, F. J. (1995). The myth of Eve: molecular biology and human origins. Science 270, 19301936.
[3] Bernstein, S. (1946). The Theory of Probabilities. Gastehizdat, Moscow.
[4] Cann, R. L., Stoneking, M. and Wilson, A. C. (1987). Mitochondrial DNA and human evolution. Nature 325, 3136.
[5] Donnelly, P. (1986). Genealogical approach to variable-population-size models in population genetics. J. Appl. Prob. 23, 283296.
[6] Donnelly, P. and Tavaré, S. (eds.) (1997). Progress in Population Genetics and Human Evolution. Springer, New York.
[7] Dorit, R. L., Akashi, H. and Gilbert, W. (1995). Absence of polymorphism at the ZFY locus on the human Y chromosome. Science 268, 11831185.
[8] Griffiths, R. and Marjoram, P. (1997). An ancestral recombination graph. In Progress in Population Genetics and Human Evolution, eds. Tavaré, S. and Donnelly, P., Springer, New York, pp. 257270.
[9] Hudson, R. R. (1983). Properties of a neutral allele model with intragenic recombination. Theoret. Popn. Biol. 23, 183201.
[10] Hudson, R. R. (1990). Gene genealogies and the coalescent process. Oxford Surveys in Evolutionary Biology 7, 144.
[11] Kämmerle, K., (1989). Looking forwards and backwards in a bisexual model. J. Appl. Prob. 27, 880885.
[12] Kämmerle, K., (1991). The extinction probability of descendants in bisexual models of fixed population size. J. Appl. Prob. 28, 489502.
[13] Kingman, J. F. C. (1982a). Exchangeability and the evolution of large populations. In Exchangeability in Probability and Statistics, eds. Koch, G. and Spizzichino, F., North-Holland, New York, pp. 97112.
[14] Kingman, J. F. C. (1982b). On the genealogy of large populations. In Essays in Statistical Science, eds. Gani, J. and Hannan, E. J. (J. Appl. Prob. 19A,). Applied Probability Trust, Sheffield, UK, pp. 2743.
[15] Möhle, M., (1994). Forward and backward processes in bisexual models with fixed population sizes. J. Appl. Prob. 31, 309332.
[16] Möhle, M., (1997). Fixation in bisexual models with variable population sizes. J. Appl. Prob. 34, 436448.
[17] Pääbo, S., (1995). The Y chromosome and the origin of all of us (men). Science 268, 11411142.
[18] Vigilant, L., Stoneking, M., Harpending, H., Hawkes, K. and Wilson, A. C. (1991). African populations and the evolution of human mitochondrial DNA. Science 253, 15031507.
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Advances in Applied Probability
  • ISSN: 0001-8678
  • EISSN: 1475-6064
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