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An index of genealogical relatedness

Published online by Cambridge University Press:  01 July 2016

Stuart P. Lloyd
Stuart P. Lloyd*
Affiliation:
Bell Laboratories, Murray Hill, New Jersey
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Abstract

The inner product associated with the l2 analog of the Mycielski-Ulam l1 genealogical distance serves to quantify the notion of genealogical relatedness in a fairly natural way. The expected value of the relatedness is obtained for certain random population models with stratified generations, including the Mycielski-Ulam model.

Keywords

GENEALOGICAL RELATEDNESSGENEALOGICAL DISTANCERANDOM ANCESTRY
Type
Research Article
Information
Advances in Applied Probability , Volume 5 , Issue 3 , December 1973 , pp. 417 - 438
Copyright
Copyright © Applied Probability Trust 1973 

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References

[1] Mycielski, J. and Ulam, S. M. (1969) On the pairing process and the notion of genealogical distance. J. Combinatorial Theory 6, 227–234.Google Scholar
[2] Mallows, C. L. (1974) Another definition of genealogical distance. J. Appl. Prob. 11, no. 1. To appear.Google Scholar
[3] Riordan, J. (1958) An Introduction to Combinatorial Analysis. Wiley, New York.Google Scholar
[4] Doob, J. L. (1956) Stochastic Processes. Wiley, New York.Google Scholar
[5] Ehrlich, P. R. (1968) The Population Bomb. Ballantine Books, New York.Google Scholar
[6] Kahane, J. and Marr, R. (1972) On a class of stochastic pairing processes and the Mycielski-Ulam notions of genealogical distance. J. Combinatorial Theory (A) 13, 383–400.Google Scholar
[7] Karlin, S. (1969) Equilibrium Behavior of Population Genetic Models with Non-random Mating. Gordon and Breach, New York.Google Scholar
[8] Malécot, G. (1948) Les Mathématiques de L'Hérédité. Masson et Cie, Paris.Google Scholar
[9] Lloyd, S. P. and Mallows, C. L. (1973) An index of genealogical relatedness derived from a genetic model. Ann. of Probability. To appear.Google Scholar