Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-24T02:30:16.154Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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