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Relative extinction times for independent branching processes

Published online by Cambridge University Press:  14 July 2016

Eric Slud
Eric Slud*
Affiliation:
New Mexico State University
*
*Now at the University of Maryland, College Park.
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Abstract

The conditional probability that a Galton-Watson process with initial population j dies out before an independent Galton-Watson process initially i, is computed asymptotically as i or j gets large, given that both processes eventually die out. The results are interpreted qualitatively to discuss parameters of fitness for biological populations, especially with respect to the spread of mutant genes under evolutionary models.

Keywords

BRANCHING PROCESSESNON-CRITICAL GALTON-WATSON PROCESSESCONDITIONING ON EVENTUAL EXTINCTIONSPREAD OF MUTANT GENESFITNESSSELECTION
Type
Short Communications
Information
Journal of Applied Probability , Volume 14 , Issue 2 , June 1977 , pp. 382 - 386
Copyright
Copyright © Applied Probability Trust 1977 

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References

Harris, T. (1963) Branching Processes. Springer-Verlag, Berlin.Google Scholar
Nagaev, A. V. (1961) More exact statements of certain theorems in the theory of branching processes. (Russian), Trudy Tashkent. Gos. Univ. 189, 55–63.Google Scholar
Seneta, E. (1969) Functional equations and the Galton-Watson process. Adv. Appl. Prob. 1, 1–42.Google Scholar