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A reconsideration of Lotka's extinction probability using a bisexual branching process

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

David M. Hull
David M. Hull*
Affiliation:
Valparaiso University
*
∗ Postal address: Department of Mathematics and Computer Science, Valparaiso University, Valparaiso, IN 46383, USA. Email address: [email protected]
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Abstract

It is generally recognized that Alfred Lotka made the first application of standard Galton-Watson branching process theory to calculate an extinction probability in a specific population (using asexual reproduction). This note applies bisexual Galton-Watson branching process theory to the calculation of an extinction probability from Lotka's data, yielding a somewhat higher value.

Keywords

Standard Galton-Watson branching processbisexual Galton-Watson branching process

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 92D25: Population dynamics (general)
Type
Short Communications
Information
Journal of Applied Probability , Volume 38 , Issue 3 , September 2001 , pp. 776 - 780
Copyright
Copyright © by the Applied Probability Trust 2001 

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References

Daley, D. J. (1968). Extinction conditions for certain bisexual Galton–Watson branching processes. Z. Wahrscheinlichkeitsth. 9, 315–322.Google Scholar
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