Hostname: page-component-8448b6f56d-gtxcr Total loading time: 0 Render date: 2024-04-24T07:45:43.376Z Has data issue: false hasContentIssue false
  • English
  • Français

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: david.hull@valpo.edu
Get access Rights & Permissions [Opens in a new window]

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 

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

Daley, D. J. (1968). Extinction conditions for certain bisexual Galton–Watson branching processes. Z. Wahrscheinlichkeitsth. 9, 315–322.Google Scholar
Daley, D. J., Hull, D. M., and Taylor, J. M. (1986). Bisexual Galton–Watson branching processes with superadditive mating functions. J. Appl. Prob. 23, 585–600.Google Scholar
Hull, D. M. (1984). Conditions for extinction in certain bisexual Galton–Watson branching processes. J. Appl. Prob. 21, 414–418.CrossRefGoogle Scholar
Hull, D. M. (1998). A reconsideration of Galton's problem (using a two-sex population). Theoret. Popn Biol. 54, 105–116.Google Scholar
Kendall, D. G. (1966). Branching processes since 1873. J. London Math. Soc. 41, 385–406.Google Scholar
Lotka, A. J. (1931a). Population analysis—the extinction of families I. Washington Acad. Sci. 21, 377–380.Google Scholar
Lotka, A. J. (1931b). Population analysis—the extinction of families II. Washington Acad. Sci. 21, 453–459.Google Scholar