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Stabilities and instabilities in population dynamics

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Peter Jagers
Peter Jagers*
Affiliation:
Chalmers University of Technology and Gothenburg University
*
∗ Postal address: Department of Mathematics, Chalmers University of Technology and Gothenburg University, S-412 96 Gothenburg, Sweden.
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Abstract

Stability in population size is illusory: populations left to themselves either grow beyond all bounds or die out. But if they do not die out their composition stabilizes. These problems are discussed in terms of general abstract, multitype branching processes. The life and descent of a typical individual is described.

Keywords

BRANCHING PROCESSESKIN STRUCTURESTABLE POPULATIONSPOPULATION EXTINCTION

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 29 , Issue 4 , December 1992 , pp. 770 - 780
Copyright
Copyright © Applied Probability Trust 1992 

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Footnotes

This work has been supported by a grant from the Swedish Natural Science Research Council. It was presented as the first Applied Probability Lecture in Manchester in May 1991. The author wishes to thank the Applied Probability Trust and Professor F. Papangelou for the invitation.

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