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Criteria for extinction of certain population growth processes with interacting types

Published online by Cambridge University Press:  01 July 2016

Samuel Karlin  and
Norman Kaplan
Samuel Karlin
Affiliation:
The Weizmann Institute of Science, Rehovot, Israel, and Stanford University
Norman Kaplan
Affiliation:
University of California, Berkeley
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Abstract

A study is made of a series of stochastic growth processes related to multi-type branching models with interaction phenomena among the types with aim to ascertain criteria for extinction or non-extinction of the population. It is established that trends depicting changes of expected sizes of types generally overwhelm any effects of statistical fluctuations such that the conditions for extinction reduce to natural conditions on expected values. Three models are developed. The first two involve special mating systems for certain two sex populations. The last model is a neutralization phenomenon for two types of particles.

Keywords

MULTI-TYPE BRANCHING PHENOMENA WITH INTERACTIONSEXTINCTION PROBABILITIESPOPULATION GROWTH WITH SPECIAL MATING SYSTEMSTWO TYPES PARTICLES WITH NEUTRALIZATION EFFECTS
Type
Research Article
Information
Advances in Applied Probability , Volume 5 , Issue 2 , August 1973 , pp. 183 - 199
Copyright
Copyright © Applied Probability Trust 1973 

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References

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