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The proportions of individuals of different kinds in two-type populations. A branching process problem arising in biology

Published online by Cambridge University Press:  14 July 2016

P. Jagers
P. Jagers*
Affiliation:
Gothenburg University, Sweden
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Abstract

Consider an age-dependent branching process with two types of individuals. Suppose that individuals of one type beget children of both types, whereas those of the other type can only give birth to individuals of their own kind. This paper is a study of the relation between two random functions occurring in such processes starting from an ancestor of the first type, the two functions being the numbers of individuals of the two kinds. Under weak assumptions it is shown that the random proportion of individuals of one type converges as time passes, in mean square as well as almost surely to a non-random limit, easily determined in terms of the reproduction laws and life-length distributions of the process.

Type
Research Papers
Information
Journal of Applied Probability , Volume 6 , Issue 2 , August 1969 , pp. 249 - 260
Copyright
Copyright © Sheffield: Applied Probability Trust 

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References

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