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Uniform bounding of probability generating functions and the evolution of reproduction rates in birds

Published online by Cambridge University Press:  14 July 2016

C. C. Heyde  and
H.-J. Schuh
C. C. Heyde
Affiliation:
CSIRO Division of Mathematics and Statistics, Canberra
H.-J. Schuh
Affiliation:
CSIRO Division of Mathematics and Statistics, Canberra
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Abstract

Many species of birds have a characteristic clutch size which is either fixed at k or is of the form k or k + 1 for some appropriate integer k. In this paper we show, using a multitype Galton–Watson process to model a bird population, that such behaviour can correspond to maximization of the probability of survival of the species to time t for each finite t. This is also a conclusion which might be drawn from the theory of natural selection and hence provides some mathematical evidence of the force of evolution. The results of the paper rest on a bounding of probability generating functions.

Keywords

BRANCHING PROCESSESMULTITYPE GALTON–WATSON PROCESSPROBABILITY GENERATING FUNCTIONEVOLUTIONCLUTCH SIZE FOR BIRDSREPRODUCTION RATES
Type
Research Papers
Information
Journal of Applied Probability , Volume 15 , Issue 2 , June 1978 , pp. 243 - 250
Copyright
Copyright © Applied Probability Trust 1978 

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References

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