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An optimal branching migration process

Published online by Cambridge University Press:  14 July 2016

S. D. Durham
S. D. Durham*
Affiliation:
University of South Carolina
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Abstract

We consider a population distributed over two habitats as represented by two separate one-dimensional branching processes with random environments. The presence of random fluctuation in reproduction rates in both habitats implies the possibility that neither habitat is universally superior to the other for all times and that a maximal population size is to be achieved by having population members present in both habitats. We show that optimal population growth occurs when migration between habitats occurs at a fixed rate which can be found from the environmentally determined reproduction variables of the separate habitats. The optimal processes are themselves two-type branching processes with random environments.

Keywords

BRANCHING PROCESSOPTIMAL POPULATION CONTROL
Type
Short Communications
Information
Journal of Applied Probability , Volume 12 , Issue 3 , September 1975 , pp. 569 - 573
Copyright
Copyright © Applied Probability Trust 1975 

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