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Stability classification of a Ricker model with two random parameters

Part of: Markov processes

Published online by Cambridge University Press:  19 February 2016

Henrik Fagerholm  and
Göran Högnäs
Henrik Fagerholm*
Affiliation:
Åbo Akademi University
Göran Högnäs*
Affiliation:
Åbo Akademi University
*
∗ Postal address: Department of Mathematics, Åbo Akademi, FIN-20500 Åbo, Finland.
∗ Postal address: Department of Mathematics, Åbo Akademi, FIN-20500 Åbo, Finland.
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Abstract

We consider a stochastic version of the Ricker model describing the density of an unstructured isolated population. In particular, we investigate the effects of independently varying the per capita growth rate and the parameter governing density dependent feedback. We derive conditions on the distributions sufficient to guarantee different forms of stochastic stability such as null recurrence or positive recurrence. We find, for example, that null recurrence appears in two widely different scenarios: when there is a mean-zero growth rate or via a growth-catastrophe behaviour.

Keywords

Markov chainspopulation dynamicsinvariant measuresnonlinear stochastic difference equationsrecurrence

MSC classification

Primary: 92D25: Population dynamics (general)
Secondary: 60J05: Discrete-time Markov processes on general state spaces 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 34 , Issue 1 , March 2002 , pp. 112 - 127
Copyright
Copyright © Applied Probability Trust 2002 

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