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The policy which maximises long-term survival of an animal faced with the risks of starvation and predation

Published online by Cambridge University Press:  01 July 2016

J. M. McNamara
J. M. McNamara*
Affiliation:
University of Bristol
*
∗Postal address: School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK.
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Abstract

This paper presents a simple model of the decision problems which face many animals in the wild. Animals have an upper limit to the amount of energy reserves which can be stored as body fat. They constantly use energy and find food as a stochastic process. Death occurs if energy reserves fall to zero or if the animal is taken by a predator. Typically animals have a range of behavioural options which differ in the distribution of food gained and in the associated predation risk. There is often a trade-off between starvation and predation in that animals have to expose themselves to higher predation risks in order to gain more food.

The above situation is modelled as a finite-state, finite-time-horizon Markov decision problem. The policy which maximises long-term survival probability is characterised. As special cases two trade-offs are analysed. It is shown that an animal should take fewer risks in terms of predation as its reserves increase, and that an animal should reduce the variability of its food supply at the expense of its mean gain as its reserves increase.

Keywords

MARKOV DECISION PROCESSESNON-NEGATIVE MATRICES
Type
Research Article
Information
Advances in Applied Probability , Volume 22 , Issue 2 , June 1990 , pp. 295 - 308
Copyright
Copyright © Applied Probability Trust 1990 

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