Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-27T11:08:11.199Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Grey, D. R. (1984) Non-negative matrices, dynamic programming and a harvesting problem. J. Appl. Prob. 21, 685–694.Google Scholar
[2] Kennedy, D. P. (1978) On sets of countable non-negative matrices and Markov decision processes. Adv. Appl. Prob. 10, 633–646.Google Scholar
[3] Mcnamara, J. M. and Houston, A. I. (1986) The common currency for behavioural decisions. Am. Nat. 127, 358–378.Google Scholar
[4] Mcnamara, J. M. and Houston, A. I. (1990) Starvation and predation in a patchy environment. To appear in Living in a Patchy Environment , ed. Shorrocks, B. and Swingland, I.. Oxford University Press.Google Scholar
[5] Mandl, P. and Seneta, E. (1969) The theory of non-negative matrices in a dynamic programming problem. Austral. J. Statist. 11, 85–96.Google Scholar
[6] Schneider, K. J. (1984) Dominance predation and optimal foraging in white-throated sparrow flocks. Ecology 65, 1820–1827.Google Scholar
[7] Sladký, K. (1976) On dynamic programming recursions for multiplicative Markov decision chains. Mathematical Programming Study 6, North-Holland, Amsterdam, 216–226.Google Scholar
[8] Stephens, D. W. and Krebs, J. R. (1987) Foraging Theory. Princeton University Press, Princeton, NJ. Google Scholar