OPTIMAL FORAGING OF A REPRODUCING ANIMAL AS A DISCOUNTED REWARD PROBLEM

A model in which a foraging animal can reproduce if its energy reserve s reach a critical level is presented. The animal's reserves are model led as a finite-state Markov chain. The animal has the choice between foraging options which may have the same mean net gain but differ in t heir variances. In addition to starvation, animals are subject to deat h because of predation, bad weather, and so on. We focus on the case w here the rate of mortality due to these sources is the same under all options. We investigate policies that maximise the expected lifetime r eproductive success. It is found that the optimal value function is co ncave at low reserves (low-variance action region) and convex at high reserves (high-variance action region). The value function under the l ow-variance action has also the same shape and the same inflexion poin t. This result allows us to compute optimal policies just by looking a t the low-variance value function. The result is also used to show tha t increasing the mortality rate increases the high-variance region und er the optimal policy. The pattern of risk-sensitive behaviour predict ed by this model is in contrast to that predicted by a similar model i n which no reproduction occurs and the optimality criterion is to mini mise the probability of death (McNamara (1990)).