Optimal Bayesian foraging policies and prey population dynamics - Some comments on Rodriguez-Girones and Vasquez

In this paper we show the density-dependent harvest rates of optimal Bayesi an foragers exploiting prey occurring with clumped spatial distribution. Ro driguez-Girones and Vasquez (1997) recently treated the issue, but they use d a patch-leaving rule (current value assessment rule) that is not optimal for the case described here. An optimal Bayesian forager exploiting prey wh ose distribution follows the negative binomial distribution should leave a patch when the potential land not instantaneous) gain rate in that patch eq uals the best long-term gain rate in the environment (potential value asses sment rule). It follows that the instantaneous gain rate at which the patch es are abandoned is an increasing function of the time spent searching in t he patch. It also follows that the proportion of prey harvested in a patch is an increasing sigmoidal function of the number of prey initially present . In this paper we vary several parameters of the model to evaluate the eff ects on the forager's intake rate, the proportion of prey harvested per pat ch, and the prey's average mortality rate in the environment. In each case, we study an intake rate maximizing forager's optimal response to the param eter changes. For the potential value assessment rule we find that at a hig her average prey density in the environment, a lower proportion of the prey is taken in a patch with a given initial prey density. The proportion of p rey taken in a patch of a given prey density also decreases when the varian ce of the prey density distribution is increased and if the travel time bet ween patches is reduced. We also evaluate the effect of using predation min imization, rather than rate maximization, as the currency. Then a higher pr oportion of the prey is taken for each given initial prey density. This is related to the assumption that traveling between patches is the most risky activity. Compared to the optimal potential value assessment rule, the curr ent value assessment rule performs worse, in terms of long-term intake rate achieved. The difference in performance is amplified when prey density is high or highly aggregated. These results pertain to the foraging patch spat ial scale and may have consequences for the spatial distribution of prey in the environment, (C) 2000 Academic Press.