A THEORETICAL-STUDY OF THE SOCIOECOLOGY OF UNGULATES

In the framework of optimal foraging theory we present an optimization model for herd size selection by ungulates. The model is constructed on the basis of a survey of the pertinent literature concerning the social behavior and ecology of ungulates. The use of the optimization model relies on the idea that natural selection shapes the policy of choice of herd sizes in the sense that the animals tend to maximize their individual "fitness." The model concerns animals that perform a daily selection of herd size during a period of N days, the Nth day corresponding to the beginning of the reproductive season. We assume that the herdmates share the food in the patch and that the per-individual mortality rate (due to predation) is a decreasing function of herd size. Further constraints are introduced for minimal and maximal levels of energy storage. We consider three different optimization strategies based on maximizing (i) the final energy level EN′ (ii) the final survival probability PN′ and (iii) their product ENPN. Strategy (iii) is the most relevant since it corresponds to maximizing the effective expected reproductive fitness (i.e., the expected number of offspring). We present explicit solutions for the three problems of optimization and we examine the optimal policies in relation to predation pressure and to food distribution patterns. Finally we present a comparison of our theoretical predictions with the biological evidence. There appears to be good qualitative agreement. © 1992.