On the Theory of Optimal Diets

Using techniques of stochastic theory, I develop a new aproach to predicting optimal diets. The models developed are for a mobile predator feeding on stationary prey; however, the models can easily be extended to include mobile prey. Parameters used in the models are caloric content, time to pursue and density of each prey type, and the speed of the predator. Both clumped and random prey distribution are considered. The models predict the optimal diet of a predator faced with a variety of potential prey types. The optimal diet is predicted as the set of successive prey choices which maximizes the rate of caloric intake or, alternatively, minimizes the time required to find a food ration. Also predicted are the criteria for specialization and switching from a specialist diet to a generalist diet. The criteria for specialization and for switching are independent of the density of the alternate prey type. Also, a predator feeding so as to maximize the rate of caloric intake should take a prey on every encounter with it or not take it at all. Thus, the model predicts that an animal feeding according to the dictates of the optimal diet should show no partial preferences. The role of predator satiation in affecting prey selection is discussed in light of the above findings. Criteria for optimal diet with clumped prey distributions are identical to the criteria in the case of random prey distributions except that the increased diameter of a prey clump leads to greater predator specialization. This arises because the prey become more conspicuous, thus reducing the time to search for prey. The relevance of this finding to pollinator specificity is discussed.