A stochastic dynamic programminng model is developed of prey choice by three-spined stickleback. The fitness function relates growth rate k from the von bertalanffy growth equation to stomach fullness. It is shown that the model predicts experimental results. Emphasis is given to handling time as an important variable determining diet. Two handling line vectors are defined, each of which is used to represent the benthic and limnetic morphs found in Paxton Lake, Texada Island, BC, Canada. The model is then used to examine the growth rates to be expected from these two morphs in habitats which vary in the distribution of encounter probabilities with each prey size and the distribution of prey size specific risk of predation. The benthic morph grows faster than the limnetic in most habitats but often the two do as well as each other. In the one habitat where limnetics grow better, they do so because their shorter handling times for small prey counteract the effect of a constant but high risk of predation. The results are discussed in the context of what is known of the ecology and evolution of the two morphs in Paxton Lake. It is concluded tha the model is only dealing with conditions in the benthic habitat and data are required on encounter rates and prey size distributions in the limnetic habitat so that the model can be used to predict growth for limnetics.
