Allocation Patterns and Diel Vertical Migration: Modeling the Optimal Daphnia

I present a model which at the same time evaluates optimal diel vertical migration (DVM) and optimal allocation patterns to growth or reproduction in the cladoceran Daphnia magna. The combined policies that maximize the intrinsic rate of increase r are found using the Perron Frobenius Theorem and dynamic programming. The model attempts to incorporate two traditions in aquatic behavioral ecology within the same model framework: variations in vertical migrations (short time behavior) and age or size at maturity (life history models). The predictions from the model are compared with observations from an experiment in thermally stratified flow-through tubes containing various concentrations of fish exudates. The model is able to reproduce many of the observations of both DVM and allocation, though there are some interesting deviations. I look at theoretical behavior and life history consequences of various size dependencies in mortality. Finally, I do a comparative analysis of two fitness measures, the intrinsic rate of increase r, and the net lifetime reproduction, R0, where it turns out that the use of r makes predictions in better agreement with the observations.