Ideal free distribution of copepods under predation risk

Optimal vertical distribution of a copepod population of equal competitors under predation hazard is modelled by ideal free distribution (IFD). The foragers may be limited by both depletable (food) and non-depletable (temperature) resources. Individuals are assumed to maximize growth rate per mortality risk (g/M). Mortality risk is assumed density-dependent whenever the copepod concentration is high enough to satiate predators. The growth rate depends upon temperature or food concentration in absence of competition, and is density-dependent under competition. These relationships may yield peaked habitat profitability curves. For L depths with peaked profitability curves, the computational complexity scales to 3L. Simplifying restrictions to allow numerical solutions when a large number of depths are available are presented and discussed. At moderate and high copepod stock size, the restrictions find the optimal distribution much faster, but at low stock sizes they may predict suboptimal distributions. The model predicts that individuals shall be more sensitive to predation risk at low and moderate competitor abundance and more sensitive to resource input rate at higher competitor abundances. Deviations from a food-based IFD are therefore most pronounced at low copepod population size. The IFDs are compared with predictions from a dynamic programming model with state- and time-resolved motivation of the copepods.