Animals are frequently faced with trade-offs created by the fact that both resource acquisition and risk of mortality increase with activity, for example, with foraging speed or time spent foraging. We develop models predicting adaptive responses for both foraging speed and proportion of time active when individual growth rate and mortality risk are functions of these variables. Using the criterion that animals should minimize the ratio of mortality to growth rates, we show that, when both growth and mortality rates are linear with activity levels, the latter should be either maximal or minimal depending on resource level. If growth rate is a decelerating function of activity, then speed or time active should decrease with increases in resources, handling time, or the effect of activity on mortality rate. By contrast, if mortality rate unrelated to activity increases, then activity rate also should increase. We also develop predictions for cases in which time horizon is critical using a dynamic programming framework. The general patterns of predicted activity responses are similar to the time-invariant analytical solutions, but foraging speed is reduced relative to the analytical solutions when time remaining is long or when accumulated reserves are high. This effect is ameliorated when accumulated reserves (size) increase resource capture efficiency or reduce mortality risk. If resources decline with time (e.g., because of competition) optimal foraging speeds are also higher than predicted by the analytical solutions. We discuss the relation of our predictions to previous models and the available empirical evidence. The majority of available data appear to be consistent with our models, and in some cases quantitative comparisons are quite close. Finally, we discuss the implications of our results for ontogenetic changes in behavior and for population- and community-level phenomena, particularly the role of activity responses in competitive interactions and indirect effects and patterns of coexistence among competitors.
