GENERAL RESULTS CONCERNING THE TRADE-OFF BETWEEN GAINING ENERGY AND AVOIDING PREDATION

When animals can choose from a range of feeding options, often those o ptions with a higher energetic gain carry a higher risk of predation. This paper analyses the optimal trade-off between food and predation. We are primarily interested in how an animal's decisions and its state change over time. Our models are very general. They can be applied to growth decisions, such as choice of habitat, in which case we might c onsider how the state variable size changes over an animal's lifetime. Equally our models are applicable to short-term foraging decisions, s uch as vigilance level, in which case we might consider how energy res erves vary over a day. We concentrate on two cases: (i) the animal mus t reach a fixed state, its fitness depending on when this is attained; (ii) the animal must survive to a fixed time, its fitness depending o n its final state.In case (i) minimization of mortality per unit incre ase of state is optimal under certain baseline conditions. In case (ii ) behaviour is constant over time under baseline conditions (the 'Risk -spreading Theorem'). We analyse how these patterns are modified by co mplicating factors, e.g. time penalties, premature termination of the food supply, stochasticity in food supply or in metabolic expenditure, and state-dependence in the ability to obtain food, in metabolic expe nditure and in predation risk. From this analysis we obtain a variety of possible explanations for why an animal should reduce its intake ra te over time (i.e. show satiation). We show how -earlier work can be v iewed as special cases of our results.