A Theoretical Investigation into the Direct and Indirect Effects of State on the Risk of Predation

As well as there being a direct physical effect of the state (for example fat reserves, or size) of an animal on the risk of being caught by a predator, state also has an effect on predation risk indirectly through changes in behaviour. We present a mathematical model which looks at these two components of the effect of state on predation risk. We focus on two different models, (i) where the animal must achieve a fixed state and its fitness depends on the time at which this state is reached and (ii) where the animal must survive until a fixed time and its fitness depends on its final state. We investigate conditions under which the indirect effect of increased state is to increase or decrease predation risk, and give some numerical illustrations. Under certain conditions in the fixed-state model, the indirect effect of state is to increase predation risk, whereas under certain conditions in the fixed-time model the indirect effect of state is to decrease predation risk. We discuss the implications of our results for empirical investigations into the effect of state on predation risk.