Should prey overestimate the risk of predation

Mathematical models are used to determine the optimal foragnig effort of individuals that face increased risk of predation when they exert greater foraging effort but have imperfect information about the degree of risk. If the fitness cost of underestimating predation risk is less than that of overestimating risk, imperfect information should lead to behavior that is appropriate for a lesser risk than is actually present. Overestimation is favored under the opposite condition. If there is a trade-off between starvation and predation, an animal will usually underestimate (overestimate) risk if the third derivative of the starvation-versus-risk relation is positive (negative), provided uncertainty is not too large. Different, plausible starvation functions can favor either under- or overestimation of risk. If there is a trade-off between reproduction and predation, a more complex condition determines which type of bias is adaptive; this condition involves the reproduction-versus-risk function and its first three derivatives, and again, over- or underestimation of risk can be advantageous. In almost all models, increased accuracy of estimation is favored when costs of increased accuracy are sufficiently small. These results differ from those of previous analyses, and reasons for these differences are discussed.