Optimal time to emerge from refuge

Factors affecting emergence by prey that enter refuges when approached by predators have been studied intensively, but only two theoretical models predict how long prey should remain in a refuge before emerging. We argue that prey can make better decisions than allowed by one model; the other model describes cases in which predators wait for prey to emerge. We present optimality models that permit prey to select a time to emerge that maximizes fitness. When in a refuge, a prey cannot obtain benefits outside; emerging too soon can be catastrophic, but delaying emergence entails loss of fitness. If predators resume foraging quickly rather than engaging in strategic waiting games, current theory suggests that prey emerge when the costs of remaining in a refuge and of emerging are equal. However, prey often can do better by emerging at the time maximizing fitness rather than when benefits equal costs (i.e. when prey break even). Optimal emergence time depends on initial fitness, benefits lost by remaining in refuge, and the decay rate of predation risk. Benefits lost if a prey is killed are modelled separately from benefits that contribute to lifetime fitness, even if the prey is killed (individual reproduction, altruism). Fitness of prey emerging at the optimal emergence time may be greater than, equal to or less than initial fitness. Break‐even and optimality models base predictions on the opposing effects of risk and loss of benefits. Thus, many empirically verified predictions are identical at the ordinal level although differing quantitatively. Optimality models provide novel testable predictions for the effects of initial fitness, benefits, and, for ectotherms, the rate of cooling in refuge. They predict earlier emergence for equal retainable benefits than for those lost upon death. © 2007 The Linnean Society of London, Biological Journal of the Linnean Society , 2007, 91 , 375–382.