The waiting game: a "battle of waits" between predator and prey

Many prey respond to the presence of a predator by retreating into a shell or burrow, or by taking refuge in some other way that guarantees their safety but restricts further information from being obtained about the predator's continued presence. When this occurs, the individual predator and prey involved become opponents in a "waiting game." The prey must decide how long to wait for the predator to depart before re-emerging and potentially exposing itself to attack. The predator must decide how long to wait for the prey to re-emerge before departing in search of other foraging opportunities. I use a numerical approach to determine the evolutionarily stable waiting strategy of both players and examine the effects of various parameters on the ESS. The model predicts that each player's waiting distribution--the distribution of waiting times one would expect to observe for individuals in that role--will have a characteristic shape: the predator's distribution should resemble a negative exponential function, whereas the waiting time of the prey is predicted to be more variable and follow a positively skewed distribution. The model also predicts that very little overlap will occur between the players' waiting distributions, and that the predator will rarely outwait the prey. Empirical studies relating to the model and comparisons between the waiting game and the asymmetric war of attrition are discussed. Copyright 2003.