Animals attempting to avoid predators can do so in a number of ways. They can wait for them to arrive and then try to escape. They can time their activity out of phase with predator foraging. Or they can attempt to satiate predators with fellow members of the species. All of these behaviors could gain from event timers.
There are several methods of escape in the sense that I use it above. An animal might run for cover, or it might trick the predator into thinking it is not a prey item. In either case, learning the principles of predator vigilance can increase foraging efficiency. In some cases, the presence of predators may actually enhance foraging efficiency (Holtcamp et al., 1997).
For an animal foraging in the open, attention to predators is necessary for survival. But how much time should an animal devote to vigilance? Animals that economize predator vigilance strike an optimal relationship between eating and being eaten (Dukas, 1998). Potential environmental factors are the nearest possible escape and the proximity of possible predators. In the latter case, there is evidence that adult ground squirrels with obstructed views of their surroundings are more vigilant than those with clear views (Arenze and Leger, 1997). Juveniles were undeterred, suggesting the behavior learned.
A useful trick against predators is feigning death. Vigilance is helpful here, but of equal importance is how long one should stay down for. Anxious resurrection will indubitably lead to real mortality. But staying dead until a predator unbeguiled by death arrives is an equally poor outcome. Domestic chicks perform the death feigning behavior instinctively. Predictably then, the time spent inanimate appears to be affected by the circadian period (Richelle and Lejeune, 1980), suggesting a connection with the courtship song of flies.
Predator avoidance can also take the form of knowing when predators are active and choosing to be active at other times. This is exemplified by the behavior of baby alligators (Alligator spp.), which when heavily preyed upon by African fish eagles (Haliatus vocifer) move from diurnal to nocturnal activity rhythms (Curio, 1976). This suggests a phenotypic plasticity in the way behaviors are linked to circadian clocks, reminiscent of honeybees learning the daily cycles of nectar production.
By far one of the most popular forms of predator avoidance is feeding them your neighbors. Plants do this in the form of masting (Silvertown, 1980). Periodical cicada (Magicicada spp.) are one of the more artful exemplars of this phenomenon (Lloyd and Dybas, 1966). Having the longest known life cycles of any insect (barring some queen ants), they emerge from the ground to mate, lay eggs, and die within weeks of one another every seventeen or thirteen years, depending on the species. The behavior is hypothesized to be a predator satiating mechanism above ground and a predator avoidance mechanism below ground (Lloyd and Dybas, 1966).
The predator satiating mechanism works on the premise that predators are limited in their maximal intake rate of prey. This can be due to simple satiation or to prey handling times. For example, when guillemot fledglings (Uria lomvia) jump from their breeding cliffs the probability of death is significantly enhanced if the bird jumps alone (Daan, 1981). The usual strategy is to jump with everyone else, so that the fledglings are shielded from the predatory glaucous gulls (Larus hyperboreus) by other members of their cohort. If the glaucous gulls did not have a maximal intake rate they would presumably eat everyone as soon as they were exposed.