Generalized optimal risk allocation: foraging and antipredator behavior in a fluctuating environment

Animals live in complex environments in which predation risk and food availability change over time. To deal with this variability and maximize their survival, animals should take into account how long current conditions may persist and the possible future conditions they may encounter. This should affect their foraging activity, and with it their vulnerability to predation across periods of good and bad conditions. Here we develop a comprehensive theory of optimal risk allocation that allows for environmental persistence and for fluctuations in food availability as well as predation risk. We show that it is the duration of good and bad periods, independent of each other, rather than the overall proportion of time exposed to each that is the most important factor affecting behavior. Risk allocation is most pronounced when conditions change frequently, and optimal foraging activity can either increase or decrease with increasing exposure to bad conditions. When food availability fluctuates rapidly, animals should forage more when food is abundant, whereas when food availability fluctuates slowly, they should forage more when food is scarce. We also show that survival can increase as variability in predation risk increases. Our work reveals that environmental persistence should profoundly influence behavior. Empirical studies of risk allocation should therefore carefully control the duration of both good and bad periods and consider manipulating food availability as well as predation risk.