Uncertainty in foraging success and its consequences on fitness

Optimal foraging models are commonly used to determine the strategy maximizing the proxies for fitness, such as foraging success. The strategies maximizing the proxy for fitness and fitness are assumed to be the same. However, this study shows that this assumption can be invalid when the relationship between the proxy for fitness and fitness is nonlinear and the foraging success is uncertain. A well-known prey choice model that uses long-term energy intake rate as the proxy for fitness was used as an example. This model considers a situation where predators predate on two types of prey that differ in quality, that is, one (primary prey) has higher quality than the other (alternative prey). A strategy can be represented by the probability of attacking alternative prey upon encounter while always attacking primary prey. The probability of attacking alternative prey that maximizes the expected rate of energy intake is either 0 or 1 depending on the density of primary prey (known as the zero-one rule). Meanwhile, the density of alternative prey has no influence on the optimal strategy. A simulation model was used to characterize the stochastic outcomes in the rate of energy intake in a finite foraging duration. The results revealed that foraging strategy influences the expected rate of energy intake and the uncertainty around the expectation. Consequently, the strategies maximizing the rate of energy intake and fitness may not be the same when the relationship between the rate of energy intake and fitness is nonlinear due to Jensen's inequality. Previous results such as the zero-one rule and the independence of the optimal strategy on the availability of alternative prey are no longer valid when fitness, rather than the proxy for fitness, is explicitly considered in a finite foraging duration.