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such as the zero–one rule and the independence of the optimal strategy on the availability of alternative prey are no longer valid when fitness, rather than the proxy for fitness, is explicitly considered in a finite foraging duration.

最佳觅食模型通常用于确定最大化代理适应度的策略，例如觅食成功。假设最大化适应度和适应度代理的策略是相同的。然而，这项研究表明，当适应度代理和适应度之间的关系是非线性的并且觅食成功不确定时，这个假设可能是无效的。以一个著名的猎物选择模型为例，该模型使用长期能量摄入率作为适应度的代理。该模型考虑了捕食者捕食两种质量不同的猎物的情况，即一种（主要猎物）的质量高于另一种（替代猎物）。策略可以表示为在遇到时攻击替代猎物的概率，同时始终攻击主要猎物。根据主要猎物的密度（称为零一规则），攻击使预期能量摄入率最大化的替代猎物的概率为 0 或 1。同时，替代猎物的密度对最优策略没有影响。使用模拟模型来表征有限觅食期间能量摄入率的随机结果。结果表明，觅食策略会影响预期的能量摄入率和预期的不确定性。因此，当能量摄入率和适应度之间的关系由于 Jensen 不等式而呈非线性关系时，最大化能量摄入率和适应度的策略可能不同。