Foraging in an uncertain environment: Patch exploitation

Abstract

Effects of environmental uncertainty on the expected future rewards and the expected long-term reward rate of foraging animals in a patchy environment was analyzed for two types of forager; a continuous feeder which exploits a resource continuously in a patch, and a prey hunter which takes at most only one prey per patch. The environmental uncertainty was represented by random variation in parameters expressing patch quality. That is, environmental stochasticity was characterized by two parameters in each case. The total resource amount in one patch (noted r ) and resource exploitation efficiency (noted λ ) were varied for a continuous feeder. Prey size (noted r ) and prey encounter rate (noted λ ) were varied for a prey hunter. The decision process proceeds as follows; (1) the objective function to be maximized is the expected long-term reward rate of resource intake; (2) the forager discriminates patch types, each of which is assigned particular probability density functions of environmental parameters, by appearance or other indirect cues; (3) decision making (patch residence time for a continuous forager, and giving up time for a prey hunter, respectively) is conducted at the time of entering a patch by evaluating the expectation of some criterion such as the expected future gain and the expected waiting time in a given patch type. Scenario (1) is a general assumption of the intake maximization models. Scenarios (2) and (3) stress between patch uncertainty. When the two environmental parameters are independent, the stochasticity of r does not affect the expected long-term reward rate for either type of forager. However, the stochasticity of λ does reduce the expected future gain for both types of forager. Furthermore, it also increase the expected waiting time for the prey hunter. These effects depend on magnitudes of the even-order moments, and signs and magnitudes of the odd-order moments of the probability density function of λ around its mean. Positive correlation between the two stochastic parameters ( r and λ ) increases the expected future gain, and negative correlation decreases it. For the continuous feeder a stochastic environment with a positive correlation between r and λ yields the larger long-term reward rate at the optimal patch exploitation time than a deterministic environment. On the other hand, the prey hunter does not have any advantage by the stochasticity. Only when a positive correlation is extremely high does the hunter have a slightly higher expected long-term reward rate compared with the deterministic case.