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Figure 2.4. The relationship between p (probability of food in partially full patches) and optimal giving-up time (GUT). As p increases, the optimal giving-up time decreases. This is a discrimination effect; when p is near zero, a larger sample is required to discriminate empty patches from partially full patches. Predicted giving-up times are also generally longerwhen q (the probability of partially full patches in the environment) is small.

Figure 2.4. The relationship between p (probability of food in partially full patches) and optimal giving-up time (GUT). As p increases, the optimal giving-up time decreases. This is a discrimination effect; when p is near zero, a larger sample is required to discriminate empty patches from partially full patches. Predicted giving-up times are also generally longerwhen q (the probability of partially full patches in the environment) is small.

In agreement with the general development of our model, the value of information is (approximately) proportional to the variance in ideal behaviors (s2q (1 — q), which is the variance of the random process in which a forager spends either s or 0 time units in a patch). Notice especially that the value of information peaks at intermediate q values (i.e., q ^ 1/2). On the other hand, information has less value when q takes extreme values. For example, if we assume that a forager must pay a cost to implement a giving-up time, then we might predict that a forager will adopt a fixed, non-information-gathering strategy when q is near 0 or 1.

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