Sudden Patch Exhaustion

The availability of food in a patch may suddenly drop to zero. Faced with this situation, a forager needs to detect the change in status of the patch and move on to a new patch, because a forager that remains in an empty patch will be wasting time searching for food that is not there. Sometimes there may be visual or auditory cues available to the forager to indicate that a patch is exhausted, but if there are no such cues, a forager might be able to use its internal clock to detect patch exhaustion. Consider the situation in which there is a fixed intercapture interval and constant probability of sudden patch exhaustion after each prey encounter or after arrival in the patch. If the forager can learn the interfood interval, then it can use this knowledge to detect patch exhaustion. The optimal departure rule is to leave the patch as soon as exhaustion is detected, namely, as soon as the period since the last prey capture exceeds the normal intercapture interval. This optimal departure rule is independent of the time taken to travel to a new patch (Kacelnik et al., 1990).

The foraging of spotted flycatchers (MuscĂ­capa striata) provides a possible example of sudden patch exhaustion (Davies, 1977). These birds hunt from a fixed perching site, making periodic forays to catch flying insects that have entered their range. Usually following a capture, the bird returns to the same or a nearby perch, but occasionally it will leave the site and travel to a new perch to continue hunting. Davies was interested in establishing what caused a bird to abandon a foraging site and move on to the next. He found that the birds would move sites when they had waited 1.5 times the average intercapture interval without making a foray, and on the basis of this finding, he suggested that the birds might be using a rule that involved estimating the average intercapture interval and moving on to a new perch when no insect had appeared within a given multiple of this time (specifically, 1.5 times). Such a moving-on rule might be optimal in an environment in which patches of prey deplete suddenly and completely, as might be the case, for instance, if a swarm of flies moves away from the immediate vicinity of the bird's perch, and where there are no external cues to indicate that the patch is now empty. Unfortunately, with the available data, it is impossible to prove that the flycatchers are really using such a time-based moving-on rule (Kacelnik et al., 1990). Proof that the birds are using an internal clock to judge their departure from a site would require eliminating the possibility that the birds do not just move on when they can no longer detect any prey items within their range. Additionally, proof that the birds wait for a fixed multiple of the intercapture interval before moving on would require manipulating intercapture intervals and demonstrating the predicted effects on mov-ing-on times.

5.3.2.2 Gradual Depletion

The rate of food intake within a patch will often be a decelerating function of the amount of time the forager has already spent foraging in the patch. In this situation the forager is faced with the decision about when to leave the current patch and pay the cost of traveling to a new patch. The marginal value theorem (MVT) (Charnov, 1976) describes the behavior that maximizes the long-term rate of energy intake in such a situation. Long-term rate is maximized if the forager stays in each patch until its instantaneous rate within the patch falls below the background rate of gain in the environment as a whole. This background rate will be affected by the travel time between patches, and as the travel time between patches increases, the optimal patch residence time also increases. Because rates are equal to amounts per unit of time, computation of rate requires the ability to time intervals. An important prediction of the MVT is that although patch residence time is predicted to be sensitive to the average travel time, it should not be affected by variance in travel time.

A number of studies have tested the prediction that patch residence time should be positively related to the travel time between patches. Perhaps the most well known is the study by Kacelnik (1984) on European starlings (Sturnus vulgaris). During the breeding season starlings make regular forays from their nest to collect food for their chicks. As required by the MVT within each foraging bout, the starling suffers a decelerating rate of food acquisition. This occurs due to the starling's method of foraging, whereby it probes the ground to look for invertebrates, such as leather-jackets, hidden beneath the surface of the soil. As the starling's bill fills up with prey, the bird becomes progressively less efficient at probing the ground for further prey and its rate of prey acquisition declines. Kacelnik tested the MVT prediction that travel time should affect patch residence time by setting up feeding stations for starlings at different distances from their nests. He simulated the loading curve by delivering worms to the birds at progressively greater intervals the longer they stayed at the feeding station. He was able to show that the number of worms the starling collected before returning to its nest increased as the travel distance to the feeder increased. The observed behavior was approximately as predicted if the bird were maximizing the rate at which it delivered worms to its chicks.

5.3.3 How to Respond to Variability

Many natural food sources are variable either in the exact amount of food they provide or in the time associated with finding or extracting the food. For example, consider a forager faced with one feeding option that it knows will yield food after 5 min of searching vs. another feeding option that it knows will yield the same amount of food after the same average searching time, but the actual time taken to find the food could vary between 1 and 9 min. A rate-maximizing forager should be indifferent to such variability because the computation of the long-term rate of energy intake involves averaging the amounts and times associated with each food source, with the result that both food sources are perceived to be of equal value. However, there are circumstances where the long-term rate of energy intake may not be the currency that correlates best with fitness. Consider a small bird in winter faced with one more foraging decision before the rapidly approaching night. It is vitally important for this bird to achieve a threshold level of energy reserves before dusk in order to survive the long cold night. In this situation, it can be optimal for the forager to pay attention to the variance, or risk, as it is called in the foraging literature, in its food sources. If the bird has no chance of meeting the required threshold for survival in time by choosing the fixed option (i.e., it is on a negative energy budget), then its only chance of survival is to choose the risky option in the hope that it will be lucky and find food quickly. Conversely, if the fixed option will easily take the bird above threshold (i.e., it is on a positive energy budget), then it would be foolish to choose the variable option and risk not getting its final prey item before nightfall. These arguments are summarized in the daily energy budget rule that states that a forager on a positive energy budget should be risk averse, while one on a negative budget should be risk prone.

There is a large literature showing that animals are sensitive to risk in both the amount of food and in the delay associated with obtaining food (Kacelnik and Bateson, 1996; Bateson and Kacelnik, 1998). Unfortunately, though, there is little good empirical support for functional explanations for risk sensitivity such as the energy budget rule (but for a beautiful demonstration of the energy budget rule in yellow-eyed juncos, see Caraco et al., 1990). The overall pattern in the literature is that animals tend to be risk averse when there is variability in amount of reward, but risk prone when variability is in delay to reward. This pattern is not readily explained by any of the optimal foraging models, and there has been an ongoing discussion in the literature about whether risk sensitivity is an adaptive response to environmental variability or instead is an artifact of the cognitive mechanisms animals use to assess quantities such as amount, time, and rate (e.g., Bateson and Kacelnik, 1995b; Reboreda and Kacelnik, 1991).

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