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Figure 5. If starlings are maximizing net rate of energy gain, longer traveling time results in larger optimum load. Adapted from Krebs and Davies.[4]

The foraging behavior of the European starling, Sturnus vulgaris, provides an example of how marginal value theorem is used to model optimal foraging. Starlings leave their nests and travel to food patches in search for larval leatherjackets to bring back to their young. The starlings must determine the optimal number of prey items to take back in one trip (i.e. the optimal load size). While the starlings

The foraging behavior of the European starling, Sturnus vulgaris, provides an example of how marginal value theorem is used to model optimal foraging. Starlings leave their nests and travel to food patches in search for larval leatherjackets to bring back to their young. The starlings must determine the optimal number of prey items to take back in one trip (i.e. the optimal load size). While the starlings forage within a patch, they experience diminishing returns: the starling is able to hold only so many leatherjackets in its bill, so the speed with which the parent picks up larvae decreases with the number of larvae that it already has in its bill. Thus, the constraints are the shape of the curve of diminishing returns and the travel time (the time it takes to make a round trip from the nest to a patch and back). In addition, the currency is hypothesized to be net energy gain per unit time.[4] Using this currency and the constraints, the optimal load can be predicted by drawing a line tangent to the curve of diminishing returns, as discussed previously (Figure 3).

Kacelnik et al. wanted to determine if this species does indeed optimize net energy gain per unit time as hypothesized.[17] They designed an experiment in which the starlings were trained to collect mealworms from an artificial feeder at different distances from the nest. The researchers artificially generated a fixed curve of diminishing returns for the birds by dropping mealworms at successively longer and longer intervals. The birds continued to collect mealworms as they were presented, until they reached an "optimal" load and flew home. As Figure 5 shows, if the starlings were maximizing net energy gain per unit time, a short travel time would predict a small optimal load and a long travel time would predict a larger optimal load. In agreement with these predictions, Kacelnik found that the longer the distance between the nest and the artificial feeder, the larger the load size. In addition, the observed load sizes

Kacelnik et al. wanted to determine if this species does indeed optimize net energy gain per unit time as hypothesized.[17] They designed an experiment in which the starlings were trained to collect mealworms from an artificial feeder at different distances from the nest. The researchers artificially generated a fixed curve of diminishing returns for the birds by dropping mealworms at successively longer and longer intervals. The birds continued to collect mealworms as they were presented, until they reached an "optimal" load and flew home. As Figure 5 shows, if the starlings were maximizing net energy gain per unit time, a short travel time would predict a small optimal load and a long travel time would predict a larger optimal load. In agreement with these predictions, Kacelnik found that the longer the distance between the nest and the artificial feeder, the larger the load size. In addition, the observed load sizes quantitatively corresponded very closely to the model's predictions. Other models based on different currencies, such as energy gained per energy spent (i.e. energy efficiency), failed to predict the observed load sizes as accurately. Thus, Kacelnik concluded that starlings maximize net energy gain per unit time. This conclusion was not disproved in later experiments.[18][19]

Worker bees provide another example of the use of marginal value theorem in modeling optimal foraging behavior. Bees forage from flower to flower collecting nectar to carry back to the hive. While this situation is similar to that of the starlings, both the constraints and currency are actually different for the bees.

A bee does not experience diminishing returns because of nectar depletion or any other characteristic of the flowers themselves. The total amount of nectar foraged increases linearly with time spent in a patch. However, the weight of the nectar adds a significant cost to the bee's flight between flowers and its trip back to the hive. Wolf and Schmid-Hempel s

A bee does not experience diminishing returns because of nectar depletion or any other characteristic of the flowers themselves. The total amount of nectar foraged increases linearly with time spent in a patch. However, the weight of the nectar adds a significant cost to the bee's flight between flowers and its trip back to the hive. Wolf and Schmid-Hempel showed, by experimentally placing varying weights on the backs of bees, that the cost of heavy nectar is so great that it shortens the bees' lifespan.[20] The shorter the lifespan of a worker bee, the less overall time it has to contribute to its colony. Thus, there is a curve of diminishing returns for the net yield of energy that the hive receives as the bee gathers more nectar during one trip.[4]

The cost of heavy nectar also impacts the currency used by the bees. Unlike the starlings in the previous example, bees maximize energy efficiency (energy gained per energy spent) rather than net rate of energy gain (net energy gained per time). This is because the optimal load predicted by maximizing net rate of energy gain is too heavy for the bees and shortens their lifespan, decreasing their overall productivity for the hive, as explained earlier. By maximizing energy efficiency, the bees are able to avoid expending too much energy per trip and are able to live long enough to maximize their lifetime productivity for their hive.[4] In a different paper, Schmid-Hempel showed that the observed relationship between load size and flight time is well correlated with the predictions based on maximizing energy efficiency, but very poorly correlated with the predictions based on maximizing net rate of energy gain.[21]

The nature of prey selection by two centrarchids (white crappie and bluegill) has been presented as a model incorporating optimal foraging strategies by Manatunge & Asaeda .[22] The visual field of the foraging fish as represented by the reactive distance was analysed in detail to estimate the number of prey encounters per search bout. The predicted reactive distances were compared with experimental data. The energetic cost associated with fish foraging behaviour was calculated based on the sequence of events that takes place for each prey consumed. Comparisons of the relative abundance of prey species and size categories in the stomach to the lake environment indicated that both white crappie and bluegill (length < 100 mm) strongly select prey utilizing an energy optimization strategy. In most cases, the fish exclusively selected large Daphnia ignoring evasive prey types (Cyclops, Diaptomids) and small cladocera. This selectivity is the result of fish actively avoiding prey with high evasion capabilities even though they appear to be high in energetic content and having translated this into optimal selectivity through capture success rates. The energy consideration and visual system, apart from the forager's ability to capture prey, are the major determinants of prey selectivity for large-sized bluegill and white crappie still at planktivorous stages.

Criticism and limitations of the optimal foraging theory