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The marginal value theorem (MVT) is an optimality model that usually describes the behavior of an optimally foraging individual in a system where resources (often food) are located in discrete patches separated by areas with no resources. Due to the resource-free space, animals must spend time traveling between patches. The MVT can also be applied to other situations in which organisms face diminishing returns.

The MVT was first proposed by Eric Charnov in 1976. In his original formulation: "The predator should leave the patch it is presently in when the marginal capture rate in the patch drops to the average capture rate for the habitat."[1]

The optimal time spent in a patch is given by the tangent to the resource intake curve that departs from the expected transit time value. Any other line crossing the resource intake curve has a shallower slope and thus a sub-optimal resource intake rate.

Modeling

As animals forage in patchy systems, they balance resource intake, traveling time, and foraging time. Resource intake within a patch diminishes with time, as shown by the solid curve in the graph to the right. The curve follows this pattern because resource intake is initially very fast, but slows as the resource is depleted. Traveling time is shown by the distance from the leftmost vertical dotted line to the y-axis. Optimal foraging time is modeled by connecting this point on the x-axis tangentially to the resource intake curve. Doing so maximizes the ratio between resource intake and time spent foraging and traveling.

At the extremes of the loading curve, animals spend too much time traveling for a small payoff, or they search too long in a given patch for an ineffective load. The MVT identifies

When an animal is foraging in a system where food sources are patchily distributed, the MVT can be used to predict how much time an individual will spend searching for a particular patch before moving on to a new one. In general, individuals will stay longer if (1) patches are farther apart or (2) current patches are poor in resources. Both situations increase the ratio of travel cost to foraging benefit.

As animals forage in patchy systems, they balance resource intake, traveling time, and foraging time. Resource intake within a patch diminishes with time, as shown by the solid curve in the graph to the right. The curve follows this pattern because resource intake is initially very fast, but slows as the resource is depleted. Traveling time is shown by the distance from the leftmost vertical dotted line to the y-axis. Optimal foraging time is modeled by connecting this point on the x-axis tangentially to the resource intake curve. Doing so maximizes the ratio between resource intake and time spent foraging and traveling.

At the extremes of the loading curve, animals spend too much time traveling for a small payoff, or they search too long in a given patch for an ineffective load. The MVT identifies the best possible intermediate between these extremes.

Assumptions

  1. The individual is assumed to control when it leaves the patch in order to maximize the ratio between resource intake and time.
  2. The consumer depletes the amount of resources in the patch where they are foraging; therefore, the rate of intake of food in that patch decreases as a function of time.
  3. If there is variation in the quality of patches, the MVT assumes that different patches are distributed randomly throughout the landscape.

Examples

Great tits are a species of bird found throughout Europe, northern Africa, and Asia. They are known to forage in “patchy” environments, and research has shown that their behavior can be modeled by optimal foraging models, including the MVT. In a 1977 study by R.A. Cowie,[3] birds were deprived of food and then allowed to forage through patches in two different environments (the environments differed only in distance between patches). As predicted, in both cases birds spent more time in one area when the patches were farther away or yielded more benefits, regardless of the environment. In a similar experiment by Naef-Daenzer (1999),[4] great tits were shown to have a foraging efficiency 30% be

Great tits are a species of bird found throughout Europe, northern Africa, and Asia. They are known to forage in “patchy” environments, and research has shown that their behavior can be modeled by optimal foraging models, including the MVT. In a 1977 study by R.A. Cowie,[3] birds were deprived of food and then allowed to forage through patches in two different environments (the environments differed only in distance between patches). As predicted, in both cases birds spent more time in one area when the patches were farther away or yielded more benefits, regardless of the environment. In a similar experiment by Naef-Daenzer (1999),[4] great tits were shown to have a foraging efficiency 30% better than random foraging would yield. This is because great tits were specifically spending more time in resource-rich areas, as predicted by the MVT. This data supports the use of the MVT in predicting the foraging behavior of great tits.

Feeding in hairy armadillos and guinea pigs

The MVT can be used to model foraging in plants as well as animals. Plants

The MVT can be used to model foraging in plants as well as animals. Plants have been shown to preferentially place their roots, which are their foraging organs, in areas of higher resource concentration. Recall that the MVT predicts that animals will forage for longer in patches with higher resource quality. Plants increase root biomass in layers/areas of soil that are rich in nutrients and resources, and decrease root growth into areas of poor-quality soil. Thus, plants grow roots into patches of soil according to their wealth of resources in a manner consistent with the MVT.[6] Additionally, plant roots grow more quickly through low-quality patches of soil than through high-quality patches of soil, just as foraging animals are predicted to spend less time in low-quality areas than high-quality areas.

Copulation time in dung flies