Marginal value theorem

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."

All animals must forage for food in order to meet their energetic needs, but doing so is energetically costly. It is assumed that evolution by natural selection results in animals utilizing the most economic and efficient strategy to balance energy gain and consumption. The Marginal Value Theorem is an optimality model that describes the strategy that maximizes gain per unit time in systems where resources, and thus rate of returns, decrease with time. The model weighs benefits and costs and is used to predict giving up time and giving up density. Giving up time (GUT) is the interval of time between when the animal last feeds and when it leaves the patch. Giving up density (GUD) is the food density within a patch when the animal will choose to move on to other food patches.

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 and thus there is a higher cost of travel or (2) current patches are rich in resources.

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.

A common illustration of the MVT is apple picking in humans. When one first arrives at a new apple tree, the number of apples picked per minute is high, but it rapidly decreases as the lowest-hanging fruits are depleted. Strategies in which too few apples are picked from each tree or where each tree is exhausted are suboptimal because they result, respectively, in time lost travelling among trees or picking the hard to find last few apples from a tree. The optimal time spent picking apples in each tree is thus a compromise between these two strategies, which can be quantitatively found using the MVT.

...
Wikipedia