Animals often live in habitats that are patchy in that the places they look for food are scattered around, such as bees collecting nectar from flower patches. Animals gather food from patches and so reduce the chances of finding more food as they go. They must decide when to give up on the current patch, and travel to a new one which they have not yet depleted. Whilst they are travelling they are not losing energy, so they shouldn’t leave too soon. Ecologists often predict animal behaviour by assuming they are optimising some measure, such as the rate of energy gain (e.g. calories per minute). This approach can be used to predict when a forager should leave a patch that it is depleting.
The main result is that the animal should leave any patch when the rate of collecting energy has dropped to the average rate for the whole habitat, including the cost of travelling between patches. This means that they will leave before they’ve found all the food in a patch. The travel time depends on whether the forager rejects patches, and will increase if some kinds of patch are ignored altogether. As the travel time increase, the rate drops and so animals should spend longer in patches
The model predicts that animals should leave any patch at a ‘giving up time’ that is constant for all patches. This means that we expect animals to leave a patch when it takes them a certain time to find another item of food, and this should be the same all the time. This prediction, termed the marginal value theorem, is the basis of how researchers study animal movements across habitats. The result is very broad, because it applies to any situation of searching for something that is not evenly distributed in space, but is used up over time by the searcher.