The Marginal Value Theorem
Charnov (1976) is the first serious treatment that I know of using optimality modelling in the issue of foraging. Postulates that animals should use the information at hand to predict the future value of a resource patch and make decisions about patch departure based on their assessment of that value.
Much theory has been developed around the assumption that, to the foragers
perception, food items occur in patches. Thus having discovered a patch, the
forager balances the future yield of that patch versus the future yield that
would be obtained by moving on to another patch. Cost of search and handling
time should remain constant, but rate of encounter and energy gained per encounter
will vary between patches and in most systems will decline as the patch is exploited
(ie, the resource is depleted). This is the MARGINAL VALUE THEOREM (MVT) of
Charnov. Absent complicting factors, an animal should leave a resource patch
when the rate of payoff falls below the average rate of payoff for the entire
This works if the forager can instaneously assess the value of the patch (for example, different size prey animals in a situation in which each prey item is a ³patch²). Think about a sit and wait predator, such as a snake, which rejects patches that are too large or too small as they walk by, waiting for one that is large enough to be worth the effort, but not so large that it canıt be handled. A kind of reverse logic can be applied here to assess foraging yields for animals. Under the MVT, food should be left in a patch after an animal quits the patch, as departure is determined by the relationship between the yield rate for that patch and the yield rate of the larger environment, rather than simple complete depletion of the food resource.
The GIVING UP DENSITY (GUD) is the density of food remaining in the patch, which, in fact, is often measurable. If you know the GUD then you can extrapolate the yield rate of the area. Brown, J. S., B P. Kotler and W A. Mitchell. 1997. Competition between birds and mammals: a comparison of giving-up densities between crested larks and gerbils. Evol. Ecol. 11:757-771. This study shows that while gerbils and larks appear to coexist on the same seed resources in the Negev desert, gerbils have lower giving-up densities (less food left behind) under virtually all conditions (bush vs. open habitat, stabilized vs. semi-stabilized sand habitats), indicating that gerbils are able to more efficiently exploit the food resource. The authors postulate that larks can co-exist by being ³cream skimmers on the high spatial and temporal variability in seed abundances. Larks may rely on insects, fruit or smaller seeds. Or, larks may rely on adjacent rocky habitats.² In contrast to the cream skimming larks, gerbils are ³crumb-pickers². Larks do not deplete the food patches, from the gerbilsı perspective, but gerbils make them unacceptable to larks. Larks must, therefore, have ways of finding patches more quickly than gerbils or exploit other food resources.
If patch assessment is a continuous process while an animal is in a patch, the GIVING UP TIME (GUT) models are more appropriate. In GUT models, residency in the patch increases with the quality of patch. These models fit well for nectivores and can be used to analyze the rewards that plant present in order to secure pollinator visits. Iıve done some work on giving up times in a tropical ant. Breed, M. D. R. M. Bowden, M. F. Garry, and A. L. Weicker. 1996. Giving-up time variation in response to differences in nectar volume and concentration in the giant tropical ant, Paraponera clavata. J. Ins. behav. 9:659-672
Charnov, E. L. 1976. Optimal foraging, the marginal value theorem. Theor. Pop. Biol. 9:129-136.