The model for optimal foraging time in a patch from Example 4.4.2 of the textbook has been used extensively in the study of animal behavior. It has been tested experimentally in a variety of species, including bumblebees.
One test of the model looks at a more general formulation of Example 4.4.2 as follows. Instead of assuming that the travel time between flowers is 4 seconds, let’s instead let it be some arbitrary constant ‘a’. In this case the function f(t) in Example 4.4.2 becomes
As practice, you should verify that the optimal forging time is then given by
Notice that this reduces to the answer in Example 4.4.2 when a = 4. It also reveals the prediction that, as the travel time a between flowers increases, the optimal amount of time to forage on each flower increases.
The above prediction was tested with bumblebees of the species Bombus flavifrons foraging on the flower Delphinium nelsonii (Cibula and Zimmerman 1984). The researchers manipulated the distance between flowers in natural populations and found that the bumblebees did in fact increase their forage time on each flower when the distance was increased.
References
Cibula, D.A. and M. Zimmerman. 1984. The effect of plant density on departure decisions: testing the marginal value theorem using bumblebees and Delphinium nelsonii. Oikos 43:154-158