It is hypothesized that the body size of a bumblebee will be that size which maximizes its average net rate of energy intake while collecting nectar. A mathematical model is developed with the result that the net rate of energy intake of a nectar-collecting bumblebee is expressed as a function of the body size of the bumblebee. From this model the body size which maximizes the net rate of energy intake (i.e., optimal body size) is found (as the solution of an implicit equation). In this situation the advantage of large size is that larger bumblebees fly faster and hence take less flight time than smaller bumblebees. The disadvantage of larger size is greater energetic costs.
The parameters of the model are estimated using data obtained from the foraging behavior of bumblebees on monkshood (Aconitum columbianum). The optimal body size is then calculated for workers of Bombus appositus which obtained almost all their nectar from monkshood. The observed and expected (i.e., optimal) body size are found to be close and not significantly different.
The model also predicts that, from the bumblebee's point of view, there should be a positive correlation between the size of the bumblebee and the average amount of nectar obtained per flower. Evidence of this correlation is presented and the possible significance of the correlation from the plant's point of view is discussed. A possible extension of the model to general relationships between predator body size, prey size and prey density is discussed.