Optimal Foraging by Nectarivores: A Test of the Marginal-Value Theorem

Abstract

After visiting a flower, a nectarivore must decide whether to visit another flower on the inflorescence or move to a new inflorescence. I consider a rule for making this decision based on the marginal-value theorem (MVT). The MVT departure rule I propose states that an optimal forager should leave an inflorescence if the nectar amount it has just received indicates that its expected reward-intake rate for staying (S) will be less than its expected reward-intake rate for leaving (L). The nectar amount for which S = L is defined as a departure threshold. Predictions of the MVT departure rule were tested using published data from studies of bumblebees foraging on the larkspur Delphinium nelsonii. Computer simulations were made of bees foraging in the same nectar standing-crop environment as actual bees. Various departure thresholds were examined, and the behavior of simulated bees was compared with the observed behavior of bees. Four questions were addressed. (1) What is the optimal departure threshold, that is, the one that maximizes the reward-intake rate? (2) Does the MVT departure rule identify the optimal threshold? (3) Do bees appear to forage according to the MVT departure rule? (4) How might the cognitive abilities of bees influence the operation of this rule? The threshold predicted by the MVT was found to be an optimal threshold. Two previous versions of the MVT departure rule did not identify the optimal threshold. The MVT departure rule predicted that there should be two departure thresholds, one for the first flower visited and another for the second. The behavior of simulated bees using the predicted multiple thresholds was indistinguishable from actual behavior. Several stochastic-threshold rules were also examined. For these the threshold varied as a function of a bee's recent reward experience and memory of it. Again, a multiple-threshold rule accurately described bee behavior. Several rules of thumb incorporating shortcuts that bees might use to estimate expected reward-intake rates for the next flower were also explored, but none adequately described bee behavior. The MVT approach to examining optimal foraging was found to provide more insights into foraging strategy than previous approaches.