The problem of temporal scale in optimization: three contrasting views of hummingbird visits to flowers.

We modeled hummingbird visits to flowers on three temporal scales: tongue loading, the licking cycle, and entire visits to flowers. The nectar concentration that maximizes energy intake rate increases with the temporal scale of integration; therefore, optimal nectar concentration for nectar volumes that require many licks is higher than predicted by models that assume single licks. Since birds must position, insert, and withdraw their bills in addition to licking nectar, the optimum at the scale of flower visits is even higher. This "overhead time cost" of handling flower morphology, for most nontraplining hummingbirds under most natural conditions, is as great as or greater than the cost of handling nectar. For these birds, the potential variation in the fine-scale factors that determine nectar intake rate during licking has little effect on flower-handling time and therefore is unlikely to determine optimal nectar concentration or the profitability of visiting flowers. The conclusion that energy intake rate and optimal nectar concentration are sensitive to temporal scale of integration applies at all scales in hummingbird foraging systems, and we suggest that it also generalizes across systems.