Variation in pollination: causes and consequences for plant reproduction.

Pollen dispersal by animals varies extensively because of differences in pollinator visitation rates among plants, dissimilar pollination by the various pollinators that visit individual plants, and stochastic variation in deposition as an individual pollinator disperses a plant's pollen to subsequently visited recipient flowers. Such variation reduces expected female and male success if seed production decelerates with increasing pollen receipt, because less than average receipt diminishes mean seed production more than copious pollination increases it (Jensen's inequality). We report empirical studies of the nature and magnitude of pollen dispersal variance, which provide the basis for a numerical model of the consequences of dispersal for expected seed production. Model fitting revealed that dispersal of Brassica napus pollen by bumblebees and especially butterflies exhibited much more variation than is expected of a binomial process and was best modeled as a beta-binomial process with a constant mean. Overdispersion arose primarily during pollen dispersal by individual insects, since differences between individuals of the same pollinator type were limited. Our model revealed variance limitation as a previously unrecognized, substantial, and ubiquitous component of pollen limitation of seed production. Variance limitation should select for floral traits that increase pollinator visitation, reduce dispersal variance, or reduce the postpollination nonlinearities that cause Jensen's inequality.