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We recently introduced a model that predicts the degree to which a plant's lifetime seed production may be constrained by unpredictable shortfalls of pollen receipt ("pollen limitation"). Burd's comment in this issue criticized our analysis, first by arguing that the empiricalliteraturedocumentsmuchhigherlevelsofpollenlimitation than our model predicts and then suggesting that the apparent dis- crepancy stemmed from our (1) underestimating the costs of securing a fertilized ovule and (2) assuming too little unpredictability in whole- plant pollen receipt. We reply as follows. First, the empirical literature must be consulted carefully. Burd relies on pollen supplementation experiments performed on parts of plants or on whole plants but dur- ing only one reproductive season for polycarpic perennials; in both cases, resource reallocation often leads to gross overestimates of pol- lenlimitation.Wecomprehensivelyreviewpollenlimitationestimates that are free of these estimation problems and find strong agreement with our model predictions. Second, although cost estimates for dif- ferent components of seed production are imprecise, errors are likely to be small relative to the 11,000-fold differences observed across plant species, the primary focus of our article. Finally, contrary to Burd's argument, pollen receipt by entire plants is much more pre- dictable than that by individual flowers because the flower-to-flower variation "averages out" when summed across many flowers. Our model usesparametervalues that arein broad agreement with theem- pirical record of modest plant-to-plant variation in pollen receipt and thuspredictsthegenerallymodestpollen limitationthatisobservedin nature.

Many organisms exhibit parental optimism, producing more of the initial stages of offspring (e.g., eggs, embryos) than they can usually mature. For plants, parental optimism may be linked to the risk of seed production being limited by pollen receipt (pollen limitation). Here we elaborate a stochastic model of pollen limitation developed by Haig and Westoby (1988) and Burd (2008) and link it with published data on the magnitudes of prepollination costs versus postpollination costs of seed production in 80 plant species. We demonstrate that parental optimism should be expected when prepollination costs of seed production are small relative to postpollination costs. This was observed for most (62 of 80) of the plant taxa surveyed. Under parental optimism, plants overinvest in securing fertilized ovules, and consequently pollen limitation is predicted to be uncommon. However, for a sizable minority of plant species (18 of 80), prepollination costs approach or exceed postpollination costs. For these s...

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.