Evolutionary change in response to natural selection will occur only if a trait confers a selective advantage and there is heritable variation. Positive connections between pollen traits and fitness have been found, but few studies of heritability have been conducted, and they have yielded conflicting results. To understand better the evolutionary significance of pollen competition and its potential role in sexual selection, the heritability of pollen tube-growth rate and the relationship between this trait and sporophytic offspring fitness were investigated in Collinsia heterophylla. Because the question being asked was if female function benefited from obtaining genetically superior fathers by enhancing pollen competition, one-donor (per flower) crosses were used in order to exclude confounding effects of post-fertilization competition/allocation caused by multiple paternity. Each recipient plant was crossed with an average of five pollen donors. Pollen-tube growth rate and sporophytic traits were measured in both generations. Pollen-tube growth rate in vitro differed among donors, and the differences were correlated with in vivo growth rate averaged over two to four maternal plants. Pollen-tube growth rate showed significant narrow-sense heritability and evolvability in a father-offspring regression. However, this pollen trait did not correlate significantly with sporophytic-offspring fitness. These results suggest that pollen-tube growth rate can respond to selection via male function. The data presented here do not provide any support for the hypothesis that intense pollen competition enhances maternal plant fitness through increased paternity by higher-quality sporophytic fathers, although this advantage cannot be ruled out. These data are, however, consistent with the hypothesis that pollen competition is itself selectively advantageous, through both male and female function, by reducing the genetic load among successful gametophytic fathers (pollen), and reducing inbreeding depression associated with self-pollination in plants with mix-mating systems.