Résumé
Variation in the number of pollen apertures has been widely described among and within angiosperm species. Apertures are weak points of the pollen wall where the pollen tube germinates. Pollen aperture heteromorphism (pollen grains with different numbers of apertures in a single individual) is common in flowering plants, whereas polymorphism (among-individual variation) is rare. Previous work on Viola has shown that pollen with few apertures has a better survival rate, whereas pollen with more apertures germinates faster. Here we develop game-theoretic models of competition between several pollen donors. These show that heteromorphism can be a stable strategy for all finite numbers of competitors per stigma for some parameter values where one pollen type germinates faster but has lower longevity. In contrast, polymorphism is not stable in pairwise contests (two pollen donors). When more than two pollen donors interact on stigmas, polymorphism can be stable for certain parameter values. In both heteromorphism and polymorphism, selection operating on the number of pollen apertures is an example of soft selection if each flower in a population produces a fixed number of seeds, regardless of the average fitness of the particular pollen composition present on its stigma. This results in stigma-level and population-level frequency dependence, which makes stable heteromorphism and polymorphism possible. Selective scenarios vary among stigmas due to variation in the pollen present. Thus, a particular pollen type may be more fit than average on some stigmas but less fit on others. As a pollen strategy increases in frequency in a population, the frequency of different kinds of pollen contests shift. This may result in the pollen strategy's fitness advantage being lost at an intermediate frequency, resulting in heteromorphism or polymorphism. Low numbers of pollen donors per stigma result in greater variance in pollen composition among stigmas, resulting in a broader parameter range for stable heteromorphism or polymorphism. For any number of pollen donors per stigma, the conditions for polymorphism are a more restrictive subset of those for heteromorphism. We show that heteromorphism can invade a polymorphic population, whereas heteromorphism is stable against polymorphism, thus explaining why polymorphic species are rare.