Formulation of Competition Between Sexual and Selfing Forms: A Response to Yamauchi

Abstract

The model of autotetraploid establishment presented in Rausch and Morgan (2005) extends the minority cytotype exclusion of Levin (1975) and Felber (1991) to include variable rates of selfing and inbreeding depression among cytotypes. We agree with Yamauchi (2006) that Rausch and Morgan (2005) implicitly assume pollen limitation. We offer here additional commentary on our original formulation, the extension offered by Yamauchi (2006), and the biological context of self-pollination.In our model, a fraction of the ovules available for outcrossing remains unfertilized, and this fraction increases with the selfing rate. Yamauchi (2006) proposes that this occurs when there is both pollen discounting (Harder and Wilson 1998) and outcross pollen limitation (Knight et al. 2005). Our interpretation, however, is that a fraction of the outcross pollen pool is available for within-cytotype outcrossing (e.g., d t /(d t ϩ t t ) ϭ d t for the diploid cytotype; no pollen discounting) but only some of this results in successful outcross ovule fertilization (e.g., 1 Ϫ s d for the diploid cytotype; pollen limitation in proportion to the selfing rate). Yamauchi's extension assumes complete pollen discounting (cytotype representation in the outcross pollen pool inversely proportional to cytotype selfing rate), and no pollen limitation. Many other formulations are possible. For instance, using the symbols defined by Rausch and Morgan (2005) and used by Yamauchi, the equationsdescribe a model with neither pollen limitation nor pollen discounting. More generally, the full diversity of approaches used to investigate diploid self-fertilization can be employed to model autotetraploid establishment. The model present in Rausch and Morgan (2005) implicitly assumes that pollen limitation of outcrossed ovules increases with cytotype selfing rate. The magnitude of pollen limitation across species can be high (Burd 1994), although the relationship between selfing rate and pollen limitation of outcross ovules is not known. Nonetheless, floral morphologies resulting in high self-fertilization (e.g., reduced flower size and pollinator reward, increased proximity and hence interference between anthers and stigmas) may often contribute to changes in reproductive biology (Schoen et al. 1996) (Rausher et al. 1993; Holsinger and Thomson 1994;Kohn and Barrett 1994) or high levels of pollen discounting in highly selfing species (Ritland 1991; Holsinger 1992).Model outcomes reflect different model assumptions. To illustrate, higher selfing provides an ''automatic'' advantage (analogous to Fisher 1941) by reducing ineffective matings among cytotypes (assuming triploid lethality, Levin 1975): with no pollen limitation or discounting, more highly selfing cytotypes contribute more viable offspring to the next generation than less selfing cytotypes. Outcross pollen limitation provides additional benefit to selfing, because selfing increases fertilized ovule production. This consequence of pollen limitation is easily illustrated when there is no unreduced gam...