The Effect of Self-Fertilization, Inbreeding Depression, and Population Size on Autopolyploid Establishment

Abstract

The minority cytotype exclusion principle describes how random mating between diploid and autotetraploid cytotypes hinders establishment of the rare cytotype. We present deterministic and stochastic models to ascertain how selfing, inbreeding depression, unreduced gamete production, and finite population size affect minority cytotype exclusion and the establishment of autotetraploids. Results demonstrate that higher selfing rates and lower inbreeding depression in autotetraploids facilitate establishment of autotetraploid populations. Stochastic effects due to finite population size increase the probability of polyploid establishment and decrease the mean time to tetraploid fixation. Our results extend the minority cytotype exclusion principle to include important features of plant reproduction and demonstrate that variation in mating system parameters significantly influences the conditions necessary for polyploid establishment.

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

“…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.…”

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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.

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“…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.…”

“…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.…”

“…Many other formulations are possible. For instance, using the symbols defined by Rausch and Morgan (2005) and used by Yamauchi, the equations…”