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In plant species with mixed mating systems, differences in diverse factors-including their pollination system, flowering phenology, life form and susceptibility to inbreeding depression-cause variation in outcrossing rates among fruits within individuals, among individuals within populations and among populations within species. To quantify this hierarchical variation, we examined outcrossing rates at the seed stage in five populations of Magnolia stellata, a self-compatible, insect-pollinated and protogynous tree species. For this purpose, we sampled 1498 seeds within 204 fruits obtained from 56 individuals of the five populations, determined genotypes of the sampled seeds and maternal individuals at six polymorphic microsatellite loci, then estimated outcrossing rates and their variance components at four hierarchical levels (fruits, individuals, populations and species) using a nested analysis of variance-type linear model with a Bayesian approach. The species-level outcrossing rate was 0.730 (95% credible interval, 0.595-0.842), indicating that this species has a mixed mating system. Outcrossing rates were not significantly different among populations, but were significantly different among individuals within populations. Variance components at the levels of individual and fruit were statistically supported and were highest for the former. Thus, factors influencing outcrossing rates at the individual level, such as differences in flowering phenology and early-stage inbreeding depression, appear to have important effects within these M. stellata populations, but not among them. The method of hierarchically estimating outcrossing rates using a Bayesian approach, as applied in this study, is compared with conventional methods for estimating outcrossing rates, and the statistical properties of the Bayesian approach are discussed.

Estimation of outcrossing rates at hierarchical levels of fruits, individuals, populations and species in Magnolia stellata