  We present a Bayesian method for characterizing the mating system of
populations reproducing through a mixture of self-fertilization and random
outcrossing. Our method uses patterns of genetic variation across the genome as
a basis for inference about pure hermaphroditism, androdioecy, and gynodioecy.
We extend the standard coalescence model to accommodate these mating systems,
accounting explicitly for multilocus identity disequilibrium, inbreeding
depression, and variation in fertility among mating types. We incorporate the
Ewens Sampling Formula (ESF) under the infinite-alleles model of mutation to
obtain a novel expression for the likelihood of mating system parameters. Our
Markov chain Monte Carlo (MCMC) algorithm assigns locus-specific mutation
rates, drawn from a common mutation rate distribution that is itself estimated
from the data using a Dirichlet Process Prior (DPP) model. Among the parameters
jointly inferred are the population-wide rate of self-fertilization,
locus-specific mutation rates, and the number of generations since the most
recent outcrossing event for each sampled individual.
