Bayesian procedures for discriminating among hypotheses with discrete distributions: inheritance in the tetraploid Astilbe biternata.

Discrimination between disomic and tetrasomic inheritance aids in determining whether tetraploids originated by allotetraploidy or autotetraploidy, respectively. Past assessments of inheritance in tetraploids have used analyses whereby each inheritance hypothesis is tested independently. I present a Bayesian analysis that is appropriate for discriminating among several inheritance hypotheses and can be used in any case where hypotheses are defined by discrete distributions. The Bayesian approach incorporates prior knowledge of the probability of occurrence of disomic and tetrasomic hypotheses so that the results of the analysis are not biased by the fact that there is a single tetrasomic hypothesis and multiple disomic hypotheses. This analysis is used to interpret data from crosses in the tetraploid Astilbe biternata, a herbaceous plant native to the southern Appalachians. The progeny ratios from all crosses favored the hypothesis of disomic inheritance at both the PGM and slow-PGI loci. These results support earlier cytogenetic evidence for the allotetraploid origin of Astilbe biternata.