Resolution of the branching order of taxa that have undergone rapid cladogenesis is an extraordinarily difficult task for systematists. Unless the pace of molecular or morphological evolution is accelerated during bursts of speciation, few evolutionary changes will mark the existence of short branches between speciation events. It is possible that simultaneous (with respect to the absence of demonstrable evolutionary transformations) cladogenetic events will produce multiple daughter lineages in a hard polytomy. The task of correctly inferring the phylogeny of a rapid radiation, then, includes discriminating multifurcating evolution from lack of power in phylogenetic analyses (soft polytomies). Recently, several procedures have been proposed to test for hard polytomies, typically under a maximum likelihood (ML) framework. However, such approaches are computationally intensive and not feasible for clades with a large number of taxa. Markov chain Monte Carlo methods in a Bayesian framework offer a method to efficiently evaluate the probabilities of branches of a phylogenetic tree using the same models of evolution employed in ML analyses. I conducted Bayesian analyses of two poorly resolved, and presumably rapid, radiations: the relatively old (c. 100 mya) radiation of Saxifragales and the relatively recent (c. 5 mya) radiation of Asclepias (Asclepiadaceae). These analyses found slightly greater resolution for the phylogeny of Saxifragales, but most of the basal nodes still received very low probabilities. This result is consistent with a near simultaneous origin of the major lineages of this clade. Analyses of Asclepias resulted in no increase in resolution; in fact some crucial nodes (e.g., the monophyly of American Asclepias) received no support. This result is consistent with simultaneous cladogenesis, but in this case is more likely due to insufficient character sampling.

Key words: Asclepias, Bayesian analysis, hard polytomy, maximum likelihood, rapid radiation, Saxifragales