Algorithmic improvements to species delimitation and phylogeny estimation under the multispecies coalescent

The focus of this article is a Bayesian method for inferring both species delimitations and species trees under the multispecies coalescent model using molecular sequences from multiple loci. The species delimitation requires no a priori assignment of individuals to species, and no guide tree. The method is implemented in a package called STACEY for BEAST2, and is a extension of the author’s DISSECT package. Here we demonstrate considerable efficiency improvements by using three new operators for sampling from the posterior using the Markov chain Monte Carlo algorithm, and by using a model for the population size parameters along the branches of the species tree which allows these parameters to be integrated out. The correctness of the moves is demonstrated by tests of the implementation. The practice of using a pipeline approach to species delimitation under the multispecies coalescent, has been shown to have major problems on simulated data (Olave et al. in Syst Biol 63:263–271. doi:10.1093/sysbio/syt106, 2014). The same simulated data set is used to demonstrate the accuracy and improved convergence of the present method. We also compare performance with *BEAST for a fixed delimitation analysis on a large data set, and again show improved convergence.