  We describe a new and computationally efficient Bayesian methodology for inferring species trees and demographics from unlinked binary markers. Likelihood calculations are carried out using diffusion models of allele frequency dynamics combined with a new algorithm for numerically computing likelihoods of quantitative traits. The diffusion approach allows for analysis of datasets containing hundreds or thousands of individuals. The method, which we call \snapper, has been implemented as part of the Beast2 package. We introduce the models, the efficient algorithms, and report performance of \snapper on simulated data sets and on SNP data from rattlesnakes and freshwater turtles. 
Bayesian inference of species trees using diffusion models