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 novel numerical algorithms. 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 conducted simulation experiments to assess numerical error, computational requirements and accuracy recovering known model parameters. A re-analysis of soybean SNP data demonstrates that the models implemented in \snapp and \snapper can be difficult to distinguish in practice, a characteristic which we tested with further simulations. We demonstrate the scale of analysis possible using a SNP dataset sampled from 399 fresh water turtles in 41 populations.

This data file contains posterior statistics for (1) an analysis of soybean SNP data and (2) an analysis of SNP data from 399 fresh water turtles in 41 populations.