Bayesian inference of tree species using diffusion models: tabulated posterior statistics for SNAPP and SNAPPER analyses

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.