The multispecies coalescent provides a natural framework for accommodating ancestral genetic polymorphism and coalescent processes that can cause different genomic regions to have different genealogical histories. The Bayesian program BPP includes a full-likelihood implementation of the multispecies coalescent, using transmodel Markov chain Monte Carlo to calculate the posterior probabilities of different species trees. BPP is suitable for analyzing multilocus sequence data sets and it accommodates the heterogeneity of gene trees (both the topology and branch lengths) among loci and gene tree uncertainties due to limited phylogenetic information at each locus. Here, we provide a practical guide to the use of BPP in species tree estimation. BPP is a command-line program that runs on linux, macosx, and windows. This protocol shows how to use both BPP 3.4 (http://abacus.gene.ucl.ac.uk/software/) and BPP 4.0 (https://github.com/bpp/).

Recent analyses suggest that cross-species gene flow or introgression is common in nature, especially during species divergences. Genomic sequence data can be used to infer introgression events and to estimate the timing and intensity of introgression, providing an important means to advance our understanding of the role of gene flow in speciation. Here, we implement the multispecies-coalescent-with-introgression model, an extension of the multispecies-coalescent model to incorporate introgression, in our Bayesian Markov chain Monte Carlo program Bpp. The multispecies-coalescent-with-introgression model accommodates deep coalescence (or incomplete lineage sorting) and introgression and provides a natural framework for inference using genomic sequence data. Computer simulation confirms the good statistical properties of the method, although hundreds or thousands of loci are typically needed to estimate introgression probabilities reliably. Reanalysis of data sets from the purple cone spruce confirms the hypothesis of homoploid hybrid speciation. We estimated the introgression probability using the genomic sequence data from six mosquito species in the Anopheles gambiae species complex, which varies considerably across the genome, likely driven by differential selection against introgressed alleles.

We present results obtained by applying our BAyesian HierArchical Modeling for the Analysis of Supernova cosmology (BAHAMAS) software package to the 740 spectroscopically confirmed supernovae of type Ia (SNe Ia) from the "Joint Light-curve Analysis" (JLA) data set. We simultaneously determine cosmological parameters and standardization parameters, including corrections for host galaxy mass, residual scatter, and object-by-object intrinsic magnitudes. Combining JLA and Planck data on the cosmic microwave background, we find significant discrepancies in cosmological parameter constraints with respect to the standard analysis: we find W =  0.399 0.027 m , s 2.8 higher than previously reported, and = - w 0.910 0.045, s 1.6 higher than the standard analysis. We determine the residual scatter to be s =  0.104 0.005 res . We confirm (at the 95% probability level) the existence of two subpopulations segregated by host galaxy mass, separated at, differing in mean intrinsic magnitude by 0.055 ± 0.022 mag, lower than previously reported. Cosmological parameter constraints, however, are unaffected by the inclusion of corrections for host galaxy mass. We find s4 evidence for a sharp drop in the value of the color correction parameter, ( ) b z , at a redshift =  z 0.662 0.055 t . We rule out some possible explanations for this behavior, which remains unexplained.

Multispecies coalescent (MSC) is the extension of the single-population coalescent model to multiple species. It integrates the phylogenetic process of species divergences and the population genetic process of coalescent, and provides a powerful framework for a number of inference problems using genomic sequence data from multiple species, including estimation of species divergence times and population sizes, estimation of species trees accommodating discordant gene trees, inference of cross-species gene flow, and species delimitation. In this review, we introduce the major features of the MSC model, discuss full-likelihood and heuristic methods of species tree estimation, and summarize recent methodological advances in inference of cross-species gene flow. We discuss the statistical and computational challenges in the field and research directions where breakthroughs may be likely in the next few years.