The computer program BPP (Yang 2015, Flouri et al 2018) implements the multi-species coalescent model for Bayesian inference of species trees, species delimitation and demographic parameters using molecular data.

For species delimitation, a reversible-jump MCMC algorithm is used to calculate the posterior probabilities of the different delimitation models for a given molecular dataset. However, when the amount of molecular data is very large, the rjMCMC algorithm is inefficient, so that it would take too long a time to complete the analysis. Rannala and Yang (2017) have implemented sampling from power posteriors in BPP, allowing calculation of marginal likelihoods (Bayes factors) for model selection. Rannala and Yang use thermodynamic integration (Gaussian quadrature) to integrate over the power posteriors and obtain the marginal likelihood. However, thermodynamic integration suffers from discretisation bias and a large number of points (read: a large number of MCMC runs) is necessary to calculate the marginal likelihoods accurately. The alternative stepping-stones method (Xie et al. 2011) appears more efficient as it requires less computation.

I have written a small R package, bppr, that can be used to:

  • Prepare the appropriate control files to obtain samples from the power posterior with BPP, and then calculate Bayes factors by the stepping-stones or thermodynamic integration (with Gaussian quadrature) methods. See the bppr: stepping stones tutorial.

  • Calibrate BPP phylogenies to geological time using a fossil calibration on a node age, or a prior on the molecular evolutionary rate, using the method of Angelis and dos Reis (2015, see also Yoder et al. 2016). See the bppr: time estimation tutorial.

The bbpr package is available from


  • Angelis, K. and dos Reis, M. 2015. The impact of ancestral population size and incomplete lineage sorting on Bayesian estimation of species divergence times. Current Zoology, 61: 874–885.

  • Flouri T, Xiyun J, Rannala B, Yang Z. 2018. Species tree inference with BPP using genomic sequences and the multispecies coalescent. Mol Biol Evol.

  • Rannala, B., and Z. Yang. 2017. Efficient Bayesian species tree inference under the multispecies coalescent. Systematic Biology, 66: 823-842.

  • Xie et al. (2011) Improving marginal likelihood estimation for Bayesian phylogenetic model selection. Systematic Biology, 60: 150–160.

  • Yang, Z. 2015. The BPP program for species tree estimation and species delimitation. Current Zoology, 61: 854-865.

  • Yoder, A. et al. 2016. Geogenetic patterns in mouse lemurs (genus Microcebus) reveal the ghosts of Madagascar’s forests past. Proceedings of the National Academy of Sciences, 113: 8049–8056.