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. 2022 Oct 12;71(6):1549-1560.
doi: 10.1093/sysbio/syac015.

An Efficient Coalescent Epoch Model for Bayesian Phylogenetic Inference

Remco R Bouckaert  1
Affiliations

An Efficient Coalescent Epoch Model for Bayesian Phylogenetic Inference

Remco R Bouckaert. Syst Biol. .

Abstract

We present a two-headed approach called Bayesian Integrated Coalescent Epoch PlotS (BICEPS) for efficient inference of coalescent epoch models. Firstly, we integrate out population size parameters, and secondly, we introduce a set of more powerful Markov chain Monte Carlo (MCMC) proposals for flexing and stretching trees. Even though population sizes are integrated out and not explicitly sampled through MCMC, we are still able to generate samples from the population size posteriors. This allows demographic reconstruction through time and estimating the timing and magnitude of population bottlenecks and full population histories. Altogether, BICEPS can be considered a more muscular version of the popular Bayesian skyline model. We demonstrate its power and correctness by a well-calibrated simulation study. Furthermore, we demonstrate with an application to SARS-CoV-2 genomic data that some analyses that have trouble converging with the traditional Bayesian skyline prior and standard MCMC proposals can do well with the BICEPS approach. BICEPS is available as open-source package for BEAST 2 under GPL license and has a user-friendly graphical user interface.[Bayesian phylogenetics; BEAST 2; BICEPS; coalescent model.].

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Figures

<sc>Figure</sc> 1.
Figure 1.
The traditional scale operator that gets often rejected when there are many tip data (formula image) because of high probability of negative branch lengths when scaling down or inappropriately stretching short branches into older tips when scaling up. Tree stretch proposal moves nodes near tips (e.g., node D) less far than nodes away from tips (e.g., node E), b) for scale factor formula image where lighter trees are the original state and darker trees are proposals, and c) for scale factor larger than one.
<sc>Figure</sc> 5.
Figure 5.
BSP and BICEPS compared. a) Difference in clade support and clade heights for the Bayesian skyline analysis from Douglas et al. (2021) and the same analysis with a BICEPS prior. Red dots indicate clade support between 0 and 1 on both axis, blue dots indicate mean clade heights with cross hairs showing the 95% HPD intervals of height estimates. The axis are scaled between zero and the highest tree height found in either tree set. b) Population history for COVID-19 inferred with the BSP model and c) BICEPS model. Dark middle line indicates the median, lighter outer lines cover the 95%HPD intervals. The x-axis shows time in years going backward from left to right, the y-axis shows population size on a log scale. BSP and BICEPS analyses largely agree.
<sc>Figure</sc> 2.
Figure 2.
Epoch operator selects lower bound L, upper bound L, and scale factor s and scale all nodes between L and U. Nodes above U are moved to make space for the newly scaled epoch. a) applied to light tree giving dark tree when scale factor less than one, and b) when scale factor larger than one.
<sc>Figure</sc> 3.
Figure 3.
Performance of epoch flexer and tree stretch operators. Operator are weighted such that run times of various combinations are similar, so ESSs are comparable. ESSs improve a little, and weights favor the new operators over standard ones. a) ESSs on a scale of 500–2500 of the prior for different operator combinations—classic, with epoch operator and with epoch operator and scaler. b) ESSs for posterior, c) ESSs for tree length. d) Weights on a scale of 0–1 assigned to operators by the adaptable operator sampler for standard tree scaler, up/down operator and tree stretcher. e) Weights for standard tree scaler, tree stretcher, up/down operator, and tree stretcher with up/down combination.
<sc>Figure</sc> 4.
Figure 4.
MCMC efficiency a) Trace of tree length for BSP (green line with very low period), BSP with new operators (blue line with higher period) and BICEPS analysis (red line forming a satisfying hairy caterpillar pattern). The BSP analysis typically does not reach an ESS of 10 when the BICEPS analysis already has ESSs around 200. b) Posterior ESS for 10 runs of BSP, BSP formula image new operators, and BICEPS with variable and fixed group sizes. Both new operators and the BICEPS prior contribute to improving ESSs.
<sc>Figure</sc> 6.
Figure 6.
Primate analysis. a) ESS over 10 runs for posterior when using Yule with standard operators, Yule with BICEPS operators and Yule skyline with BICEPS operators. b) ESSs for the likelihood. Note the change in scale. c) Reconstruction of birth rates with Yule Skyline showing median and 95% HPD intervals. The dashed line shows the mean birth rate for a Yule analysis.
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