DOI: 10.5061/dryad.qrfj6q5nq
title: Data and supplementary information from: Sequential bayesian phylogenetic inference

description: The ideal approach to Bayesian phylogenetic inference is to estimate all
 parameters of interest jointly in a single hierarchical model. However,
 this is often not feasible in practice due to the high computational cost.
 Instead, phylogenetic pipelines generally consist of sequential analyses,
 whereby a single point estimate from a given analysis is used as input for
 the next analysis (e.g., a single multiple sequence alignment is used to
 estimate a gene tree). In this framework, uncertainty is not propagated
 from step to step, which can lead to inaccurate or spuriously certain
 results. Here, we formally develop and test the sequential approach for
 Bayesian phylogenetic inference, which uses importance sampling to
 generate observations for the next step of an analysis pipeline from the
 posterior produced in the previous step. The sequential approach presented
 here not only accounts for uncertainty between analysis steps, but also
 allows for greater flexibility in software choice (and hence model
 availability) and can be more efficient computationally than the
 traditional joint approach when multiple models are being tested. We show
 that the sequential approach is identical in practice to the joint
 approach only if sufficient information in the data is present (a narrow
 posterior distribution) and/or sufficiently many importance samples are
 used. Conversely, we show that the common practice of using a single point
 estimate can be biased, e.g., a single phylogeny estimate to transform an
 unrooted phylogeny into time-calibrate phylogeny. We demonstrate the
 theory of sequential Bayesian inference using both a toy example and an
 empirical case study of insect divergence times estimation using a relaxed
 clock model from transcriptome data. In the empirical example, we estimate
 three posterior distributions of branch lengths from the same data (DNA
 character matrix with a GTR+Gamma+I substitution model, an amino acid data
 matrix with empirical substitution models, and an amino acid data matrix
 with the PhyloBayes CAT-GTR model). Finally, we apply three different-node
 calibration strategies and show that both, the data source and underlying
 substitution process to estimate branch lengths as well as the
 node-calibration strategies, impact divergence time estimates. Thus, our
 new sequential Bayesian phylogenetic inference provides the opportunity to
 efficiently test different approach for divergence time estimation,
 including branch lengths estimation from other software.
description: # Sequential Bayesian Phylogenetic Inference ## Empirical Data Analysis
 (Divergence Times of Insects) The data are retrieved from Misof, Bernhard
 et al. (2015). Data from: Phylogenomics resolves the timing and pattern of
 insect evolution [Dataset]. Dryad.
 [https://doi.org/10.5061/dryad.3c0f1](https://doi.org/10.5061/dryad.3c0f1)
 This repository contains five files from that study, where we simply
 transformed the data into a different file format. The files are: 1.
 BLOSUM62.nex, JTT.nex and LG.nex which contain the amino acid dataset for
 the empirical amino acid substitution model analysis. 2.
 supermatrix_C.nuc.all.fas which contains the DNA supermatrix 3.
 supermatrix_D.phy which contains the amino acid supermatrix in Phylip
 format for PhyloBayes.