Locally adaptive Bayesian birth-death model successfully detects slow and rapid rate shifts.

Sebastian Höhna,Vladimir N Minin,Adam D Leaché,Tetyana I Vasylyeva,Andrew F Magee,David A Rasmussen

doi:10.1371/journal.pcbi.1007999

Abstract

Birth-death processes have given biologists a model-based framework to answer questions about changes in the birth and death rates of lineages in a phylogenetic tree. Therefore birth-death models are central to macroevolutionary as well as phylodynamic analyses. Early approaches to studying temporal variation in birth and death rates using birth-death models faced difficulties due to the restrictive choices of birth and death rate curves through time. Sufficiently flexible time-varying birth-death models are still lacking. We use a piecewise-constant birth-death model, combined with both Gaussian Markov random field (GMRF) and horseshoe Markov random field (HSMRF) prior distributions, to approximate arbitrary changes in birth rate through time. We implement these models in the widely used statistical phylogenetic software platform RevBayes, allowing us to jointly estimate birth-death process parameters, phylogeny, and nuisance parameters in a Bayesian framework. We test both GMRF-based and HSMRF-based models on a variety of simulated diversification scenarios, and then apply them to both a macroevolutionary and an epidemiological dataset. We find that both models are capable of inferring variable birth rates and correctly rejecting variable models in favor of effectively constant models. In general the HSMRF-based model has higher precision than its GMRF counterpart, with little to no loss of accuracy. Applied to a macroevolutionary dataset of the Australian gecko family Pygopodidae (where birth rates are interpretable as speciation rates), the GMRF-based model detects a slow decrease whereas the HSMRF-based model detects a rapid speciation-rate decrease in the last 12 million years. Applied to an infectious disease phylodynamic dataset of sequences from HIV subtype A in Russia and Ukraine (where birth rates are interpretable as the rate of accumulation of new infections), our models detect a strongly elevated rate of infection in the 1990s.

Highlights

Studying variation in the rates of speciation and extinction enables researchers to examine the patterns and processes that shape the diversity of life on earth
We develop an efficient, tuning-parameterfree Markov chain Monte Carlo (MCMC) algorithm for sampling high dimensional parameter vectors associated with Gaussian Markov random field (GMRF)- and horseshoe Markov random field (HSMRF)-based models
The remaining piece of the puzzle, and our contribution in this paper, is in the specification of Pr(λ(t)), for which we use Markov random field models. (Note that our implementation and theory of the GMRF and HSMRF can be applied to all time-varying rates; we focused on the birth rate only for simplicity.) Our simplified posterior distribution takes the following form: Prðθ; T; to; lðtÞ; m; ; r; j yÞ /

Summary

Introduction

Studying variation in the rates of speciation and extinction enables researchers to examine the patterns and processes that shape the diversity of life on earth. The first class of questions, including the question about nectar spurs, concerns variation in diversification rates across lineages In these scenarios, models are built that allow the birth and death rates to vary across the branches of the phylogenetic tree [2, 3]. The second class of questions, including the question about intervention efficacy, concerns temporal variation in diversification rates shared by all lineages [4, 5, 6] In these scenarios, the birth and death rates are modeled as functions of time, but at any instant in time all branches of the tree share a common birth rate and a death rate. Our aim is to develop flexible Bayesian nonparametric methods for accurately estimating changes of birth and death rates over time without sacrificing precision

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