AbstractBirth-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.Author summaryBoth the growth of groups of species and the spread of infectious diseases through populations can be modeled as birth-death processes. Birth events correspond either to speciation or infection, and death events to extinction or becoming noninfectious. The rates of birth and death may vary over time, and by examining this variation researchers can pinpoint important events in the history of life on Earth or in the course of an outbreak. Time-calibrated phylogenies track the relationships between a set of species (or infections) and the times of all speciation (or infection) events, and can thus be used to infer birth and death rates. We develop two phylogenetic birth-death models with the goal of discerning signal of rate variation from noise due to the stochastic nature of birth-death models. Using a variety of simulated datasets, we show that one of these models can accurately infer slow and rapid rate shifts without sacrificing precision. Using real data, we demonstrate that our new methodology can be used for simultaneous inference of phylogeny and rates through time.
Representations for the Decay Parameter of a Birth-Death Process Based on the Courant-Fischer Theorem