Exact Bayesian inference for phylogenetic birth-death models

Motivation Inferring the rates of change of a population from a reconstructed phylogeny of genetic sequences is a central problem in macro-evolutionary biology, epidemiology and many other disciplines. A popular solution involves estimating the parameters of a birth-death process (BDP), which links the shape of the phylogeny to its birth and death rates. Modern BDP estimators rely on random Markov chain Monte Carlo (MCMC) sampling to infer these rates. Such methods, while powerful and scalable, cannot be guaranteed to converge, leading to results that may be hard to replicate or difficult to validate. Results We present a conceptually and computationally different parametric BDP inference approach using flexible and easy to implement Snyder filter (SF) algorithms. This method is deterministic so its results are provable, guaranteed and reproducible. We validate the SF on constant rate BDPs and find that it solves BDP likelihoods known to produce robust estimates. We then examine more complex BDPs with time-varying rates. Our estimates compare well with a recently developed parametric MCMC inference method. Lastly, we perform model selection on an empirical Agamid species phylogeny, obtaining results consistent with the literature. The SF makes no approximations, beyond those required for parameter quantization and numerical integration and directly computes the posterior distribution of model parameters. It is a promising alternative inference algorithm that may serve either as a standalone Bayesian estimator or as a useful diagnostic reference for validating more involved MCMC strategies. Availability and implementation The Snyder filter is implemented in Matlab and the time-varying BDP models are simulated in R. The source code and data are freely available at https://github.com/kpzoo/snyder-birth-death-code.