Bayesian Estimation of Population Size Changes by Sampling Tajima’s Trees

The large state space of gene genealogies is a major hurdle for inference methods based on Kingman9s coalescent. Here, we present a new Bayesian approach for inferring past population sizes which relies on a lower resolution coalescent process we refer to as "Tajima9s coalescent". Tajima9s coalescent has a drastically smaller state space, and hence it is a computationally more efficient model, than the standard Kingman coalescent model. We provide a new algorithm for efficient and exact likelihood calculations, which exploits a directed acyclic graph and a correspondingly tailored Markov Chain Monte Carlo method. We compare the performance of our Bayesian Estimation of population size changes by Sampling Tajima9s Trees (BESTT) with a popular implementation of coalescent-based inference in BEAST using simulated data and human data. We empirically demonstrate that BESTT can accurately infer effective population sizes, and it further provides an efficient alternative to the Kingman9s coalescent. The algorithms described here are implemented in the R package phylodyn, which is available for download at https://github.com/JuliaPalacios/phylodyn.