An efficient coalescent model for heterochronously sampled molecular data

Molecular sequence variation at a locus informs about the evolutionary history of the sample and past population size dynamics. The Kingman coalescent is used in a generative model of molecular sequence variation to infer evolutionary parameters. However, it is well understood that inference under this model does not scale well with sample size. Here, we build on recent work based on a lower resolution coalescent process, the Tajima coalescent, to model longitudinal samples. While the Kingman coalescent models the ancestry of labeled individuals, we model the ancestry of individuals labeled by their sampling time. We propose a new inference scheme for the reconstruction of effective population size trajectories based on this model and the infinite-sites mutation model. Modeling of longitudinal samples is necessary for applications (e.g., ancient DNA and RNA from rapidly evolving pathogens like viruses) and statistically desirable (variance reduction and parameter identifiability). We propose an efficient algorithm to calculate the likelihood and employ a Bayesian nonparametric procedure to infer the population size trajectory. We provide a new MCMC sampler to explore the space of heterochronous Tajima's genealogies and model parameters. We compare our procedure with state-of-the-art methodologies in simulations and an application to ancient bison DNA sequences.