The observed sequence variation at a locus informs about the evolutionary history of the sample and past population size dynamics. The standard Kingman coalescent model on genealogies - timed trees that represent the ancestry of the sample - is used in a generative model of molecular sequence variation to infer evolutionary parameters. However, the state space of Kingman's genealogies grows superexponentially with sample size n, making inference computationally unfeasible already for small n. We introduce a new coalescent model called Tajima heterochronous n-coalescent with a substantially smaller cardinality of the genealogical space. This process allows to analyze samples collected at different times, a situation that in applications is both met (e.g. ancient DNA and RNA from rapidly evolving pathogens like viruses) and statistically desirable (variance reduction and parameter identifiability). We propose an  algorithm to calculate the likelihood efficiently and present a Bayesian nonparametric procedure to infer the population size trajectory. We provide a new MCMC sampler to explore the space of  Tajima's genealogies and model parameters. We compare our procedure with state-of-the-art methodologies in simulations and applications . We use our method to re-examine the scientific question of how Beringian bison went extinct analyzing modern and ancient molecular sequences of bison in North America, and to reconstruct population size trajectory of SARS-CoV-2 from viral sequences collected in France and Germany .
The observed 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, the heterochronous Tajima coalescent models 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 with the potential to improve computational efficiency. 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 applications .
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standard Kingman coalescent model on genealogies - timed trees that represent the ancestry of the sample -
Kingman coalescent
R
the state space of Kingman's genealogies grows superexponentially
it is well understood that inference under this model does not scale well
R
n, making inference computationally unfeasible already for small n. We introduce a new coalescent model called Tajima heterochronous n-coalescent with a substantially smaller cardinality of the genealogical space. This process allows to analyze samples collected at different times, a situation that in applications is both met
. 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, the heterochronous Tajima coalescent models 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 with the potential to improve computational efficiency. Modeling of longitudinal samples is necessary for applications
A
efficient
R
efficiently and present
and employ
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heterochronous
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. We use our method to re-examine the scientific question of how Beringian bison went extinct analyzing modern and ancient molecular sequences of bison in North America, and to reconstruct population size trajectory of SARS-CoV-2 from viral sequences collected in France and Germany