Exact Decoding of a Sequentially Markov Coalescent Model in Genetics

AbstractIn statistical genetics, the sequentially Markov coalescent (SMC) is an important family of models for approximating the distribution of genetic variation data under complex evolutionary models. Methods based on SMC are widely used in genetics and evolutionary biology, with significant applications to genotype phasing and imputation, recombination rate estimation, and inferring population history. SMC allows for likelihood-based inference using hidden Markov models (HMMs), where the latent variable represents a genealogy. Because genealogies are continuous, while HMMs are discrete, SMC requires discretizing the space of trees in a way that is awkward and creates bias. In this work, we propose a method that circumvents this requirement, enabling SMC-based inference to be performed in the natural setting of a continuous state space. We derive fast, exact procedures for frequentist and Bayesian inference using SMC. Compared to existing methods, ours requires minimal user intervention or parameter tuning, no numerical optimization or E-M, and is faster and more accurate. Supplementary materials for this article are available online.Keywords: ChangepointCoalescentHidden Markov modelPopulation genetics Supplementary MaterialsIn the supplement we present supporting lemmas, proofs of the theorems, and additional plots and tables. (pdf)Disclosure StatementNo potential conflict of interest was reported by the author(s).Data Availability StatementAll of the data analyzed in this article are either simulated, or publicly available. A Python package implementing our method is available at https://terhorst.github.io/xsmc. Code which reproduces all of the figures and tables in this article is available at https://terhorst.github.io/xsmc/paper.Additional informationFundingThis research was supported by the National Science Foundation (grant number DMS-2052653, and a Graduate Research Fellowship), and the National Institute of General Medical Sciences of the National Institutes of Health under award number R35GM151145. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.