Decoding coalescent hidden Markov models in linear time

TL;DR

This paper introduces a linear-time algorithm for coalescent hidden Markov models, significantly improving computational efficiency and enabling more accurate demographic inference from genomic data.

Contribution

The authors develop a novel linear-time algorithm for coalescent HMMs that maintains accuracy and can be integrated into existing models like PSMC and diCal.

Findings

The linear-time algorithm reconstructs population size history more accurately than quadratic-time methods.

The method successfully infers high-resolution demographic history from 1000 Genomes data.

Speedup allows analysis of larger datasets with improved precision.

Abstract

In many areas of computational biology, hidden Markov models (HMMs) have been used to model local genomic features. In particular, coalescent HMMs have been used to infer ancient population sizes, migration rates, divergence times, and other parameters such as mutation and recombination rates. As more loci, sequences, and hidden states are added to the model, however, the runtime of coalescent HMMs can quickly become prohibitive. Here we present a new algorithm for reducing the runtime of coalescent HMMs from quadratic in the number of hidden time states to linear, without making any additional approximations. Our algorithm can be incorporated into various coalescent HMMs, including the popular method PSMC for inferring variable effective population sizes. Here we implement this algorithm to speed up our demographic inference method diCal, which is equivalent to PSMC when applied to a sample of two haplotypes. We demonstrate that the linear-time method can reconstruct a population size change history more accurately than the quadratic-time method, given similar computation resources. We also apply the method to data from the 1000 Genomes project, inferring a high-resolution history of size changes in the European population.