The SMC' is a highly accurate approximation to the ancestral recombination graph

TL;DR

This paper introduces a Markov process for the SMC' model, analytically compares it to the ancestral recombination graph (ARG), and demonstrates that SMC' provides a more accurate approximation for population genetics inference.

Contribution

We derive a new Markov process for the SMC' model, quantifying its similarity to the ARG and showing its superiority in population size estimation accuracy.

Findings

SMC' and ARG have identical pairwise coalescence time distributions at recombination sites.

SMC' is the most appropriate first-order Markov approximation to the ARG.

Population size estimates are approximately unbiased under SMC' but biased under SMC.

Abstract

Two sequentially Markov coalescent models (SMC and SMC') are available as tractable approximations to the ancestral recombination graph (ARG). We present a Markov process describing coalescence at two fixed points along a pair of sequences evolving under the SMC'. Using our Markov process, we derive a number of new quantities related to the pairwise SMC', thereby analytically quantifying for the first time the similarity between the SMC' and ARG. We use our process to show that the joint distribution of pairwise coalescence times at recombination sites under the SMC' is the same as it is marginally under the ARG, which demonstrates that the SMC' is, in a particular well-defined, intuitive sense, the most appropriate first-order sequentially Markov approximation to the ARG. Finally, we use these results to show that population size estimates under the pairwise SMC are asymptotically biased, while under the pairwise SMC' they are approximately asymptotically unbiased.