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

Peter R. Wilton*, Shai Carmi, Asger Hobolth

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


Two sequentially Markov coalescent models (SMC and SMC9) 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 SMC9. Using our Markov process, we derive a number of new quantities related to the pairwise SMC9, thereby analytically quantifying for the first time the similarity between the SMC9 and the ARG. We use our process to show that the joint distribution of pairwise coalescence times at recombination sites under the SMC9 is the same as it is marginally under the ARG, which demonstrates that the SMC9 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 SMC9 they are approximately asymptotically unbiased.

Original languageAmerican English
Pages (from-to)343-355
Number of pages13
Issue number1
StatePublished - 1 Jan 2015
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2015 by the Genetics Society of America.


  • Ancestral recombination graph
  • Consistency
  • Ergodicity
  • Markov approximation
  • Sequentially markov coalescent


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