title: The SMC' is a highly accurate approximation to the ancestral recombination graph.
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 the 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.
authors: Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, Massachusetts 02138 pwilton@fas.harvard.edu.
authors: Peter R
authors: PR
authors: Wilton
authors: Department of Computer Science, Columbia University, New York, New York 10027.
authors: Shai
authors: S
authors: Carmi
authors: Bioinformatics Research Centre, Aarhus University, 8000 Aarhus C, Denmark.
authors: Asger
authors: A
authors: Hobolth
mesh_terms: D000465:Algorithms; D019143:Evolution, Molecular; D014644:Genetic Variation; D008390:Markov Chains; D008957:Models, Genetic; D011995:Recombination, Genetic; D012680:Sensitivity and Specificity
keywords: Markov approximation; ancestral recombination graph; consistency; ergodicity; sequentially Markov coalescent