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

摘要

Two sequentially Markov coalescent models (SMC and SMC') are available astractable approximations to the ancestral recombination graph (ARG). We presenta Markov process describing coalescence at two fixed points along a pair ofsequences evolving under the SMC'. Using our Markov process, we derive a numberof new quantities related to the pairwise SMC', thereby analyticallyquantifying for the first time the similarity between the SMC' and ARG. We useour process to show that the joint distribution of pairwise coalescence timesat recombination sites under the SMC' is the same as it is marginally under theARG, which demonstrates that the SMC' is, in a particular well-defined,intuitive sense, the most appropriate first-order sequentially Markovapproximation to the ARG. Finally, we use these results to show that populationsize estimates under the pairwise SMC are asymptotically biased, while underthe pairwise SMC' they are approximately asymptotically unbiased.