Accuracy of the SMC Approximation of Structured Coalescent

Coalescent with recombination is one of the most important population models in population genetics. This model is very efficient for simulating realistic genealogies and genetic data. But due the complexity of its state space, in particular due to the combinatorial reasons, the inference under this model is computationally intensive and often infeasible. The Sequential Markovian Coalescent (SMC), and its modification SMC , are approximations to the full coalescent with recombination. Many methods use SMC for inference purposes, often by applying Hidden Markov Model framework. It was shown that SMC is a very accurate approximation of the coalescent with recombination in the case of a panmictic population. But in reality population histories are much more complex, in particular due to migrations. Here we investigate the accuracy of the SMC approximation in case of structured coalescent with recombination, more precisely in case of two populations with continuous symmetric migration between them.