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We analyse sequential Markov coalescent algorithms for populations withdemographic structure: for a bottleneck model, a population-divergence model,and for a two-island model with migration. The sequential Markov coalescentmethod is an approximation to the coalescent suggested by McVean and Cardin,and Marjoram and Wall. Within this algorithm we compute, for two individualsrandomly sampled from the population, the correlation between times to the mostrecent common ancestor and the linkage probability corresponding to twodifferent loci with recombination rate R between them. We find that thesequential Markov coalescent method approximates the coalescent well in generalin models with demographic structure. An exception is the case whereindividuals are sampled from populations separated by reduced gene flow. Inthis situation, the gene-history correlations may be significantlyunderestimated. We explain why this is the case.

Sequential Markov coalescent algorithms for population models with demographic structure