  We analyse sequential Markov coalescent algorithms for populations with
demographic structure: for a bottleneck model, a population-divergence model,
and for a two-island model with migration. The sequential Markov coalescent
method is an approximation to the coalescent suggested by McVean and Cardin,
and Marjoram and Wall. Within this algorithm we compute, for two individuals
randomly sampled from the population, the correlation between times to the most
recent common ancestor and the linkage probability corresponding to two
different loci with recombination rate R between them. We find that the
sequential Markov coalescent method approximates the coalescent well in general
in models with demographic structure. An exception is the case where
individuals are sampled from populations separated by reduced gene flow. In
this situation, the gene-history correlations may be significantly
underestimated. We explain why this is the case.
