Tuning the SMC: efficient simulation and the structure of ARGs

Sequentially Markovian Coalescent (SMC) models are a central element of contemporary population genetics, underlying many inferential methods. While the SMC has been shown to closely approximate the canonical Coalescent with Recombination (CwR) in terms of low-dimensional, two-locus summaries, its effects on the deeper structural properties of Ancestral Recombination Graphs (ARGs) are less well understood. Here, we define a general SMC approximation, SMC(k), in which a single parameter k controls the physical scale over which common-ancestor events between non-overlapping ancestral segments are permitted. The model encompasses the standard SMC and SMC' as special cases and converges to the CwR as k increases, providing a tunable trade-off between computational efficiency and fidelity to the full recombination process. Using recently developed summaries of ARG structure, we show that SMC approximations systematically truncate the persistence of ancestral haplotypes across the genome, despite preserving marginal coalescent properties, and that increasing k progressively recovers this long-range ancestral structure. We implement the SMC(k) in msprime and show that, for small samples, it makes whole-chromosome simulation in species with large population-scaled recombination rates several orders of magnitude faster than the CwR. Finally, we use SMC simulations for chromosome-scale parametric bootstrapping of demographic inference and find that the SMC' captures uncertainty in SFS-based estimates remarkably well, with only modest changes as k increases despite substantial differences in long-range ARG structure. Thus, the importance of SMC approximation error depends strongly on which properties of ancestry are relevant to the downstream analysis.