Estimating waiting distances between genealogy changes under a multi-species extension of the sequentially Markov coalescent

Genomes are composed of a mosaic of segments inherited from different ancestors, each separated by past recombination events. Consequently, genealogical relationships among multiple genomes vary spatially across different genomic regions. Genealogical variation among unlinked (uncorrelated) genomic regions is well described for either a single population (coalescent) or multiple structured populations (multispecies coalescent). However, the expected similarity among genealogies at linked regions of a genome is less well characterized. Recently, an analytical solution was derived for the distribution of the waiting distance for a change in the genealogical tree spatially across a genome for a single population with constant effective population size. Here we describe a generalization of this result, in terms of the distribution of waiting distances between changes in genealogical trees and topologies for multiple structured populations with branch-specific effective population sizes (i.e., under the multispecies coalescent). We implemented our model in the Python package ipcoal and validated its accuracy against stochastic coalescent simulations. Using a novel likelihood framework, we show that tree and topology-change waiting distances in an ARG can be used to fit species tree model parameters, demonstrating an application of our model for developing new methods for phylogenetic inference. The Multi-Species Sequentially Markov Coalescent (MS-SMC) model presented here represents a major advance for linking local ancestry inference to hierarchical demographic models.