Estimating Waiting Distances Between Genealogy Changes under a Multi-Species Extension of the Sequentially Markov Coalescent

Abstract

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. Expectations for the amount of 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 expected distribution of waiting distances between changes in genealogical trees 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 expected 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). Our solutions establish an expectation for genetic linkage in multispecies datasets and provide a new likelihood framework for linking demographic models with local ancestry inference across genomes.