Identifiability and Reconstructibility of Species Phylogenies Under a Modified Coalescent

Coalescent models of evolution account for incomplete lineage sorting by specifying a species tree parameter which determines a distribution on gene trees, and consequently, a site pattern probability distribution. It has been shown that the unrooted topology of the species tree parameter of the multispecies coalescent is generically identifiable, and a reconstruction method called SVDQuartets has been developed to infer this topology. In this paper, we describe a modified multispecies coalescent model that allows for varying effective population size and violations of the molecular clock. We show that the unrooted topology of the species tree parameter for these models is generically identifiable and that SVDQuartets can still be used to infer this topology.