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. It has been shown that the unrooted topology of the species tree parameter of the multispecies coalescent is generically identifiable. Moreover, a statistically consistent reconstruction method called SVDQuartets has been developed to recover this parameter. 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 for these models is generically identifiable and that SVDQuartets is still a statistically consistent method for inferring this parameter.