  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.
