  The inference of the evolutionary history of a collection of organisms is a
problem of fundamental importance in evolutionary biology. The abundance of DNA
sequence data arising from genome sequencing projects has led to significant
challenges in the inference of these phylogenetic relationships. Among these
challenges is the inference of the evolutionary history of a collection of
species based on sequence information from several distinct genes sampled
throughout the genome. It is widely accepted that each individual gene has its
own phylogeny, which may not agree with the species tree. Many possible causes
of this gene tree incongruence are known. The best studied is incomplete
lineage sorting, which is commonly modeled by the coalescent process. Numerous
methods based on the coalescent process have been proposed for estimation of
the phylogenetic species tree given DNA sequence data. However, use of these
methods assumes that the phylogenetic species tree can be identified from DNA
sequence data at the leaves of the tree, although this has not been formally
established. We prove that the unrooted topology of the n-leaf phylogenetic
species tree is generically identifiable given observed data at the leaves of
the tree that are assumed to have arisen from the coalescent process under a
time-reversible substitution process with the possibility of site-specific rate
variation modeled by the discrete gamma distribution and a proportion of
invariable sites.
