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DNA sequence alignments have provided the majority of data for inferring phylogenetic relationships with both concatenation and coalescent methods. However, DNA sequences are susceptible to extensive homoplasy, especially for deep divergences in the Tree of Life. Retroelement insertions have emerged as a powerful alternative to sequences for deciphering evolutionary relationships because these data are nearly homoplasy-free. In addition, retroelement insertions satisfy the “no intralocus-recombination” assumption of summary coalescent methods because they are singular events and better approximate neutrality relative to DNA loci commonly sampled in phylogenomic studies. Retroelements have traditionally been analyzed with parsimony, distance, and network methods. Here, we analyze retroelement data sets for vertebrate clades (Placentalia, Laurasiatheria, Balaenopteroidea, Palaeognathae) with 2 ILS-aware methods that operate by extracting, weighting, and then assembling unrooted quartets into a species tree. The first approach constructs a species tree from retroelement bipartitions with ASTRAL, and the second method is based on split-decomposition with parsimony. We also develop a Quartet-Asymmetry test to detect hybridization using retroelements. Both ILS-aware methods recovered the same species-tree topology for each data set. The ASTRAL species trees for Laurasiatheria have consecutive short branch lengths in the anomaly zone whereas Palaeognathae is outside of this zone. For the Balaenopteroidea data set, which includes rorquals (Balaenopteridae) and gray whale (Eschrichtiidae), both ILS-aware methods resolved balaeonopterids as paraphyletic. Application of the Quartet-Asymmetry test to this data set detected 19 different quartets of species for which historical introgression may be inferred. Evidence for introgression was not detected in the other data sets.

ILS-Aware Analysis of Low-Homoplasy Retroelement Insertions: Inference of Species Trees and Introgression Using Quartets