  The classic multispecies coalescent (MSC) model provides the means for
theoretical justification of incomplete lineage sorting-aware species tree
inference methods. A large body of work in phylogenetics is dedicated to the
design of inference methods that are statistically consistent under MSC. One of
such particularly popular methods is ASTRAL, a quartet-based species tree
inference method. A few recent studies suggested that ASTRAL also performs well
when given multi-locus gene trees in simulation studies. Further, Legried et
al. recently demonstrated that ASTRAL is statistically consistent under the
gene duplication and loss model (GDL). Note that GDL is prevalent in
evolutionary histories and is a part of the powerful
duplication-loss-coalescence evolutionary model (DLCoal) by Rasmussen and
Kellis. In this work we prove that ASTRAL is statistically consistent under the
general DLCoal model. Therefore, our result supports the empirical evidence
from the simulation-based studies. More broadly, we prove that a randomly
chosen quartet from a gene tree (with unique taxa) is more likely to agree with
the respective species tree quartet than any of the two other quartets.
