  Species tree reconstruction is complicated by effects of Incomplete Lineage
Sorting (ILS), commonly modeled by the multi-species coalescent model. While
there has been substantial progress in developing methods that estimate a
species tree given a collection of gene trees, less attention has been paid to
fast and accurate methods of quantifying support. In this paper, we propose a
fast algorithm to compute quartet-based support for each branch of a given
species tree with regard to a given set of gene trees. We then show how the
quartet support can be used in the context of the multi-species coalescent
model to compute i) the local posterior probability that the branch is in the
species tree and ii) the length of the branch in coalescent units. We evaluate
the precision and recall of the local posterior probability on a wide set of
simulated and biological data, and show that it has very high precision and
improved recall compared to multi-locus bootstrapping. The estimated branch
lengths are highly accurate when gene trees have little error, but are
underestimated when gene tree estimation error increases. Computation of both
branch length and local posterior probability is implemented as a new feature
in ASTRAL.
