  Phylogenetic species trees typically represent the speciation history as a
bifurcating tree. Speciation events that simultaneously create more than two
descendants, thereby creating polytomies in the phylogeny, are possible.
Moreover, the inability to resolve relationships is often shown as a (soft)
polytomy. Both types of polytomies have been traditionally studied in the
context of gene tree reconstruction from sequence data. However, polytomies in
the species tree cannot be detected or ruled out without considering gene tree
discordance. In this paper, we describe a statistical test based on properties
of the multi-species coalescent model to test the null hypothesis that a branch
in an estimated species tree should be replaced by a polytomy. On both
simulated and biological datasets, we show that the null hypothesis is rejected
for all but the shortest branches, and in most cases, it is retained for true
polytomies. The test, available as part of the ASTRAL package, can help
systematists decide whether their datasets are sufficient to resolve specific
relationships of interest.
