Inconsistency of parsimony under the multispecies coalescent

While it is known that parsimony can be statistically inconsistent under certain models of evolution due to high levels of homoplasy, the consistency of parsimony under the multispecies coalescent (MSC) is less well studied. Previous studies have shown the consistency of concatenated parsimony (parsimony applied to concatenated alignments) under the MSC for the rooted 4-taxa case under an infinite-sites model of mutation; on the other hand, other work has also established the inconsistency of concatenated parsimony for the unrooted 6-taxa case. These seemingly contradictory results suggest that concatenated parsimony may fail to be consistent for trees with more than 5 taxa, for all unrooted trees, or for some combination of the two. Here, we present a technique for computing the expected internal branch lengths of gene trees under the MSC. This technique allows us to determine the regions of the parameter space of the species tree under which concatenated parsimony fails for different numbers of taxa, for rooted or unrooted trees. We use our new approach to demonstrate that while parsimony succeeds in the unrooted 5-taxa case, there are regions of statistical inconsistency for concatenated parsimony for rooted 5+-taxa cases and unrooted 6+-taxa cases. Our results therefore suggest that parsimony is not generally dependable under the MSC.