On the consistency of duplication, loss, and deep coalescence gene tree parsimony costs under the multispecies coalescent

Gene tree parsimony (GTP) is a common approach for efficient reconciliation of multiple discordant gene tree phylogenies for the inference of a single species tree. However, despite the popularity of GTP methods due to their low computational costs, prior work has shown that some commonly employed parsimony costs are statistically inconsistent under the multispecies coalescent process. Furthermore, a fine-grained analysis of the inconsistency has indicated potentially complementary behavior of duplication and deep coalescence costs for symmetric and asymmetric species trees. In this work, we prove inconsistency of GTP estimators for all linear combinations of duplication, loss, and deep coalescence scores. We also explore empirical implications of this result by evaluating inference results of several GTP cost schemes under varying levels of incomplete lineage sorting.