Sample Complexity of Species Tree Estimation From a Linear Combination of Internode Distances

We consider the problem of estimating the species tree from large numbers of unrooted gene tree topologies in the presence of incomplete lineage sorting, a phenomenon which enforces heterogeneity among the set of gene trees. This phenomenon is modeled with the Multispecies Coalescent Process. We make progress towards deriving a sample complexity bound for species tree reconstruction methods based on sample averages of graph distances. The sample complexity depends poly-logarithmically on N, the number of species in the tree.