Evaluating Variations on the STAR Algorithm for Relative Efficiency and Sample Sizes Needed to Reconstruct Species Trees

Many methods for inferring species trees from gene trees have been developed when incongruence among gene trees is due to incomplete lineage sorting. A method called STAR (Liu et al, 2009), assigns values to nodes in gene trees based only on topological information and uses the average value of the most recent common ancestor node for each pair of taxa to construct a distance matrix which is then used for clustering taxa into a tree. This method is very efficient computationally, scaling linearly in the number of loci and quadratically in the number of taxa, and in simulations has shown to be highly accurate for moderate to large numbers of loci as well as robust to molecular clock violations and misestimation of gene trees from sequence data. The method is based on a particular choice of numbering nodes in the gene trees; however, other choices for numbering nodes in gene trees can also lead to consistent inference of the species tree. Here, expected values and variances for average pairwise distances and differences between average pairwise distances in the distance matrix constructed by the STAR algorithm are used to analytically evaluate efficiency of different numbering schemes that are variations on the original STAR numbering for small trees.