Minimum variance rooting of phylogenetic trees and implications for species tree reconstruction

Phylogenetic trees inferred using commonly-used models of sequence evolution are unrooted, but the root position matters both for interpretation and downstream applications. This issue has been long recognized; however, whether the potential for discordance between the species tree and gene trees impacts methods of rooting a phylogenetic tree has not been extensively studied. In this paper, we introduce a new method of rooting a tree based on its branch length distribution; our method, which minimizes the variance of root to tip distances, is inspired by the traditional midpoint rerooting and is justified when deviations from the strict molecular clock are random. Like midpoint rerooting, the method can be implemented in a linear time algorithm. In extensive simulations that consider discordance between gene trees and the species tree, we show that the new method is more accurate than midpoint rerooting, but its relative accuracy compared to using outgroups to root gene trees depends on..., All the data sets are the results of simulations generated using Simphy.

D1—30-taxon heterogeneous dataset: The number of ingroup species was fixed to 30. We include 100 replicates, each with 500 gene trees. 
D2—Large heterogeneous dataset: Has two subsets, one with 2000 and another with 5000 taxa, each with 20 replicates and 50 gene trees.
D3—ASTRAL-II dataset: We reused a previously published dataset (http://www.ncbi.nlm.nih.gov/pubmed/26072508) with the number of species varying: 10, 50, 100, 200, 500, and 1000.
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