Supplement

They are additional graphs so that we compared the Bayes estimator (BE) trees with 5 random initial trees and the BE trees with 20 random initial trees. PS PS and PS Bayes ("B") represent the BE trees with 5 random initial trees and Bayes20 ("X") represents the BE trees with 20 random initial trees.
They are additional graphs so that we compared the ML tree under the HKY model (ML) trees via PHYML 3.0 and the ML trees under the K2P model via PHYML 3.0 (ML(K2P)). PS PS and PS ML trees reconstructed via PHYML 3.0 under HKY model are represented by ML denoted by("L") and ML trees reconstructed via PHYML 3.0 under K2P (Kimura 2 parameters) model are represented by ML(K2P) denoted by ("X").
They are additional graphs so that we computed confidence bands of fitted curves as well as computing the plot with 2 standard deviations: PS for plots with confidence interval bands (i.e., the plot with 2 standard deviations) in terms of the path difference and PS for plots with confidence interval bands (i.e., the plot with 2 standard deviations) in terms of the RF distance.
MrBayes suggests running the chains until the standard deviation of the chains' split frequencies is less than 0.01. As can be seen in the box plot, 996 out of 1000 experiments satisfied this condition.

This is a software to reconstruct a phylogenetic tree using Bayes estimators for phylogenetic reconstruction ZIP and README file