Figure 2

Comparative performance with simulated data: correct model, single long branch, symmetric distance Performance at different branch-length ratios of ML and Bayesian inference with simulated protein-sequence data evolved on a tree having a single long branch, measured as Robinson-Foulds symmetric distance. The JTT model was used for both sequence evolution and tree inference. Number (out of 50) of accurately reconstructed topologies (vertical axes) versus branch-length ratio (horizontal axes), where inference was by (A) gamma-corrected PROML, (B) Bayesian uncorrected for ASRV, with uniform prior, (C) gamma-corrected Bayesian with uniform prior, and (D) gamma-corrected Bayesian with exponential prior. Shading codes for each different distance are shown in the small box at the right of each panel (A-D). Thus the right-hand bar in panel B shows that using Bayesian inference uncorrected for ASRV and assuming a uniform prior, with a dataset generated on a tree in which one branch was lengthened 70-fold, 33 of 50 independent trees recovered the correct topology (Robinson-Foulds symmetric distance zero); 6 differed topologically in ways that involved a single node (distance two); 2 differed in ways that involved two adjacent nodes (distance four); 4 were at distance six; and the remaining 5 were at the maximum symmetric distance, eight. See text for explanation of dual bars in Panel A.