Utility of characters evolving at diverse rates of evolution to resolve quartet trees with unequal branch lengths: analytical predictions of long-branch effects

Background: The detection and avoidance of long-branch effects in phylogenetic inference represents a longstanding challenge for molecular phylogenetic investigations. A consequence of parallelism and convergence, long-branch effects arise in phylogenetic inference when there is unequal molecular divergence among lineages, and they can positively mislead inference based on parsimony especially, but also inference based on maximum likelihood and Bayesian approaches. Long-branch effects have been exhaustively examined by simulation studies that have compared the performance of different inference methods in specific model trees and branch length spaces. Results: In this paper, by generalizing the phylogenetic signal and noise analysis to quartets with uneven subtending branches, we quantify the utility of molecular characters for resolution of quartet phylogenies via parsimony. Our quantification incorporates contributions toward the correct tree from either signal or homoplasy (i.e. the right result for either the right reason or the wrong reason). We also characterize a highly conservative lower bound of utility that incorporates contributions to the correct tree only when they correspond to true, unobscured parsimony-informative sites (i.e. the right result for the right reason). We apply the generalized signal and noise analysis to classic quartet phylogenies in which long-branch effects can arise due to unequal rates of evolution or an asymmetrical topology. Application of the analysis leads to identification of branch length conditions in which inference will be inconsistent and reveals insights regarding how to improve sampling of molecular loci and taxa in order to correctly resolve phylogenies in which long-branch effects are hypothesized to exist. Conclusions: The generalized signal and noise analysis provides analytical prediction of utility of characters evolving at diverse rates of evolution to resolve quartet phylogenies with unequal branch lengths. The analysis can be applied to identifying characters evolving at appropriate rates to resolve phylogenies in which long-branch effects are hypothesized to occur.