The likelihood node density effect and consequences for evolutionary studies of molecular rates.

Many molecular phylogenies show longer root-to-tip path lengths in species-rich groups, encouraging hypotheses linking cladogenesis with accelerated molecular evolution. However, the pattern can also be caused by an artifact called the node density effect (NDE): this effect occurs when the method used to reconstruct a tree underestimates multiple hits that would have been revealed by extra nodes, leading to longer root-to-tip path lengths in clades with more terminal taxa. Here we use a twofold approach to demonstrate that maximum likelihood and Bayesian methods also suffer from the NDE known to affect parsimony. First, simulations deliberately mismatching the simulation and reconstruction models show that the greater the model disparity, the greater the gap between actual and reconstructed tree lengths, and the greater the NDE. Second, taxon sampling manipulation with empirical data shows that NDE can still be present when using optimized models: across 12 datasets, 70 out of 109 sister path comparisons showed significant evidence of NDE. Unless the model fairly accurately reconstructs the real tree length-and given the complexity of real sequence evolution this may be uncommon -- it will consistently produce a node density artifact. At commonly encountered divergence levels, a 10% underestimation of tree length results in > or = 80% of simulated phylogenies showing a positive NDE. Bayesian trees have a slight but consistently stronger effect. This pervasive methodological artifact increases apparent rate heterogeneity, and can compromise investigations of factors influencing molecular evolutionary rate that use path lengths in topologically asymmetric trees.