Linking Branch Lengths Across Loci Provides the Best Fit for Phylogenetic Inference

Evolution leaves heterogeneous patterns of nucleotide variation across the genome, with different loci subject to varying degrees of mutation, selection, and drift. Appropriately modelling this heterogeneity is important for reliable phylogenetic inference. One modelling approach in statistical phylogenetics is to apply independent models of molecular evolution to different groups of sites, where the groups are usually defined by locus, codon position, or combinations of the two. The potential impacts of partitioning data for the assignment of substitution models are well appreciated. Meanwhile, the treatment of branch lengths has received far less attention. In this study, we examined the effects of linking and unlinking branch-length parameters across loci. By analysing a range of empirical data sets, we find that the best-fitting model for phylogenetic inference is consistently one in which branch lengths are proportionally linked: gene trees have the same pattern of branch-length variation, but with varying absolute tree lengths. This model provided a substantially better fit than those that either assumed identical branch lengths across gene trees or that allowed each gene tree to have its own distinct set of branch lengths. Using simulations, we show that the fit of the three different models of branch lengths varies with the length of the sequence alignment and with the number of taxa in the data set. Our findings suggest that a model with proportionally linked branch lengths across loci is likely to provide the best fit under the conditions that are most commonly seen in practice. In future work, improvements in fit might be afforded by models with levels of complexity intermediate to proportional and free branch lengths. The results of our study have implications for model selection, computational efficiency, and experimental design in phylogenomics.