The Meaning and Measure of Concordance Factors in Phylogenomics

As phylogenomic datasets have grown in size, researchers have developed new ways to measure biological variation and to assess statistical support for specific branches. Larger datasets have more sites and loci and therefore less sampling variance. While we can more accurately measure the mean signal in these datasets, lower sampling variance is often reflected in uniformly high measures of branch support-such as the bootstrap and posterior probability-limiting their utility. Larger datasets have also revealed substantial biological variation in the topologies found across individual loci, such that the single species tree inferred by most phylogenetic methods represents a limited summary of the data for many purposes. In contrast to measures of statistical support, the degree of underlying topological variation among loci should be approximately constant regardless of the size of the dataset. "Concordance factors" (CFs) and similar statistics have therefore become increasingly important tools in phylogenetics. In this review, we explain why CFs should be thought of as descriptors of topological variation rather than as measures of statistical support, and argue that they provide important information about the predictive power of the species tree not contained in measures of support. We review a growing suite of statistics for measuring concordance, compare them in a common framework that reveals their interrelationships, and demonstrate how to calculate them using an example from birds. We also discuss how measures of topological variation might change in the future as we move beyond estimating a single "tree of life" toward estimating the myriad evolutionary histories underlying genomic variation.