A test statistic to quantify treelikeness in phylogenetics

Most phylogenetic analyses assume that the evolutionary history of an alignment (either that of a single locus, or of multiple concatenated loci) can be described by a single bifurcating tree, the so-called the treelikeness assumption. Treelikeness can be violated by biological events such as recombination, introgression, or incomplete lineage sorting, and by systematic errors in phylogenetic analyses. The incorrect assumption of treelikeness may then mislead phylogenetic inferences. To quantify and test for treelikeness in alignments, we develop a test statistic which we call the tree proportion. This statistic quantifies the proportion of the edge weights in a phylogenetic network that are represented in a bifurcating phylogenetic tree of the same alignment. We extend this statistic to a statistical test of treelikeness using a parametric bootstrap. We use extensive simulations to compare tree proportion to a range of related approaches. We show that tree proportion successfully identifies non-treelikeness in a wide range of simulation scenarios, and discuss its strengths and weaknesses compared to other approaches. The power of the tree-proportion test to reject non-treelike alignments can be lower than some other approaches, but these approaches tend to be limited in their scope and/or the ease with which they can be interpreted. Our recommendation is to test treelikeness of sequence alignments with both tree proportion and mosaic methods such as 3Seq. The scripts necessary to replicate this study are available at https://github.com/caitlinch/treelikeness