Abstract 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.