 Explaining character distributions thus requires knowing which groups are clades (i.e., monophyletic groups). Phylogenetic trees depict precisely that, stating which groups are clades. This information is called the topology of the tree, which conveys the relative order of the nodes and nothing about their absolute dating in time. Knowing which groups are clades allows us to reconstruct the evolution of character traits, and it is the distribution of character traits that is the basic way that we infer which groups are clades in the first place. This style of reasoning (dubbed “reciprocal illumination” by Willi Hennig (1966) led to charges of circular reasoning from critics of phylogenetic inference (e.g., Sokal &amp; Sneath 1963), whereas advocates have sought to explain why this worry is misplaced (see Wiley 1975; Sober 1988b, among many others). In fact, the nested hierarchies of traits is what led systematists to classify taxa into a nested hierarchy in the first place, and it was the nested hierarchy of the taxonomic system that Darwin took to be the most important evidence for common ancestry (Winsor 2009; Sober 2009, 2010). The problems of understanding what it means for traits to be homologous and of inferring homology will be discussed later  (§2.1).  Complicating things, groups of homologies do not always form unambiguous nested hierarchies, and sorting out what phylogenetic hypotheses are best supported in these cases is a big part of what generates debates over phylogenetic inference (more on this in  §2  and  §3.