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There has long been ambiguity in the use of the term tree in phylogenetic systematics, which is a continuous source of misinterpretation of evolutionary relationships. The basic problem is that while many trees with phylogenetic or evolutionary relevance, such as cladograms, are consistent with graph theory, tree-like visualization of phylogeny may also be done via other types of graphics, especially botanical (or literal) tree drawings. As a consequence, the meaning of such diagrams is not always clear: a given picture may have multiple interpretations in its different parts and two figures that look similar may actually carry quite different information. I show that these are not merely metaphors of phylogeny and may be defined mathematically as geometric shapes called branching silhouette diagrams, the name referring to their most apparent features. They have four basic forms depending on whether the time factor is considered in their construction and the relationships portrayed are of the ancestor-descendant or sister group type. By revitalizing Darwin's early suggestions on the illustration of change in the living world, I propose the term coral for the most common forms of branching silhouette which consider time and show ancestry. The others appear rarely in present-day practice and are mostly of historical value-these are cacti (named after one of Bessey's diagrams) and two types of oaks (with reference to several of Haeckel's motifs used in depicting phylogeny in the nineteenth century). The use of these terms in phylogenetic systematics facilitates better understanding of how organization of biodiversity has been visualized in science [Bessey; cladograms; coral-thinking; Darwin; graph theory; Haeckel; phylogeny; tree thinking.].

Different from Trees, more than Metaphors: Branching Silhouettes—Corals, Cacti, and the Oaks