A year ago I mentioned a published discussion of the different branching diagrams that have been used for phylogenetic relationships (Tree metaphors and mathematical trees). If we consider the form of the relationship and whether time is involved, we get the following four possible diagram types:
Most current phylogenetic diagrams claim to show sister-group relationships (which means that ancestors are inferred only), with a time-order to the branching sequence. There is a broad range of diagram types in use, both mathematical and metaphorical. For example, the top four in this next diagram are mathematical and the bottom four are metaphorical variants of the above 2x2 table:
The connection between these different diagrams has both conceptual and practical problems, although these seem to be overlooked by most practitioners. This issue as been addressed by János Podani in a paper that is now online:
The Coral of Life. Evolutionary Biology (2019).To quote from the Abstract:
The Tree of Life (ToL) has been of central importance in the biological sciences, usually understood as a model or a metaphor, and portrayed in various graphical forms to summarize the history of life as a single diagram. If it is seen as a mathematical construct — a rooted graph theoretical tree or, as more recently viewed, a directed network, the Network of Life (NoL) — then its proper visualization is not feasible, for both epistemological and technical reasons. As an overview included in this study demonstrates, published ToLs and NoLs are extremely diverse in appearance and content ... Metaphorical trees are even less useful for the purpose, because ramification is the only property of botanical trees that may be interpreted in an evolutionary or phylogenetic context. This paper argues that corals, as suggested by Darwin in his early notebooks, are superior to trees as metaphors, and may also be used as mathematical models. A coral diagram is useful for portraying past and present life because it is suitable: (1) to illustrate bifurcations and anastomoses, (2) to depict species richness of taxa proportionately, (3) to show chronology, extinct taxa and major evolutionary innovations, (4) to express taxonomic continuity, (5) to expand particulars due to its self-similarity, and (6) to accommodate a genealogy-based, rank-free classification.It is worth checking out this paper, even if only for the new Coral of Life diagram that is presented in its Figure 3, which synthesizes much of our current knowledge.