25 February 2010

Names on Nodes: MathML Definitions (Version 1.1)

After posting Version 1.0 earlier this week, I had a revelation: the cladogen functions are completely unnecessary, and everything would work a lot nicer if I just tossed them. I also realized that there really was no reason I couldn't include the various relations (precedence, immediate precedence, proper precedence, etc.), just in case anyone wanted to do some seriously non-standard definitions. After some significant revisions, I present Version 1.1.

Some examples of the updated notation, using humans (Homo sapiens), platypuses (Ornithorhynchus anatinus), and Dimetrodon grandis, a stem-mammal:

Union. Homo sapiensOrnithorhynchus anatinus = all humans and all platypuses (polyphyletic taxon, also monothetic)

Exclusive Predecessors. Homo sapiensOrnithorhynchus anatinus = humans and all of their ancestors, except for the ancestors shared with platypuses (lineage)

Synapomorphic Predecessors. "milk glands" @ Homo sapiens = humans and all human ancestors to possess milk glands synapomorphic with those in humans (lineage)

Node-Based Clade. Clade(Homo sapiensOrnithorhynchus anatinus) = Mammalia

Branch-Based Clade (simple). Clade(Homo sapiensOrnithorhynchus anatinus) = "Pan-Theria"

Branch-Based Clade (multiple external specifiers). Clade(Homo sapiensOrnithorhynchus anatinusDimetrodon grandis) = "Pan-Theria"

Branch-Based Clade (multiple internal specifiers). Clade(Homo sapiensOrnithorhynchus anatinusDimetrodon grandis) = (unnamed clade comprised mostly of Therapsida)

Null Branch-Based Definition (multiple internal specifiers). Clade(Homo sapiensDimetrodon grandisOrnithorhynchus anatinus) = ∅

Apomorphy-Based Clade. Clade("milk glands" @ Homo sapiens) = "Apo-Mammalia"

Node-Modified Crown Clade. Crown(Homo sapiensDimetrodon grandis, "extant as of or after 2010") = Mammalia

Branch-Modified Crown Clade. Crown(Homo sapiensOrnithorhynchus anatinus, "extant as of or after 2010") = Theria

Apomorphy-Modified Crown Clade. Crown("milk glands" @ Homo sapiens, "extant as of or after 2010") = Mammalia

Total Clade. Total(Mammalia, "extant as of or after 2010") = Synapsida (or "Pan-Mammalia")

Image showing a node-based clade (Mammalia) under a given phylogenetic hypothesis. Click to enlarge. More here.


  1. Very nice!

    I now feel that we have all been really dumb in not spotting long ago that this was the way to go :-)

  2. Thanks! I'm not sure I would have thought of it had you not pointed out some issues with my thinking on the previous version.

    Incidentally, this also suggests that we could call the definition styles union-, exclusion-, and synapomorphy-based instead of node-, branch-, and apomorphy-based. I'm not about to start doing that, though, because the existing terms are fine and pretty well-entrenched. (Not to mention that even the well-reasoned switch from "stem-based" to "branch-based" has had trouble getting a toehold.)