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Re: Notarium question

----- Original Message ----- From: "David Peters" <davidpeters@att.net>
Sent: Friday, February 13, 2009 4:56 AM
Subject: Notarium question

Some pterosaurs have an obvious notarium.

Others obviously have no notarium.

And then there are others.... somewhere in between... it seems to start with a anteroproximal lengthening of the vertebral spines... in the next taxon they're touching one another... in the taxon thereafter some actually fuse in certain portions, but not all the way...

And I haven't even mentioned the scapulae yet. In some they are nearly parallel to the vertebral spines, so, no factor. In others they are transversely opposed and obviously somehow joined to the vertebral spines, but in some cases the spines remain unfused. No notarium.

Question is, when is it valid to call the structure a notarium? What
Rubicon must be crossed?

Is there such a thing as a pre-notarium? or proto-notarium?

The point of all this is how we should treat this when making a data matrix, right?

If so, then simply don't worry about the terminology. Rid yourself of nominalism. Don't make a character "notarium present/absent" and then agonize over what a notarium is. Instead, make an ordered (!!!) multistate character and give it as many states as you see in the material.

_Off the top of my head_, that would be: "Vertebrae free (0); zygapophyses sutured (1); zygapophyses fused (2); centra sutured (3); centra fused (4); ribs sutured (5); ribs fused (6); neural spines fused into continuous sheet (7); scapulae articulating with that sheet (8)".

Which state(s) of this character you call "notarium" is completely irrelevant. PAUP* doesn't care about such things.

It goes without saying that this was just an example. You need to find out on your own what states exist and what the correct order is. If you can't find out what the exact order is, don't simply order the character, but make a stepmatrix that allows all possibilities that you cannot exclude (and you probabl. That means a bit more work, but it will be worth it.

If you're uncomfortable with the high weight that the high number of states gives to the higher states of this character, run the analysis twice, with and without scaled weighting. Scaled weighting means to divide the weight of the character by the number of states and then multiply it either by 1 or (perhaps better) by the average number of states of all other characters together.

You _can_ score immature/paedomorphic specimens for such a character: simply give them the observed state _or higher_ (that means partial uncertainty).

And if such a structure evolved more than once, should we
differentiate these? Should we score them differently?

Absolutely not, because how often it evolved is exactly what you're trying to test. Phylogenetic analysis requires just two assumptions about the phylogeny of the taxon sample: that the ingroup is monophyletic with respect to the outgroup, and that each OTU is monophyletic with respect to each other. You should not use any other assumptions in your coding, because that would be circular logic.

_Morphologically_ different notaria, however, should not be coded as the same thing. They should be coded as different states of the same character. For example, Cracraft should have* scored the cnemial crest as a character with four states and a stepmatrix: "cnemial crest composed of tibia alone, tibia and patella, patella alone, or absent", with all transitions having a cost of 1, except for the transitions from "tibia alone" to "patella alone" and back getting a weight of 2 each.

*And maybe he did (I have no idea), and the actual problem was that he used way too few characters and too few taxa. I have no idea. However, stepmatrices were in any case really not fashionable in 1988 -- OK, they still aren't really en vogue outside of molecular phylogenetics, but it isn't that bad anymore.