Re: Notarium question

["David Marjanovic" <david.marjanovic@gmx.at>]

----- 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.