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Theropod taxonomy based only on shed teeth (Re: Dromaeosaur questions (long, I think))

> You can only design a 
> slicing-cutting tooth in a limited number of variants before you 
> start repeating: long, recurved, large chiseled denticles; long, 
> recurved, small chiseled denticles; long, straight, large chiseled 
> denticles, long, straight small chiseled denticles, etc. I think you 
> could work out the total number of possibilities on  paper in less 
> than a half-hour 

Tp = X1 * X2 * X3 * ....... Xn

Where Tp is the total number of character trait combinations.

And where X1.....Xn  is the number of states within Character 1 through
Character Xn.

Before I continue my post, I have to ask:  Is the above equation the
correct one to use?

Even if one uses a small character set (and assuming my math is correct),
then the total number of possible combinations of traits is huge: over a
million combinations, in fact.
Below is my conservative (and probably very incomplete) list of 15
theropod tooth characters, each character having between 2 and 4 possible
states.  I ran these numbers through the above algorithm (again, someone
*please* comment if I calculated it wrong!).  I found that there are
1,119,744 possible combinations of the 15 character states (see below)
that a hypothetical theropod tooth could have.  Someone who is more
knowledgeable that I am could find 15 or so different (aka, "better")
tooth characters of their choice, but the resulting number of
combinations should be roughly the same.  I have some further comments
after my list of characters (below).

Crown length:

Character 1
- 1 Elongated
- 2 Short/stubby

Cross-sectional appearance:

Character 2
- 1 Crown rounded in cross-section
- 2 Crown laterally compressed in cross-section
- 3 Crown has other shape in cross-section

Overall appearance:

Character 3
- 1 Peg-like
- 2 Knife-like
- 3 Other appearance (meaning, add 1 or more additional states to this

Character 4
- 1 Recurved crown
- 2 Crown not recurved

Texture of crown:

Character 5
- 1 Smooth surface
- 2 Fluted surface (example: _Spinosaurus_)


Character 6
- 1 Anterior carina curved (example:  _Dromaeosaurus_)
- 2 Anterior carina not curved


Character 7
- 1 Anterior denticles present; posterior denticles present
- 2 Anterior denticles present; posterior denticles absent
- 3 Anterior denticles absent; posterior denticles present
- 4 Anterior denticles absent; posterior denticles absent

Character 8
- 1 Denticles have appearance of cubes on-edge (example: Tyrannosauridae)
- 2 Denticles pointed

Character 9
- 1 "Blood grooves" below denticles (example: Tyrannosauridae)
- 2 "Blood grooves" absent

Character 10
- 1 Denticles angled toward root
- 2 Denticles angled toward tip of tooth
- 3 Denticles not angled

Character 11
- 1 Anterior denticles larger than posterior denticles
- 2 Anterior denticles smaller than posterior denticles
- 3 Anterior denticles same size as posterior denticles

Crown width:

Character 12
- 1 Crown surface flush with surface of root
- 2 Crown wider than root (example: _Archaeopteryx_)


Character 13
- 1 Strongly recurved
- 2 Slightly recurved
- 3 Nearly straight

Character 14
- 1 Root circular in cross-section
- 2 Laterally compressed in cross-section
- 3 Other shape in cross-section (groove only on one side; bi-grooved,

Pulp cavity:

Character 15
- 1 Circular in cross-section
- 2 Laterally compressed in cross-section
- 3 Other shape in cross-section


And now, a few ramblings:

The above is probably a very incomplete list.  A more rigorous search of
the scientific literature would probably add another 10 or so common
character traits for theropod teeth.  And what about enamel
microstructure?  In mammalian teeth, enamel microstructure is a highly
diagnostic character.  Is it also the case with theropod teeth?.  Even if
one used a slightly revised total of 25 tooth characters with, say, a
*conservative* two states per character, that would mean that there are a
whopping 33,554,432 possible combinations of characters that a
hypothetical theropod tooth could possess!  (Again, correct my math if I
did it wrong).

I haven't checked Dino George's Taxonomy List recently, but I think it is
safe to assume that the number of possible combinations of "common"
theropod tooth character states vastly outnumbers the number of named
species.  That's just an observation; I make no inferences from it.

However, not all combinations of tooth character states are beneficial in
an evolutionary sense.  For instance, long, laterally-compressed teeth
are biomechanically worthless because they will easily break.  Similarly,
a bi-cusped theropod fang is redundant (and it would probably be
biomechanically weak).  So, how many of those 1,119,744 character combos
should we throw out because they don't make any
evolutionary/biomechanical sense?  Beats me.  At any rate, I think it's
*very* unlikely that there are between 1,119,744 to 33,554,432 theropod
tooth morphotypes waiting to be dug up.  But we already suspected that,
didn't we?  ;-)

> > (Someone interested in a Master's thesis?).

Smells Like "Post-Grad Spirit".
I will include it on my "Suggestions For Research" web page.
http://www.scn.org/~bh162/suggested_research.html  .  As always, other
ideas are welcome.  It looks like I need to remove some old suggestions. 
A new paper on K-T soot has recently been published, so I'll have to nuke
that one.

> > It could be set up as a table, with the same features along the top 
> > and side, and an X in the cell for the X-Y combo. Then, using this 
> > predictive tool, to look at the fossil record for examples. It would 
> > be interesting to see if any combination pattern is more 
> > common/frequent than another.

Also, it would be useful to check the table for infrequently-found
combinations of character traits, and for character trait combinations
that haven't yet been found.

A Monte Carlo simulation could be useful in such a study.  Route the
output of the simulations into a CAD/CAM carving machine and manufacture
some hypothetical teeth.  Then analyze the teeth for stress/strain
moduli, etc. and for cutting/piercing/scraping properties.

A simpler and much cheaper research project would be to use the Monte
Carlo simulations (one would only need the images) and compare them with
images of all known theropod tooth morphotypes.  How well do the Monte
Carlo simulations and the real-world morphotypes match?

Infrequently-occuring character combinations would require an
explaination as to why they are seldom found in the fossil record.  For
example, why are Troodon teeth so distinctive compared to other tiny
theropod teeth?

> > This type of analysis has NEVER been 
> > done.

That's not surprising.  A comprehensive cataloging, classification, and
analysis of predator/scavenger bite marks on fossil bone for a given
paleoecosystem hasn't been conducted either.

I have no opinion on the issue of whether theropod teeth are diagnostic
enough to name a taxon on.  I have no dog in this fight.

Sorry for such a wordy post.  I have the flu, am on Nyquil, and I had
nothing better to do today.

<pb> (who has discovered that if he sneezes and coughs at the same time
after taking Nyquil, he can almost see Jimmy Hendrix)

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