Testing Harding's idea- Constraining topologies based on adding taxa in stratigraphic order

On the DML, Grant Harding proposed an idea.  Run cladistic analyses using only the earliest taxa, then sequentially add later taxa, but each time constrain the topology to match the trees found using only earlier taxa.  I tried it using my corrected TWG matrix, which at the moment covers all the taxa and characters up to Hwang et al. (2004).

So for example, the first run included only Jurassic taxa- Sinraptor, Allosaurus, Ornitholestes, Compsognathus and Archaeopteryx.  The tree found was (Sinraptor,Allosaurus(Ornitholestes(Compsognathus,Archaeopteryx))), which is standard.  It disagrees with the total data tree in having Ornitholestes and Compsognathus switched, presumably because of the lack of ornithomimosaurs, therizinosaurs, other compsognathids, etc..  If this were a more complete analysis, you'd have Haplocheirus, scansoriopterygids, Pedopenna, Lori and Anchiornis there as well as all the non-maniraptoriform Jurassic coelurosaurs. 

I then added the taxa which lived slightly later- Shenzhousaurus, Incisivosaurus and Sinovenator.  I constrained the analyses to only find trees agreeing with the relationships found using the Jurassic taxa.  This resulted in- (Sinraptor,Allosaurus(Ornitholestes(Compsognathus(Shenzhousaurus(Incisivosaurus(Sinovenator,Archaeopteryx)))))). This matches the total tree besides the point noted above.  Again, a more complete analysis would have Dilong, Kinnareemimus, Nqwebasaurus, Graciliraptor, Mei, Sinusonasus, "Eoconfuciusornis" and maybe a few other birds.

In any case, I added the following groups next-
- Harpymimus, Pelecanimimus.
- Utahraptor.
- Caudipteryx, Confuciusornis, Sinornithosaurus, Huaxiagnathus, Sinosauropteryx.
- Deinonychus, Microvenator, Sinornithoides, Alxasaurus, Microraptor, IGM 100/44.
- Garudimimus, Segnosaurus, Erlikosaurus, Achillobator.

Then I hit a snag.   The next group was Patagonykus, Unenlagia comahuensis and U? paynemili.  None of these taxa has a definite position in the cladogram when constrained to match the topology of the previous taxa.  The Unenlagia species are both some kind of paravian, while Patagonykus is at least as derived as compsognathids, but is not an ornithomimosaur, therizinosaur, avialan or eudromaeosaur.  And there's no way to constrain a tree to include uncertain relationships like these.  The only taxon left to include before the big end Campanian-Maastrichtian group was Alvarezsaurus, but it didn't help, since it emerges as a compsognathid-grade taxon without affecting Patagonykus' relationships.  So that's a problem with this kind of analysis.  The same is true of the many early fragments that show character combinations unique to certain clades (e.g. Jurassic dromaeosaurid teeth with high DSDIs).  These are normally useless to include in analyses since they don't have different codings than more complete later specimens, but in this variety of analysis, they'd be potentially useful early on but would form polytomies later if not deleted.

Another issue is that many taxa have unconstrained ages, and adding these in order of their earliest possible age, mean age, etc. is going to likely change the results.

To get a finished result of sorts, I simply did not constrain the position of Patagonykus, Unenlagia or U? paynemili in the final run with Campanian-Masstrichtian taxa, since they come out somewhere within their polytomies in the total data analysis anyway, though I did still force Alvarezsaurus to be compsognathid-grade.  The end result was a tree 19 steps longer than the unconstrained tree.  The primary differences are-

- Alvarezsaurus is by compsognathids due to its position before parvicursorines were added.
- Ornitholestes (thanks to the Jurassic analysis), therizinosaurs (thanks to Alxasaurus when analyzed with basal ornithomimosaurs) and Patagonykus+parvicursorines (probably due to following therizinosaurs) are outside Maniraptoriformes.
- Pelecanimimus is an ornithomimosaur due to alvarezsaurids not being included until after it was added.
- Microvenator is a basal maniraptoran due to the absence of more complete caenagnathoids until later runs.
- Caudipteryx is an oviraptorosaur thanks to clading with Incisivosaurus early on.
- Troodontids are paraphyletic to dromaeosaurids instead of to birds (except that Sinovenator is still an avialan), and Microraptor is a basal dromaeosaurid instead of a basal avialan.

So some results are closer to the consensus while others aren't.  I suppose the real test will be to see if any of these relationships are found when I add more taxa and characters to the complete analysis.