That said, it has been occasionally suggested that Diadectes is a basal synapsid, although the majority of studies place it outside crown-group amniotes.
Not just the majority, but all done after 1992 or so (arguably 1998), and all with a decent taxon sampling. I like the idea, but the data don't. Diadectomorpha and Amniota are sister-groups.
(Diadectomorpha contains the herbivorous Diadectidae, the carnivorous *Tseajaia*, and the carnivorous, probably amphibious and crocodile-like *Limnoscelis*.)
I will leave it for others to comment on detail, if they wish (David? Mickey?). But in brief, Peter's analyses have a lot to be desired in terms of anatomical interpretation, methodological approaches, etc.
A few years ago, David Peters kindly sent me an early version of his analysis. It turned out that: -- he had misinterpreted at least a few published line drawings of skulls, inferring a completely wrong three-dimensional shape from them; -- he had no idea how to make a data matrix for specifically phylogenetic analysis. That is, he didn't even _try_ to avoid correlated characters. There were lots of them!
I have told him so at every opportunity, in private and in public, ever since then. He has never even tried to argue that I was wrong; nor has he ever claimed, let alone tried to show, that he had corrected any such mistakes.
You will notice I haven't mentioned his "photointerpretation technique" ( = pareidolia) above. That is probably an additional problem even outside of pterosaurs. Next Tuesday, on the way to Teruel*, I'll stop by in Barcelona and have a look at *Cosesaurus* so I can compare it to his interpretation of it, which may be entirely correct but is based on a seriously crappy photo.
* 10th annual meeting of the European Association of Vertebrate Palaeontologists.
The wealth of data (genetic, genomic, morphological, developmental, etc.) pretty securely place turtles and traditional diapsids together in at least some combination, and the skeletal data for parareptiles being closer to diapsids than to synapsids is very strong.
Exactly.
The idea of a synapsid-archosaur or synapsid-diapsid clade clade has a long history (Diaptosauria; early non-computerized cladistic analyses, etc.) And you can certainly pick out a few characters to support it (thecodonty, for one). But it doesn't pop out in the really comprehensive studies of Permo-Triassic critters.
Exactly. BTW, mosasaurs, snakes, and diadectids are thecodont, too, but the earliest synapsids (like varanopids) are not, and the sister-group to all other diadectids (IIRC) has an intermediate condition.