Did the turtle nuchal evolve from cleithra?

Lyson et al.  2013
propose a homology of the turtle nuchal (central anterior roof-like bone of the carapace) with the primitive cleithra (singular: cleithrum, slender, stem-like bone anterior to the scapula). In order to do so, they produced a set of turtle ancestors (or engineering models) that is not validated by the large reptile tree (LRT, 1395 taxa).

Frogs, lepidosaurs, diadectids and para-caseasaurs,
according to Lyson et al., model the ancestry of turtle shoulders and shells (Fig. 1).

By contrast,
in the LRT Milleretta, is basal to Stephanospondylus, which is basal to diadectids on one branch and pareiasaurs, like Bunostegos, and the basal turtle Meiolania, on the other, documenting a more gradual accumulation of traits without introducing frogs and lepidosaurs. In the LRT, the gap between Bunostegos and Meiolania includes the unchronicled development of the carapace and plastron. Given that issue, almost everything else was present in the skeleton. A skull-only taxon, Elginia (not shown in Fig. 1), nests between the two. There is an online paper on turtle ancestors here.

Taxon exclusion is once again the problem.
Since Lyson et al. used inappropriate and unrelated taxa to demonstrate their hypothesis, it was invalid from the get-go. To my knowledge (let me know if I am wrong):

1. No one recently suggested that frogs, like Rana, are basal to turtles.
2. No one recently suggested that Diadectes is basal to turtles.
3. No one recently suggested that Sphenodon is basal to turtles.
4. Several authors (many from the Lyson et al. list) have suggested that Eunotosaurus was basal to turtles, but they did not test the above-listed LRT competing candidates when they published.

From Wikipedia Diadectidae
“Paleontologist E.C. Case compared diadectids to turtles in 1907, noting their large pectoral girdles, short, strong limbs, and robust skulls. Case described them as “lowly, sluggish, inoffensive herbivorous reptiles, clad in an armor of plate to protect them from the fiercely carnivorous pelycosaurs.”

The better method
for figuring out anything about turtles is to employ the valid ancestors of turtles, validated by testing against all other published candidates. I know, from testing, that all other candidates, like Eunotosaurus, nest far from turtles.

Getting back to our headline
and the title of the Lyson et al. paper, the genesis of the turtle carapace in hard-shell turtles is not preserved in the fossil record at present. Even so, the rarely preserved cleithrum gives little to no indication that it evolved into an anterior carapace bone… at present. Some day it may.

Lyson et al. note:
“unlike the other midline carapacial elements, the nuchal develops from paired mesenchymal condensations each of which contains a separate ossification center… first observed by Vallén (1942) and led him to conclude the nuchal was homologous with the supracleithra.”

The supracleithrum
by definition, “is a bone of the pectoral girdle situated dorsal to the cleithrum in some fishes and amphibians.”  That definition does not include reptiles.

If we look for a pre-nuchal in pareiasaurs
it is easy to find parasagittal osteoderms (Fig 2). Lyson et al. do not mention the word ‘pareiasaur’ in their paper.

Take the turtle pelvis, for instance.
Similar precursors can be seen in stem turtle pareiasaurs (Fig. 3). And the skull is interesting. Workers have discussed Elginia with pareiasaurs and Meiolania with turtles, but never Meiolania with pareiasaurs or Elginia with turtles. That you heard here first in a three-part series five years ago.

If you know one of the seven authors
of Lyson et al. 2013, please make sure they become aware of this critique. A few of them are among those who rejected the submitted manuscript on the origin of turtles. Evidently they prefer the invalid status quo rather than this novel hypothesis for turtle origins.

References
Case EC 1907. Restoration of Diadectes. The Journal of Geology. 15 (6): 556–559.
Lyson TR, Bhullar B-AS, Bever GS, Joyce WG, de Queiroz K, Abzhanov A and Gauthier JA 2013. Homology of the enigmatic nuchal bone reveals novel reorganization of the shoulder girdle in the evolution of the turtle shell. Evolution & Development 15(5):317–325. DOI: 10.1111/ede.12041
Vallén E 1942. Beiträge zur Kenntnis der Ontogenie und der vergleichenden. Anatomie des Schildkrötenpanzers. Acta Zool. Stockholm 23: 1–127.