Anapsid
The anapsids (Anapsida, from the Greek a (n), "no" and hapsids, "vault") were a subclass of amniotes that were primarily characterized by lacking fenestrations in the skull.
Together with synapsids and diapsids, they are one of three major lineages of amniotes, which diverged during the Carboniferous period. According to Tree of Life, the phylogenetic relationships of anapsids to other amniotes are as follows:
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Traditionally, anapsids were considered a monophyletic taxon, but today they are considered to include loosely related groups, having in common only the anapsid skull (without fenestrations), a plesiomorphic condition. Anapsids in the traditional sense of the word are not a clade, but rather a paraphyletic group made up of all the first reptiles that preserve the morphology of the primitive skull, grouped by the absence of temporal fossae. Recent fossil analyzes have suggested that turtles and cotylosaurs are unrelated to the other groups. For this reason, sauropsids are now divided into two new clades Parareptilia (which contains most anapsids) and Eureptilia (which includes diapsids and cotylosaurs).
Most saurops with anapsid skulls became extinct during the Permian-Triassic mass extinction; only the Procolophonidae survived, now also extinct.
Testudines
Traditionally, turtles were considered anapsids because they have the typical anapsid skull, but genetic and molecular studies began to suggest that they were related to diapsids. The discovery of fossil turtles such as Eunotosaurus, Pappochelys and Eorhynchochelys confirmed that turtles are diapsids that lost temporal fenestrae and were convergent with they. According to molecular and fossil studies, turtles form a Pantestudines clade with sauropterygians and some fossils such as Sinosaurosphargis, some of which were superficially similar to turtles but not considered related to them. The evidence that these fossil forms were ancestors of turtles is not yet clear.
Recent molecular studies place tortoises and pantestudines as a sister group to archosaurs, as it was tested using various molecular methods such as ultraconserved elements, DNA sequencing, mitochondrial DNA, microRNA and protein, however other studies based on anatomical similarities place them as close to lepidosaurs. Molecular studies suggest that turtles diverged from archosaurs or lepidosaurs and their related forms during the Permian between 300 and 265 million, by which time they had already diverged from fossil anapsids.
Most authors suggest that they classified turtles as anapsids based on their skull shape but that exact molecular studies or fossil samples had not been performed to determine their relationship. Although procolophonids managed to survive into the Triassic, most other reptiles with anapsid skulls, including milleretids, nicteroleterids, and pareiasaurs, became extinct during the Permian–Triassic mass extinction.
Synapsid opening in anapsids
Tsuji and Müller (2009) noted that the name "Anapsida" it implies a morphology (lack of temporal fossae) that is in fact absent in the skulls of a number of taxa traditionally included in the group. Several anapsids in the Parareptilia clade have been found to possess the synapsid opening or configuration, which is found in extant mammals and their ancestors, including (lanthanosuchoids, bolosaurids, mileretids, nicteroletherids, some procolophonids, and mesosaurs).
The presence of this cranial configuration in a large number of taxa makes it uncertain whether they are closely related to diapsids (also eureptiles) or synapsids. Many authors consider that the synapsid configuration in parareptiles is due to a case of convergent evolution, however it may be proof that they were related to synapsids.
Some suspicious relationships can be seen below:
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