Latest pterosaur cladogram fails on many levels

Buchmann and Rodrigues 2019
studied skeletal pneumatization in pterosaurs then mapped their results on a painfully antiquated pterosaur cladogram (Fig. 1, based on their mentor, Kellner 2003) that includes the basal crocodylomorph, Scleromochlus, and the basal dinosaur, Herrerasaurus as outgroup taxa.

It is embarrassing
when pterosaur experts do not know what pterosaurs really are: fenestrasaur tritosaur lepidosaurs (not archosaurs). Scleromochlus has vestigial hands that lack digit 4 and feet that lack digit 5. These traits alone do not invalidate Scleromochlus as an appropriate ancestor, and Herrerasaurus is just as bad. Pterosaur ‘experts’ are strangely content with ignoring the four cladograms in Peters 2000 that nested tiny Cosesaurus, Sharovipteryx and Longisquama closer to pterosaurs than any archosaur, simply by taxon inclusion.

When you add more pterosaurs to your cladogram
(link to cladogram here) you recover Bergamodactylus and other Triassic pterosaurs (missing in Fig. 1) at the base. The first dichotomy splits dimorphodontids + anurognathids from eudimorphodontids + all other pterosaurs. After several nodes four clades produce ‘pterodactyloid’-grade pterosaurs by convergence after phylogenetic miniaturization. Two (azdarchids and ctenochasmatids) arise from distinct tiny Dorygnathus specimens. Two others (cycnorhamphids + ornithocheirids and pterodactylids + germanodactylids) arise from tiny Scaphognathus descendants. Darwinopterus and kin are strangely absent from Fig.1 (probably because it was based on Kellner 2003). The Pterodactylus clade + the Nyctosaurus clade arise directly from Rhamphorhynchuswhile the toothy Ornithocheiridae arise from the toothless Nyctosaurus and Nemicolopterus.

Buchmann and Rodrigues break the first rule of cladogram building:
1. All sister taxa must demonstrate and document a gradual accumulation of derived traits.

And they break the second rule:
2. Outgroup taxa at every node must have plesiomorphic traits capable of evolving into the derived traits of derived members.

Clearly these two authors did not check their results.
Their referees and editors also bear part of the blame here. Putting out invalid data gives PhDs in paleontology a bad name. Their peers should have pointed this out before an amateur with no academic background in science exposed those blatant errors. At least the authors did not include the phytosaurs as outgroup taxa, as recovered by so many other workers, like Nesbitt 2011.

It goes without saying:
without a valid family tree the work Buchmann and Rodrigues did with pneumatic foramina was largely a waste of time. If they were looking for patterns they were starting with disorder. These two should redo their study with a valid and comprehensive tree topology.

The large pterosaur tree (LPT) currently includes 238 taxa, validated outgroups, several embryos/hatchlings and dozens of tiny pterosaurs, only some of which are juveniles. The LPT does not break the rules of cladogram building.

References
Buchmann R and Rodriques T 2019. The Evolution of Pneumatic Foramina in Pterosaur Vertebrae.Anais da Academia Brasileira de Ciências 91: e20180782.
DOI 10.1590/0001-3765201920180782.
Kellner AWA 2003. Pterosaur phylogeny and comments on the evolutionary history of the group. Geological Society Special Publications 217: 105-137.
Peters D 2000b. A Redescription of Four Prolacertiform Genera and Implications for Pterosaur Phylogenesis. Rivista Italiana di Paleontologia e Stratigrafia 106 (3): 293–336.