Danto et al. 2018 reports,
“Despite increasing knowledge about the fossil record of lissamphibians (frogs,salamanders, and caecilians), their origin is still unresolved and different origins within Paleozoic early tetrapods are proposed.”
By contrast
the large reptile tree (LRT, 1313 taxa; subset Fig. 1) confidently recovers a monophyletic and completely resolved lissamphibia that also includes microsaurs (Fig. 1) and other non-traditional members. Utegina is close to the ancestry of frogs + salamanders + the more distantly related caecilians.

Figure 1. Subset of the LRT focusing on basal tetrapods, colorized according to chronology. Note the wide dispersal of Early Carboniferous taxa, suggesting a Late Devonian radiation as yet largely undiscovered. Utegenia is close to the ancestry of all living amphibians (in white).
The Danto team sought the answer
to their enigma not in a phylogenetic analysis, but in a study of developing salamanders. They report, “In this study, we sought to investigate if the ossification sequence of neural arches and centra and the mode of centrum formation in extinct and extant forms could be indicative of phylogenetic relationships. Here we demonstrate that the mode of centrum formation is highly variable in early tetrapods and lissamphibians and cannot be used to determine the origin of lissamphibians within early tetrapods.”
References
Danto M et al. 2018. The implication of the vertebral development on the origin of lissamphibians. SVP abstract