When I kicked off this topical series, I modified the figure on the left to show the distribution of different clades (amphibamiforms are in the light pink). The general public is gradually becoming more familiar with these types of diagrams showing the relationships between different species or genera, whether through teaching in schools or PR releases. However, it's important to note that these "trees' as we often call them are not absolute, especially in paleontology. Like many other things, they are hypotheses that require repeated testing, and there's a lot of ways to quibble about how the tests should be done.

One of the main ones is what we call taxon sampling – in other words, which taxa do you include and which do you exclude. This can get more controversial than you might imagine. Some of the consideration is strictly logistical. The more taxa you sample, the more computationally intensive the analysis becomes. But some of it is more philosophical (in a personal way). For example, maybe you don't think a certain taxon is part of a group, so you don't include it. Somebody else might beg to differ. And the results can be very different as a result of that decision!

Amphibamus was named in 1865 by the well-known American palaeontologist Edward Cope from a horizon now known as the Francis Creek Shale and from a locality now known as Mazon Creek, in north-central-ish Illinois. Mazon Creek is well-known for producing a number of other important tetrapods, as well as having a very diverse invertebrate community, including the famed Tully Monster. For some reading on the amniotes of Mazon Creek, make sure to follow my friend and recently-minted doctor, Arjan Mann, who worked on the locality for his PhD dissertation! Arjan's ResearchGate can be found here. Back to Amphibamus...Cope's description (4 pages) was surprisingly long for a description of the time; a lot of other temnospondyls got a paragraph or two (no figures though). Cope immediately recognized the similarity of this form to modern amphibians, more specifically frogs and salamanders (collectively 'batrachians'). Cope speculated that the animal was capable of freely moving back and forth between water and land like many modern amphibians, hence the genus name. He also noted similarities between Amphibamus and what was at the time known as "Raniceps lyelli." The latter is an amphibamiform now properly known as Platyrhinops lyelli and has undergone its own substantial taxonomic revision (including lumping into Amphibamus), none the least of which is the fact that the original genus name 'Raniceps' was already taken by a genus of cod ironically known as the tadpole fish.

Amphibamiformes is a very new clade, having been named by Rainer Schoch in 2018 (in print in 2019). There are still some papers being published now that don't use the term. It encompasses what has traditionally been known as Branchiosauridae and Amphibamidae, the latter of which was redefined as part of the nomenclatural changes. Both of those historic clades are small-bodied dissorophoids, branchiosaurids (often "branchiosaurs" in older papers) being predominantly aquatic and known largely from Europe, and amphibamids being predominantly terrestrial and known largely from North America (both are almost exclusively Carboniferous–Permian in age). The new Amphibamiformes recognizes Branchiosauridae as a clade nested within the historical Amphibamidae following a number of papers in the last decade or so that provided a growing consensus for this, making the latter a paraphyletic grade, rather than as a sister group to branchiosaurids as was historically thought. This, among other reasons, led Schoch to combine them into Amphibamiformes, which makes an apt sister group to Olsoniformes, the large dissorophoids like the dissorophid Cacops and the trematopid Acheloma. Like Amphibamidae, the name 'Amphibamiformes' is derived from Amphibamus, one of the earliest dissorophoids to be recognized in North America (from the Carboniferous of Illinois). For a list of amphibamiforms, the Wikipedia page is up to date (probably because I made it).