Updated August 6, 2019 with new taxa creating a phylogenetic update.
Polypterus, Clarias and Amia are air-breathing fish more primitive than any stem tetrapod. Any of these three could have evolved to a para-tetrapod matching these tracks during the Mid-Devonian.
discusses the quandary of Middle Devonian (397mya) tetrapod tracks (Zalchemie trackway), some with finger and toe impressions, preceding the Late Devonian (360 mya) appearance of body fossils with fingers and toes.
the large reptile tree (LRT, 1308 taxa; subset Fig. 2) provides a solution to the problem. Pholidogaster has toes (fingers not preserved, Fig. 1) yet nests basal to Panderichthys, Tiktaalik, Acanthostega and Ichthyostega. Pholidogaster (Fig. 1) is an Early Carboniferous late survivor of a Middle Devonian first attempt at terrestrial locomotion that produced no extant descendants. Essentially Pholidogaster was an osteolepid with fingers and toes that were not homologous with those found in Tulerpeton and all extant tetrapods (including frogs, salamanders, sirens and amniotes). In other words, fingers and toes were re-invented after the Middle Devonian ancestors of Pholidogaster first gave it a try in the first wave of terrestrial locomotion.
The LRT confirms Ahlberg’s proposition, “As I have previously argued, even Acanthostega may, to some degree, have been secondarily aquatic, descended from more terrestrially competent ancestors.”
The problem may be
that no one has allowed the possibility that osteolepids produced more than one lineage of limbed and toed descendants. Convergence runs rampant elsewhere. The evidence shows convergence also produced at least two sets of tetrapods, the Tetrapoda and the Paratetrapoda. They existed side-by-side after the first appearance of Tetrapoda until the extinction of the Paratetrapoda.
Ahlberg PE 2018. Early vertebrate evolution. Follow the footprints and mind the gaps: a new look at the origin of tetrapods. Earth and Environmental Science Transactions of the Royal Society of Edinburgh, 1–23.