Anableps, the four-eyed fish, now nests with Periophthalmus, the mud skipper

Traditionally
Anableps, the four-eyed fish (Figs 1, 2), was considered a member of the Cyprinodontiformes (tooth carps, killifish, top minnows like Fundulus). At 32 cm in length, Anableps would be the largest of that clade.

Most recently
Anableps entered the large reptile tree (LRT, 2191 taxa, Fig 3) close to Lepidogalaxias, the salamanderfish. The large eyes, rounded fins and posterior position of the pelvic fin, a primitive trait, helped inform that decision. Turns out there was a closer match with taxa that had evolved pelvic fins closer to the skull. That means a reversal may have occurred.

Here
with new identities applied to several skull bones (Fig 2) Anableps now nests with another surface fish with elevated orbits and able to breathe air, the mudskipper, Periophthalmus (Fig 3).

Mudskippers and four-eyed fish are most closely related to frogfish
among tested taxa in the LRT. That’s the problem. Superficiifally mudskippers and four-eyed fish don’t look like frogfish, but dig down to their skelelton and their interrelationships are revealed. This phylogenetic reversal to a more plesiomorphic shape could be due to phylogenetic miniaturization, which includes neotony. The hatchlings of frogfish look more like long, small-skull primitive fish, then quickly enlarge the skull to adult frogfish proportions. This is an issue that needs further study for confirmation, refutation or modification.

Anableps has been a difficult taxon to confidently nest.
It has bounced around the LRT. Three earlier posts about Anableps have been deleted in order to reduce confusion. As mentioned earlier, hundreds of thousands of corrections have been made to the LRT and the data presented at ReptileEvolution.com. Corrections will continue to be made wherever warranted. Case in point: Anableps. If it moves again, I will be surprised.

References
Bloch ME and Schneider JG 1801. M.E. Blochii, Systema Ichthyologiae iconibus cx illustratum. Post obitum auctoris opus inchoatum absolvit, correxit, interpolavit Jo. Gottlob Schneider, Saxo. Berolini. Sumtibus Austoris Impressum et Bibliopolio Sanderiano Commissum. Pp i-lx + 1-584, Pls. 1-110.
Linnaeus C 1758. Systema naturæ per regna tria naturæ, secundum classes, ordines, genera, species, cum characteribus, differentiis, synonymis, locis. Tomus I. Editio decima, reformata.
Michel KB, Aerts P, Gibb AC and Van Wassenberg S 2015. Functional morphology and kinematics of terrestrial feeding in the largescale foureyes (Anableps anableps). Journal of Experimental Biology (2015) 218, 2951-2960 doi:10.1242/jeb.124644

wiki/Periophthalmus
wiki/Four-eyed_fish_Anableps