Updated April 3, 2023
with more taxa.
The Nile bichir
(genus: Polypterus; Fig. 1) is a small, long-bodied, extant fish at home in hot, swampy, oxygen-starved waters. It has lungs, but no trachea. It breathes through a spiracle. Juveniles have large, pink external gills for breathing underwater. For decades, the big question has been: “What is it?”
According to Wikipedia,
“Polypterus was discovered, described, and named in 1802 by Étienne Geoffroy Saint-Hilaire. It is a genus of 10 green to yellow-brown species. Naturalists were unsure whether to regard it as a fish or an amphibian. If it were a fish, what type was it: bony, cartilaginous, or lungfish? Some regarded Polypterus as a living fossil, part of the missing link between fishes and amphibians, helping to show how fish fins had evolved to become paired limbs.”

Figure 1. The Nile bichir (Polypterus), skull, skeleton and bones colorized for ease of comparison. Compare to the placoderm, Entelognathus, (Fig. 2) and the stem tetrapod Tinirau (Fig. 3).
Surprisingly,
when added to the large reptile tree (LRT, 1447 taxa then, 2223 taxa now) Polypterus did not nest with the distinctly different basal actinopterygian, Cheirolepis, but with lungfish. Thus, Polypterus is a very ancient fish, going back to the Early Devonian.
Romer (1946) wrote (quoted from Wikipedia),
“The weight of Huxley’s opinion is a heavy one, and even today many a text continues to cite Polypterus as a crossopterygian and it is so described in many a classroom, although students of fish evolution have realized the falsity of this position for many years…. Polypterus…is not a crossopterygian, but an actinopterygian, and hence can tell us nothing about crossopterygian anatomy and embryology.” If this were true, Polypterus would have nested with the actinopterygians in the LRT.
Hall (2001) reported,
“Phylogenetic analyses using both morphological and molecular data affirm Polypterus as a living stem actinopterygian.” Remember, a ‘stem’ actinopterygian, by definition, is not an actinopterygian. It’s something else preceding that clade. Currently Polypterus cannot have its genes tested against any other placoderms or crossopterygians, but we can include this taxon in trait analysis.
So often
paleontologists keep looking, too often in frustration, where they think a taxon should nest (e.g pterosaurs as archosaurs, caseids as synapsids, whales as artiodactyls, etc.), instead of just letting the taxon nest itself in a wide gamut analysis, like the LRT. It’s really that easy and you can be confident of the results because all other candidates are tested at the same time.

Figure 3. The stem tetrapod, Tinirau. Compare to Polypterus (Fig. 1) and Entelogenathus (Fig. 2).
So, where does that leave the basal actinopterygian, Cheirolepis?
In the LRT, Cheirolepis nests with other paleoniscids.
Placoderms had fleshy fins.
The pectoral fins of Cheirolepis remained lobe-like, while the pelvic fins lost their lobes. That’s the progression, not the other way around.
If you see a fish with great distance
between the pectoral and pelvic fins (e.g. Polypterus, sharks, sturgeons, paddlefish, etc.) it is primitive. In Cheirolepis the distance is shortening. In many derived fish, the pelvic girdle is just beneath the gills. Very strange, when you think about it.
Not only can Polypterus breathe air,
it can lift its chest off the substrate with its robust forelimbs (Fig. 5). It can survive on land for several months at a time. Now those Middle Devonian trackmakers no longer seem so outlandish.
The three flathead fish, Entelognathus, Polypterus and Tinirau,
lead directly to Panderichthys, Tiktaalik and other flattened basal tetrapods.
That makes Polypterus,
like Didelphis, Caluromys and Lemur, a living representative close to the direct lineage of tetrapods, mammals, primates and humans.
If you’re interested in Polypterus
the above YouTube videos will prove enlightening.
References
Geoffry Saint-Hillaire E 1802. Description d’un nouveau genre de poisson, de l’ordre des abdominaux. Bull. Sci. Soc. Philom., Paris, 3(61):97-98.
Hall BK 2001. John Samuel Budgett (1872-1904): In Pursuit of Polypterus, BioScience 51(5): 399–407.
Romer AS 1946. The early evolution of fishes, Quarterly Review of Biology 21: 33-69.
wiki/Polypterus
wiki/Tinirau
wiki/Cheirolepis
wiki/Entelognathus