When part of the jugal turned into the squamosal in Polypterus

Yes,
I am returning to an older post – with the addition of an overlooked taxon.

This fish cheekbone,
the homolog of the jugal in tetrapods (cyan Fig 1), grew from a small spot in Peltopleurus to a large square in even smaller Strunius (Fig 1). Then it grew larger and split into several parts in much larger taxa, like Onychodus and Holoptychius (Fig 1).

Then, a much smaller taxon in this lineage,
Polypterus, reduced this bone complex to two parts: a larger upper portion fused to the preoperculurm (cyan Fig 1) and a smaller lower portion, tucking itself below the rising postorbital (amber).

Polypterus is an extant taxon. The fused bones may not have been fused 400 million years in the Devonian, when these changes were underway.

At the next taxon in this phylogenetic tale,
in Eusthenopteron (Fig 1), the larger fused portion of the jugal takes a new name, the squamosal. Here we are getting closer to tetrapods… as everyone knows.

Figure 1. Polypterus is shown twice here to demonstrate the name change from secondary (and fused) jugal (as in ancestors) to squamosal (in descendants). These identities are based on size, shape and position. Others have sensed this, at times confusing, change. Note the label (sq) in some of the taxa above. Polypterus is not shown to scale. It is tiny by comparison, reflecting phylogenetic miniaturization, again.

In air-breathing Polypterus
(Fig 1, traditionally not recognized as the closest living relative of the more famous Eusthenopteron), a change of identify occurred in the large cheekbone: turning that part of the jugal into the squamosal.

Skull bone identities in this ongoing online study are determined based on their shape and position, always with an eye to related taxa going back to Cambrian fish and including extant tetrapods and their ancestors.

Unfortunately, fish workers invented many of their own names for the multitude of facial bones found in some fish taxa. And that served them well.

That won’t suffice in the LRT where all facial bones in all taxa have to be given tetrapod homologs because they need to be tested together (here for the first and still only time).

Even shark labial cartilages are former placoderm quadrates.

The preoperculum
(light yellow) is an exception with no homolog in tetrapods.

You might not notice
how this little cheekbone evolved to larger dimensions prior to seeing a series of related taxa together (Fig 1). Certainly I needed this sort of visual aid to understand skull bone identities. DGS colors are now used in many digitally published papers now that color is no longer the expense it once was in paper publication. DGS was first used in 2003.

Unfortunately, bichirs, like Polypterus,
have not been recognized as primitive, air-breathing, lobe-fin fish, even though they are primitive, breathe air and have lobe-fins. According to Wikipedia, “They are fresh-water fish preferring swampy, shallow floodplains and estuaries.” Phylogenetically, Wikipedia reports, “Polypterids and their fossil relatives, are considered the sister group to all other extant ray-finned fishes.”

The LRT does not support that hypothesis of interrelationships.

Polypterus bichir
(Geoffroy Saint-Hilaire 1802) is the extant Nile bichir. Given that it breathes air and can walk on land, early scientists were unsure whether this was a fish or an amphibian, then later unsure whether this was a crossopterygian or an actinopterygian. Here it nests between the Early Devonian dipnomorph, Powichthys and the mid-Devonian tetrapodomorphs, lobefins, like Eusthenopteron, that eventually produced descendants, like Trypanognathus, with small fingers and toes.

This appears to be a novel hypothesis of interrelationships.
If not, please provide a citation so I can provide it here.

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.

The break-up of one bone into many is called tessellation, the opposite of fusion.

wiki/Bichir
reptileevolution.com/polypterus.htm