Skull roof
The skull roof, or the roofing bones of the skull, are a set of bones covering the brain, eyes and nostrils in bony fishes and all land-living vertebrates. The bones are derived from dermal bone, hence the alternative name dermatocranium. More or less incorporated in the skull roof is the upper jaw and the endocranium.
Origin
The early armoured fish did not have a skull in the common understanding of the word, but had an endocranium that was partially open above, topped by dermal bones forming armour. The dermal bones gradually evolved into a fixed unit overlaying the endocranium like a heavy "lid", protecting the animal's head and brain from above. Cartilaginous fish whose skeleton is formed from cartilage lack a continuous dermal armour and thus have no proper skull roof. A more or less full shield of fused dermal bones was common in early bony fishes of the Devonian, and particularly well developed in shallow water species.
Bony fishes and amphibians
In early sarcopterygians the skull roof was composed of numerous bony plates, particularly around the nostrils and behind each eye. The skull proper was joined by the bones of the operculum. The skull itself was composed rather loosely, with a joint between the bones covering the brain (the parietal bones and the bones behind them) and the snout (the frontal bone, nasal bone and the bones in front and to the side of them). This joint disappeared in the evolving labyrinthodonts, at the same time the number of bones were reduced and the operculum disappeared.