How does the curvature of the upper beak bone reflect the overlying rhinotheca morphology?

The beak has independently been evolved accompanied by the edentulism in many tetrapod linages, including extant Testudinata and Aves, and its form and function have been greatly diversified. The beak is formed by beak bones and the overlying keratinous cover, although their profiles are different from each other. Therefore, it is difficult to reliably reconstruct the entire profile of the beak in extinct taxa, whose keratinous tissues are rarely preserved. For elucidation of the morphological relationship between beak bone and overlying keratinous cover, we compared the curvature distribution of the culminal profiles of the upper beak bone and the overlying keratinous cover (rhinotheca) with each other using CT-scan, in 66 extant testudinatan and avian specimens (Aves: 33 genera, 24 families; Testudinata: 12 genera seven families). In both, rhinotheca and beak bone, the curvature of the profile was nearly constant rostral to a certain point, which was defined as the transition point, and the transition points of the rhinotheca and beak bone were close to each other. The profiles of the rhinotheca and beak bone rostral to their transition point were different in curvature and length. However, the ratio between the curvatures of rhinotheca and the beak bone strongly correlated with the arc angle of the rostral culminal profiles of the beak bone. The upper beak profile in extinct taxa is expected to be reconstructed more reliably using the abovementioned relationship between the beak bone and the rhinotheca.