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Functions of the horns and frill

There has been much speculation over the functions of Triceratops ' head adornments. The two main theories have revolved around use in combat and in courtship display, with the latter now thought to be the most likely primary function.

Early on, Lull postulated that the frills may have served as anchor points for the jaw muscles to aid chewing by allowing increased size and power for the muscles. This has been put forward by other authors over the years, but later studies do not find evidence of large muscle attachments on the frill bones.

Triceratops were long thought to have used their horns and frills in combat with large predators, such as Tyrannosaurus, the idea being discussed first by Charles H. Sternberg in 1917 and 70 years later by Robert Bakker. There is evidence that Tyrannosaurus did have aggressive head-on encounters with Triceratops, based on partially healed tyrannosaur tooth marks on a Triceratops brow horn and squamosal. The bitten horn is also broken, with new bone growth after the break. Which animal was the aggressor, however, is unknown. Paleontologist Peter Dodson estimates that, in a battle against a bull Tyrannosaurus, the Triceratops had the upper hand and would successfully defend itself by inflicting fatal wounds to the Tyrannosaurus using its sharp horns. Tyrannosaurus is also known to have fed on Triceratops, as shown by a heavily tooth-scored Triceratops ilium and sacrum.

In addition to combat with predators using its horns, Triceratops are popularly shown engaging each other in combat with horns locked. While studies show that such activity would be feasible, if unlike that of present-day horned animals, there is disagreement about whether they did so. Although pitting, holes, lesions, and other damage on Triceratops skulls (and the skulls of other ceratopsids) are often attributed to horn damage in combat, a 2006 study finds no evidence for horn thrust injuries causing these forms of damage (with there being no evidence of infection or healing). Instead, non-pathological bone resorption, or unknown bone diseases, are suggested as causes. A newer study compared incidence rates of skull lesions and periosteal reaction in Triceratops and Centrosaurus, showing that these were consistent with Triceratops using its horns in combat and the frill being adapted as a protective structure, while lower pathology rates in Centrosaurus may indicate visual use over physical use of cranial ornamentation or a form of combat focused on the body rather than the head. The frequency of injury was found to be 14% in Triceratops. The researchers also concluded that the damage found on the specimens in the study was often too localized to be caused by bone disease. Histological examination reveals that the frill of Triceratops is composed of fibrolamellar bone. This contains fibroblasts that play a critical role in wound healing and is capable of rapidly depositing bone during remodeling.

One skull was found with a hole in the jugal bone, apparently a puncture wound sustained while the animal was alive, as indicated by signs of healing. The hole has a diameter close to that of the distal end of a Triceratops horn. This and other apparent healed wounds in the skulls of ceratopsians has been cited as evidence of non-fatal intraspecific competition in these dinosaurs. Another specimen, referred to as "Big John", has a similar fenestra to the squamosal caused by what appears to be another Triceratops horn and the squamosal bone shows signs of significant healing, further vindicating the hypothesis that this ceratopsian used its horns for intra-specific combat.

The large frill also may have helped to increase body area to regulate body temperature. A similar theory has been proposed regarding the plates of Stegosaurus, although this use alone would not account for the bizarre and extravagant variation seen in different members of Ceratopsidae, which would rather support the sexual display theory.

The theory that frills functioned as a sexual display was first proposed by Davitashvili in 1961 and has gained increasing acceptance since. Evidence that visual display was important, either in courtship or other social behavior, can be seen in the ceratopsians differing markedly in their adornments, making each species highly distinctive. Also, modern living creatures with such displays of horns and adornments use them similarly. A 2006 study of the smallest Triceratops skull, ascertained to be a juvenile, shows the frill and horns developed at a very early age, predating sexual development and probably important for visual communication and species recognition in general. The use of the exaggerated structures to enable dinosaurs to recognize their own species has been questioned, as no such function exists for such structures in modern species.