Using analyses that control for phylogeny, we examine whether the shapes of horns and antlers in ungulates are related to style of fighting, environmental factors, mating and social systems, or are simply arbitrary. Many of the predictions that relate horn shape to species' fighting tactics and to their mating and social systems are supported. Bovids with tips facing inwards are likely to wrestle with their horns, be monogamous and solitary, whereas those with tips facing out tend to be polygynous and live in large groups. Smooth horns are used for stabbing, and are found in females of polygynous species living in large groups. In female bovids, twisted horns are found in large species and are used in wrestling whereas, in male bovids, straight horns are found in solitary species. Finally, deer with more than five antler tines tend to be large and to fight by fencing. There was little support for shape of horns and antlers being related to environmental factors, nor were shapes arbitrary as might be expected if they had arisen through female choice. Body size had little effect on these results. In general, monogamous solitary bovids have straight inwardly facing horns whereas polygynous group-living species demonstrate a wide variety of horn shapes.
