In deer (Cervidae), antler size is positively allometric with respect to body size. If growth were prolonged growth so as to increase body size, for example as an adaptation to cold climate, antler size would be expected to increased more dramatically.

The Irish Elk (Megaloceros) is the largest deer that ever lived, and can have an antler span of 13 feet. The Irish Elk was formerly believe to be an example of Orthogenesis, a tendency of evolution to persist in one direction past the point of functionality. It was argued that the Irish Elk became extinct because it's antlers grew too big to be supported by its neck. Analysis of the allometric equation in deer shows instead that the Irish Elk has the antler span expected for a deer of its size.