RELATIVE GROWTH OF THE TITANOTHERE HORN: A NEW APPROACH TO AN OLD PROBLEM.

The evolution of the titanotheres (perissodactyl ungulates of the Eocene and Oligocene) has attracted considerable interest since Osborn (1929) analyzed their fossil record in great detail. This interest stems from the fact that during their short evolutionary history, which was confined largely to North America, the titanotheres exhibited polyphyletic increases in body size accompanied by striking allometric growth of bony protuberances on the preorbital surface of the skull. These curious structures are commonly termed horns, although they were probably covered with calloused skin rather than real horn (Osborn, 1929). The reasons for their origin and relative growth have been widely debated. Early in this century titanothere horns took their place alongside the coiled shell of Gryphaea, the canine teeth of the sabertooth cat, and the antlers of the Irish "elk" as structures that many orthogeneticists claimed had evolved inadaptively, leading ultimately to the extinction of their possessors. Just as it is impossible to prove that an exception exists to the competitive exclusion principle in ecology (Hardin, 1960), it cannot be proven that a morphologic structure is functionless. The possibility always remains that the true function has not been considered. Although relatively few living evolutionists might argue that the titanothere horn was without function, no functional analysis of the structure has ever been provided. In the following analysis the titanothere horn will be viewed in a new way that offers a reasonable explanation not only for its relative growth in evolution, but also for its change in shape. The arguments are strengthened by the fact that they also provide reasonable explanations for other correlated morphological trends in titanothere evolution. Titanothere horns arose as a pair of laterally adjacent, boss-like swellings in certain small Eocene forms that were ancestral to three major Oligocene subfamilies, the Brontopinae, Menodontinae, and Brontotheriinae. During the evolution of these subfamilies, the swellings tended to fuse basally, lengthen, and diverge to form a single V-shaped structure. In certain species their fused bases formed a broad trunk (Fig. 1). Growth of the horn relative to overall skull length exceeded the relative growth of almost every other biologic structure for which allometry has been recorded (see Gould, 1966). Comparing length of the horn to basilar length of the skull, Hersch (1934) calculated a k-value of about 9 for the power function y = bxl. Titanothere horns vary within and between lineages in shape as well as size, however, making Hersch's simple measurements of dubious significance. Still the polyphyletic enlargement of the horns was indeed remarkable. Osborn (1929) was so struck by the evidence he uncovered for relative growth of the horn in the three major Oligocene subfamilies that he adopted a rigid orthogenetic stand on the issue of adaptive value. He attributed the parallel trends to predetermined "germinal" tendencies that allegedly arose in a common ancestral stock, and he considered the incipient horns (Figs. 1B, 2C) to have been adaptively neutral. Although Osborn's species-level taxonomy is in need of considerable revision, his broader taxonomic conclusions are in better standing, and his interpretation that rela-