Heterochrony in brontothere horn evolution: allometric interpretations and the effect of life history scaling

The Brontotheriidae (Perissodactyla, Mammalia) are often used as an illustration of vertebrate macroevolutionary trends because their morphological evolution includes significant size increases accompanied by the disproportionate lengthening of bony frontonasal horns. The positive phylogenetic allometry for horn length vs. skull length is among the strongest known of such relationships in vertebrate phylogeny. Hypotheses explaining the change from small, incipient horns in Eocene ancestors to longer horns in Oligocene descendants have included two heterochronic mechanisms, hypermorphosis (extrapolation) and predisplacement (earlier onset time of horn growth). These proposed peramorphic mechanisms derive from interpretation of adult intergeneric allometries in logarithmic data spaces. Analysis of the raw (unlogged) data shows that the simple allometric model previously used is not an appropriate model for this specific problem. The heterochronic interpretations derived from them are therefore unsupported (but not disproven) by the allometries. A more appropriate allometric model for the data (full model) does not support any heterochronic interpretation. Previously unaccounted for in the heterochronic hypotheses is a complication due to body-size scaling effects on life history stage lengths. Neontological scaling patterns suggest that brontothere size increases were probably accompanied by increasing life spans and longer developmental stages. This effect broadens the types of heterochronies that may be postulated. Semiquantitative analyses comparing brontotheres with similarly sized extant ungulates show the hypothesized effect of larger size on brontothere life history stages. A scaled descendant ontogeny introduces the problem of relative vs. absolute time frames within which to view ontogenetic onset times. Thus, predisplacements, postdisplacements, or nondisplacements may be viewed as relative or absolute with respect to ancestral ontogenies. This raises a fundamental question about how development scales, which in turn affects how heterochronies are interpreted. A scaling effect suggests that brontothere horns are more likely postdisplaced in the traditional absolute time sense. Paradoxically then, while the descendant adult horn is peramorphic, its onset time may have shifted in a paedomorphic direction. Data for two Oligocene juvenile brontotheres suggest that most horn growth occurred late in their longer (i.e., descendant) ontogenies (hypermorphosis), and that the horns probably grew at faster rates (acceleration) than in Eocene taxa.