The natural selection of metabolism explains curvature in fossil body mass evolution

The natural selection of metabolism and mass can explain inter-specific allometries from prokaryotes to mammals (Witting 2017a), with exponents that depend on the selected metabolism and the spatial dimensionality (2D/3D) of intra-specific behaviour. The predicted 2D-exponent for total metabolism increases from 3/4 to 7/4 when the fraction of the inter-specific body mass variation that follows from primary variation in metabolism increases from zero to one.\n\nA 7/4 exponent for mammals has not been reported from inter-specific comparisons, but I detect the full range of allometries for evolution in the fossil record. There are no fossil data for allometric correlations between metabolism and mass, but I estimate life history allometries from the allometry [Formula] for the rate of evolution [Formula] in mass (w) in physical time (t).\n\nThe [Formula] exponent describes the curvature of body mass evolution, with predicted values being: 3/2 (2D) for within niche evolution in small horses over 54 million years. 5/4 (2D) and 9/8 (3D) for across niche evolution of maximum mass in four mammalian clades. 3/4 (2D) for fast evolution in large horses, and maximum mass in trunked and terrestrial mammals. 1 for maximum mass across major life-forms during 3.5 billion years of evolution along a metabolic bound.