Abstract
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.
A 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 
for the rate of evolution 
in mass (w) in physical time (t).
The 
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.
