The Natural Selection of Metabolism Explains Curvature in Fossil Body Mass Evolution

Abstract

The natural selection of metabolism and mass can explain inter-specific body mass allometries from prokaryotes to mammals (Witting in Theor Popul Biol 117:23–42, https://doi.org/10.1016/j.tpb.2017.08.005, 2017a), with allometric exponents that depend on the selected metabolism and the packing of home ranges in predominately one (1D), two (2D), or three (3D) spatial dimensions. The predicted exponent for total metabolism for a 2D packing of home ranges increases from 3/4 to 7/4 when the fraction of the inter-specific body mass variation that follows from the natural selection of metabolism increases from zero to one. While a 3/4 exponent is commonly observed for inter-specific comparisons in mammals, a 7/4 exponent has so far not been reported. Yet, I detect the full range of exponents for evolution over time in the fossil record. There are no fossil data for allometric correlations between metabolism and mass, but I show that the allometry $$ \left( {\dot{w} \propto w^{{\hat{\dot{w}}}} } \right) $$ for the rate of evolution $$ \left( {\dot{w} = {\text{ d }}w/{\text{ d }}t} \right) $$ in mass (w) in physical time (t) is given by the underlying set of allometries for life history parameters, including mass-specific metabolism. The $$\hat{\dot{w}}$$ exponent describes the curvature of body mass evolution in time, with predicted values including: 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. And 1 for maximum mass across major lifeforms during 3.5 billion years of evolution along a metabolic bound. These results integrate the inter-specific allometries of existing species with a deeper understanding of their natural selection during evolutionary diversification over millions of years.