Malthusian Relativityι**=7/3ψ
The bend of evolutionary time

Maximum animal mass over 3.5 billion years of evolution at the metabolic limit

A bound on mass specific metabolism generates body mass evolution that is unbend and log-linear

Given constant selection for an increase in mass specific metabolism, we may expect macro evolution at the largest scale to reach some biochemical limit where further increase in mass specific metabolism is difficult, if not impossible, to obtain.

Evolution at this limit will proceed with a mass that increases from primary selection on resource handling and/or increased resource availability. The increase in mass will generate an allometric downscaling of mass specific metabolism away from the upper limit. And if the primary increase occurs relatively slow, this will allow for a selection increase that will return mass specific metabolism to the upper limit. This form of evolution follows the yellow curves in Fig. 1, and it is log-linear in physical time with a dw/dt-exponent of one in both 2D and 3D, and a rββ/rα-ratio of 1/2 in 2D, and 1/4 in 3D.

These trajectories balance the upward bending from time contraction due to metabolic acceleration against the downward bending from the time dilation of mass-rescaling, with no overall bend in physical time.

Fig. 1 Lifespan (τ, left) and body mass (w, middle) evolution in physical time given intra-specific interactions in 2D. Evolution along an upper biochemical limit on mass specific metabolism follows the yellow curve that is characterised by a dw/dt-exponent of unity (right). From Witting (2016).


  • Witting, L. 2016. The natural selection of metabolism bends body mass evolution in time. Preprint at bioRxiv