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

Fast evolution the decelerating mass

Fast body mass evolution with time dilation and a downward bend trajectory

A rββ/rα-ratio around zero generates body mass evolution with a dw/dt exponent of

x = (2d-1)/2d , [3/4 in 2D, and 5/6 in 3D; Witting, 2016]

As illustrated by the blue curves in Fig. 1, the resulting trajectory is bend downward in physical time due a natural selection time that dilates as

∂ ln τ / ∂ ln w = 1/2d , [1/4 in 2D, and 1/6 in 3D]

Fig. 1 Lifespan (τ, left) and body mass (w, middle) evolution in physical time given intra-specific interactions in 2D. Fast body mass evolution follows the blue curve, and it is characterised by a dw/dt-exponent of 3/4 in 2D (right). From Witting (2016).

This evolution generates the typical life history correlations that we observe across the species of today, with lifespans and other biotic periods that increase to the positive 1/4 power of mass in 2D, and the positive 1/6 power in 3D. If evolution was always following this path we would, contrary to evidence, observe 1/4 and 1/6 exponents across the entire animal kingdom.

A rββ/rα-ratio around zero is expected when resource handling evolves much faster than the selected increase in the pre-mass component of mass specific metabolism. This may be the case for the largest species in an evolutionary clade that diversifies into a multitude of empty niches; especially if resource density is increasing across the gradient of niches, or if handling efficiency is increasing as a mechanistic function of the evolutionary increase in mass.


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