m.r.Life ι**=7/3ψ

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, 2020]

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 (2020).

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.


The maximum mass for trunked mammals evolved so fast that the increase in resource handling and/or resource availability outran the evolutionary increase in metabolic pace, with a rββ/rα-ratio of 0.1 and a dw/dt-exponent of 0.79 (Fig. 2). A rββ/rα-ratio of 0.1 is also found for the maximum mass across all species of terrestrial mammals (Witting, 2020).

Fig. 2 The lifespan (τ, left) and maximum body mass (w, middle) across trunked mammals, as estimated for data provided by Okie et al (2013). Trunked mammals have a dw/dt-exponent around 0.79 (right) that coincides with a rββ/rα-ratio that is close to zero, as predicted for fast body mass evolution during periods of evolutionary radiation. From Witting (2020).

Download publications

Evolutionary Biology 47:56-75 (2020)Download

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

Oikos 127:991-1000 (2018)Download

The natural selection of metabolism explains curvature in allometric scaling


  • Witting, L. 2020. The natural selection of metabolism explains curvature in fossil body mass evolution. Evolutionary Biology 47:56--75, https://dx.doi.org/10.1007/s11692--020--09493--y.