m.r.Life ι**=7/3ψ

Evolution within a niche – the accelerating mass

Body mass evolution in niches; with metabolic acceleration, maximum time contraction, and upward bend trajectories

An infinite rββ/rα-ratio generates body mass evolution with a dw/dt exponent of

x = (2d-1)/d , [3/2 in 2D, and 5/3 in 3D; Witting, 2020]

As illustrated by the red curves in Fig. 1, the resulting trajectory is bend strongly upward in physical time due to a natural selection time that contracts as

∂ ln τ / ∂ ln w = (1-d)/d , [-1/2 in 2D, and -2/3 in 3D]

Fig. 1 Lifespan (τ, left) and body mass (w, middle) evolution in physical time given intra-specific interactions in 2D. Unconstrained body mass evolution for species that are adapted to their niche follow the red curve, and it is characterised by a dw/dt-exponent of 3/2 (right). From Witting (2020).

A rββ/rα-ratio that approaches infinity can be expected for evolutionary lineages that evolve by unconstrained selection within a stable ecological niche. The handling of the resource is then optimised by natural selection, and when handling is at the selection optimum it follows that rα → 0. Net energy and mass may then continue to increase by the natural selection increase in the pre-mass component of mass specific metabolism, generating an infinitely large rββ/rα-ratio.

This fascinating increase in mass is driven entirely by a constant acceleration of the biochemical and behavioural processes; an acceleration that is generating a strong contraction of the generation time and other time periods of the organism. By speeding up the rate of net resource assimilation by increased metabolism, the individual is burning significantly more energy per unit time, but it is also generating more net energy that is first selected into population growth and then into mass by the interactive competition between the individuals in the population.


The data from MacFadden’s (1986) study on fossil horses are maybe the best long-term data for unconstrained body mass evolution within a relatively stable niche. For a time span of 57 million years he lists body mass estimates for the different lineages of fossil horses, and these provide estimates of the rate of change in body mass (dw/dt in kg per million years) as a function of mass (Fig. 2, right). With an estimated dw/dt-exponent of 1.50 (SD: ± 0.17) we find that body mass evolution in fossil horses are spot on the theoretical value of 3/2 for unconstrained 2D evolution in a stable niche (Witting, 2020).

Fig. 2 The lifespan (τ, left) and body mass (w, middle) of fossil horses, as estimated for data provided by McFadden (1986). Fossil horses have a dw/dt-exponent of 1.50 (right) that coincides with a rββ/rα-ratio of infinity, as expected for within niche evolution with optimal resource handling and unconstrained selection on the pre-mass component of mass specific metabolism. From Witting (2020).

Given these data we may calculate the life history of the horse backwards for 57 million years (Fig. 2, left). Provided that a 500 kg horse today has a lifespan around 20 years, we calculate that the 25 kg horse that lived 57 million years ago had a lifespan around 90 years. If there had been no selection on process speed, we would still have 25 kg horses that live for 90 years. And if horses had increased their size due to increased resource handling alone, the 500 kg horses of today should live for 200 years.

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.