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

Evolution across niches the symmetrical case

Body mass evolution across niches, with time contraction and upward bend trajectories

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

x = 3(2d-1)/4d , [9/8 in 2D, and 5/4 in 3D; Witting, 2016]

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

∂ ln τ / ∂ ln w = (3-2d)/4d , [-1/8 in 2D, and -1/4 in 3D]

Fig. 1 Lifespan (τ, left) and body mass (w, middle) evolution in physical time given intra-specific interactions in 3D. Unconstrained evolution across niches follow the green curve, and it is characterised by a dw/dt-exponent of 5/4 (right). From Witting (2016).

For this selection we have a generation time that is declining with mass with a -1/8 exponent in 2D (-1/4 in 3D), instead of increasing with the familiar 1/4 exponent (1/6 in 3D). This change of sign in the evolutionary direction of time is induced by the selected acceleration of mass specific metabolism that is generating half of the energy for the selection increase in mass.

A rββ/rα-ratio around unity is given by symmetrical unconstrained evolution in resource handling and metabolic pace. This is the expected base case for the evolution of maximum size in a taxonomic group that is diversifying with speciation across ecological niches. This evolution includes selection on the handling of new resources, and it allows larger species to evolve as lineages diversity into new niches where an increased resource exploitation is possible. Representing this form of diversifying evolution, a rββ/rα-ratios around unity is expected for the evolution of maximum body mass in phylogenetic clades.


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