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

The evolution of curved allometries

Primary selection of metabolism bends inter-specific allometries over time

Fig. 1 A simulated unconstrained relationship between the basal metabolic rate (BMR) and body mass (w) for a mammalian like clade that evolved for 65 million years. A straight allometric line with an exponent of 0.75 is expected only in the absence of primary selection on mass specific metabolism (rββ=0). The allometry is bend to an increasing degree when rββ increases from zero (red) to 2.4x10-8 (black). From Witting (2018).

When a clade diversifies from a common ancestor into a multitude of evolutionary lineages across ecological niches, we predict the evolution of linear inter-specific allometries with 1/4 exponents in 2D, and 1/6 exponents in 3D (Witting, 2017a).

This is because the majority of the inter-specific variation in net energy originates from primary variation in the handling and/or densities of the resources in the different niches, with only a small fraction originating from evolutionary differences in the pre-mass component of mass specific metabolism. But what happens when evolution in resource handling comes to a hold as the different lineages become well adapted to their niches?

If there is no metabolic evolution we may expect a stationary distribution over time. Yet, with primary selection on mass specific metabolism, we expect that most species will show some positive background evolution in mass specific metabolism and mass. And even though this selection on metabolism and mass is expected to be mass invariant, it will affect mainly the smaller species because they evolve through a larger number of generations than the larger species (Witting, 2018). As illustrated in Fig. 1, this creates an upward bend in the lower size range of the allometry over time, with the degree of bending being dependent on the pre-generation rate of increase in the pre-mass component of mass specific metabolism.


  • Witting, L. 2017. The natural selection of metabolism and mass selects allometric transitions from prokaryotes to mammals. Theoretical Population Biology 117:23--42,
  • Witting, L. 2018. The natural selection of metabolism explains curvature in allometric scaling. Oikos xx:xx--x,