Malthusian Relativityι**=7/3ψ
The unfolding of population dynamic feed-back selection

Metabolic rescaling allometries

Allometric intercepts evolve from primary selection on mass specific metabolism

The mass-rescaling allometries with Kleiber scaling have a mass specific metabolism that evolves only by the rescaling of the life history with the evolutionary changes in mass. This generates a time dilation, where mass specific metabolism and net energy is constant on the per generation time-scale of natural selection, while the two energetic components are declining in physical time.

Yet the intercepts of Kleiber allometries evolve by pre-mass selection on the metabolic pace that generates net energy for self-replication. This creates an additional metabolic-rescaling where the life history is evolving from correlations with pre-mass metabolism and the dependence of the selected body mass on the net energy that is generated by the pre-mass component of metabolism.

The metabolic-rescaling exponent for mass specific metabolism (ββ) is a function of the relative importance of mass specific metabolism for the evolution of mass. This is illustrated in Fig. 1 that shows how the exponent depends on the spatial dimensionality of intra-specific interactions (2D versus 3D), and on the selected rate of increase in metabolic pace (rββ) over the selected rate of increase in resource handling (rα).

Fig. 1 The mass-rescaling exponent (green), metabolic-rescaling exponent (blue), and final allometric exponent (red) for mass specific metabolism as a function of the selected rate of increase in metabolic pace (rββ) over the selected rate of increase in resource handling (rα).

When this pre-mass increase in metabolism is combined with the life history invariance of the selected density regulation optimum, we can use the equations of the feed-back selection to solve for the metabolic-rescaling exponents of the life history. This rescaling (Table 1) includes time periods, a population density and a lifetime reproduction that are inversely proportional, and a survival that is proportional, to the pre-mass component of mass specific metabolism.Table 1 The theoretical metabolic-rescaling exponents as a function of the pre-mass exponent (ββ) for mass specific metabolism; ε:net energy; β:mass specific metabolism; τ:time periods like lifespan; p:survival; R:lifetime reproduction; r:rate of exponential increase. H:home range; N:animal abundance; ρ:resource density; From Witting (2017).


  • Witting, L. 2017. The natural selection of metabolism and mass selects allometric transitions from prokaryotes to mammals. Theoretical Population Biology 117:23--42,