m.r.Life ι**=7/3ψ

Metabolic rescaling allometries

The intercepts of body mass allometries evolve from the primary selection of 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 timescale 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).


Evidence on the scaling of the intercepts of traditional Kleiber allometries is not as clear as for the mass-rescaling exponents. But with ectotherms having field metabolic rates that are 12 to 20 times smaller than in similar sized endotherms (Nagy, 2005), we expect ectotherms to have longer lifespans and to be more abundant than similar sized endotherms, and this is generally the case (Peters, 1983; Currie and Fritz, 1993; de Magalhaes et al., 2007). The predicted inverse relationship between lifetime reproduction and the mass-rescaling intercept for mass specific metabolism is also in agreement with fecundity estimates that are about ten times higher in reptiles than in mammals (Peters, 1983) reflecting, as predicted, a higher probability to survive to reproduce in mammals.

Other evidence on the metabolic-rescaling of the life history is related to the transitions in the overall exponent for mass specific metabolism across the tree of life (see next section on final body mass allometries).

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Theoretical Population Biology 117:23-42 (2017)Download

The natural selection of metabolism and mass selects allometric transitions from prokaryotes to mammals


  • Currie, D.J., and J.T. Fritz 1993. Global patterns of animal abundance and species energy use. Oikos 67:56--68.
  • es etal., 2007de:Magalhaes:Costa:2007DeMagalhaes, J.P., J.Costa and G.M. Church 2007. An analysis of the relationship between metabolism, developmental schedules, and longevity using phylogenetic independent contrasts. Journal of Gerontology: Biological Sciences 62A:149--160.
  • Nagy, K.A. 2005. Field metabolic rate and body zise. Journal of Experimental Biology 208:1621--1625.
  • Peters, R.H. 1983. The ecological implication of body size. Cambridge University Press, Cambridge.
  • Witting, L. 2017. The natural selection of metabolism and mass selects allometric transitions from prokaryotes to mammals. Theoretical Population Biology 117:23--42, https://dx.doi.org/10.1016/j.tpb.2017.08.005.