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

Body mass allometries

The importance of metabolism for the selection of mass explains allometric transitions across the tree of life

The often observed Kleiber scaling in taxa of multicellular animals (with 1/4 and 1/6 exponents) is a special case where the final allometries resemble mass-rescaling. This is because the majority of the body mass variation evolves from the handling of different resources across a variety of niches, with only minor variation in the pre-mass component of metabolism.

Allometries on other scales include metabolic-rescaling. With an apparent 5/6 exponent for mass specific metabolism (DeLong et al., 2010), prokaryotes follow the prediction for the smallest single celled self-replicators. They are predicted to have a metabolic-rescaling exponent of unity (ββ=1) and body mass variation that follows from evolutionary differences in mass specific metabolism.

Having a b-exponent that declines from about 0.61 to -0.20 with an increasing mass (Witting, 2017), protozoa follow the prediction for larger single celled self-replicators with interactive competition and a metabolic-rescaling exponent that declines from one to zero.

And mass specific metabolism is invariant of mass on the macro evolutionary scale from prokaryotes to mammals (Makarieva et al., 2005, 2008; Kiorboe and Hirst, 2014). This follows from evolution around an upper metabolic bound, where the metabolic decline from mass-rescaling is balanced by a metabolic increase from primary selection on the net energy of the organism.


  • DeLong, J.P., J.G. Okie, M.E. Moses, R.M. Sibly and J.H. Brown 2010. Shifts in metabolic scaling, production, and efficiency across major evolutionary transitions of life. Proceedings of the National Academy of Sciences 107:12941--12945.
  • rboe and Hirst, 2014Kiorboe:Hirst:2014Kiørboe, T., and A.G. Hirst 2014. Shifts in mass scaling of respiration, feeding, and growth rates across life-form transitions in marine pelagic organisms. The American Naturalist 183:E118--E130.
  • Makarieva, A.M., V.G. Gorshkov and L.Bai-Lian 2005. Energetics of the smallest: do bacteria breathe at the same rate as whales. Proceedings of the Royal Society B 272:2219--2224.
  • Makarieva, A.M., V.G. Gorshkov, B.Li, S.L. Chown, P.B. Reich and V.M. Gavrilov 2008. Mean mass-specific metabolic rates are strikingly similar across life's major domains: Evidence for life's metabolic optimum. Proceedings of the National Academy of Sciences 105:16994--16999.
  • Witting, L. 2017. The natural selection of metabolism and mass selects allometric transitions from prokaryotes to mammals. Theoretical Population Biology 117:23--42,