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

Mass rescaling allometries

Theoretical allometries agree with empirical estimates

The theoretically predicted exponents for two dimensional interactions are compared with empirical exponents for mammals, reptiles and birds in Table 1.

Table 1 Theoretical 2D exponents compared with empirical estimates for mammals, reptiles and birds. β:mass specific metabolism; τ:time periods like lifespan; N:animal abundance; H:home range; p:survival; R:lifetime reproduction; r:rate of exponential increase. For references see Witting (1997).

I have found no convincing 1D cases, but the 2D-3D-transition is supported by taxa from unicells to mammals when grouped according to empirical estimates of exponent for mass specific metabolism (Table 2). Most terrestrial and benthic taxa are classified as 2D, and pelagic taxa and primates as 3D. The 2D-3D transition is also supported by empirical estimates of the exponents for lifespan and population density (Fig. 1 and Table 3).

Table 2 Taxa grouped as 2D or 3D from empirical estimates of the exponent for mass specific metabolism. From Witting (2017).

Fig. 1 Left: The body mass (w) allometry for lifespan (T) among 195 species of terrestrial mammals where the exponents is 0.25 (SE:0.04, open circles), and among 40 species of pelagic mammals (taxa Cetacea, Pinnipedia, and Sirenia) where the exponent is 0.16 (SE:0.02, solid circles). Data from Nowak (1991); figure from Witting (1997). Right: The population density (N) allometry for 123 and 131 organisms with two- (solid circles) and three dimensional (open circles) systems, with estimated exponents of -0.79 (SE:0.09) and -0.86 (SE:0.08). Data from Pawar et al. (2012).

Table 3 The 2D-3D transition as apparent in empirical estimates of the allometric exponent for mass specific metabolism (average estimates from table 2), lifespan (mammals from Nowak, 1991), and animal abundance (from Pawar et al., 2012). From Witting (2017).


  • Nowak, R.M. 1991. Walker's mammals of the world, volume I--II. 5th ed. The Johns Hopkins University Press, Baltimore.
  • Pawar, S., A.I. Dell and V.M. Savage 2012. Dimensionality of consumer search space drives trophic interaction strengths. Nature 486:485--489.
  • Witting, L. 1997. A general theory of evolution. By means of selection by density dependent competitive interactions. Peregrine Publisher, Århus, 330 pp, URL
  • Witting, L. 2017. The natural selection of metabolism and mass selects allometric transitions from prokaryotes to mammals. Theoretical Population Biology 117:23--42,