Malthusian Relativityι**=7/3ψ
The natural selection of lifeforms

Prokaryotes - the minimum self-replicating cell

Prokaryotes are selected from replicating molecules when mass specific metabolism increases super-linearly with mass

Metabolism, net energy, cell and mass: A small self-replicating cell with an internal metabolism can be selected from replicating molecules by the dependence of mass specific metabolism on mass [ β ∝ wβββ ], when the initial ββ exponent is larger than one [ ββ,0 = max(ββ) > 1 ]. The increase in net energy with an increase in metabolism with mass is then larger than the extra energy that is required by the increased mass of the offspring. The result is a selection attractor where the exponent for the pre-mass-rescaling dependence of mass specific metabolism on mass evolves to unity [ ββ**=1; Witting, 2016b].

With an efficient metabolism being dependent upon a metabolic compartment, the selection of metabolism is driving the selection of the cell and all its mass. This mass is trimmed [ w → wβ ] by the quality-quantity trade-off that selects for the β-dependent minimum mass (wβ) that is required for a functional self-replicator with a given mass specific metabolism (β). And with mass being selected as the β-dependent minimum, there is active selection for self-replicators with no more than the single cell.

This evolution of the smallest self-replicating cells is driven entirely by the mass dependence of mass specific metabolism and the counteracting selection of the quality-quantity trade-off. Although the selection of the β-dependent minimum mass is selecting for maximal population growth, a resource bias from interactive competition has not yet evolved [ ψι** = 0 ], and nor has the associated population dynamic feed-back selection (Fig. 1, right).

Fig. 1 Left: Body mass allometry for mass specific metabolism in prokaryotes, with an overall b exponent of 0.84 [DeLong et al. (2010); RMA exponent of 0.72 ±0.07 for inactive species (shown) and 0.96 ± 0.18 for active species (not shown)]. Right: A population dynamic feed-back is missing for the frequency independent selection that predicts a b exponent of 0.83 for asexual self-replicating cells. The selected β-dependent minimum mass (wβ), generates maximal population growth (r), with a density regulated (γ) abundance (n) and some interference (ι). But with undeveloped interactive behaviour and only moderate interference there is no resource bias from interactive competition [ ψι** = 0 ] and no interactive selection of mass. The coloured circles represent the home ranges of individual prokaryotes, with the dot on the ring being the self-replicator of the reproducing unit.

Allometries: With a pre-mass exponent (ββ) for mass specific metabolism that evolves to unity, the predicted allometric exponent for mass specific metabolism b = ββ + βw is 5/6 (≈0.83), as βw=-1/6 for three dimensional interactions (Witting, 1995, 2016a). This coincides with an empirically estimated exponent of 0.84 for mass specific metabolism in prokaryotes (DeLong et al., 2010; Fig. 1, left).

Life history: These minimum prokaryote like - self-replicators are predicted to be the smallest self-replicating cells to evolve by natural selection. Having a ββ exponent of unity their metabolic pathways are underdeveloped; could they evolve a larger mass (which they cannot) they could evolve more complete pathways with a higher rate of metabolism per unit mass.

With a resource bias of zero [ ψι** = 0 ] it follows that the cost of resource sharing, the two-fold cost of the male, and the two-fold cost of meiosis are selecting for asexual reproduction with reproducing units that contain a single self-replicator only (Witting, 1997, 2002).


  • 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.
  • Witting, L. 1995. The body mass allometries as evolutionarily determined by the foraging of mobile organisms. Journal of Theoretical Biology 177:129--137.
  • 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. 2002. From asexual to eusocial reproduction by multilevel selection by density dependent competitive interactions. Theoretical Population Biology 61:171--195.
  • Witting, L. 2016a. The natural selection of metabolism and mass selects allometric transitions from prokaryotes to mammals. bioRxiv
  • Witting, L. 2016b. The natural selection of metabolism and mass selects lifeforms from viruses to multicellular animals. bioRxiv