Selection of metabolism, mass & allometries

The predicted exponents for inter-specific allometries, as they are determined by the spatial dimensionality of the foraging ecology and the pre-mass exponent for mass specific metabolism: β:mass specific metabolism; β_β:pre-mass component of β; α:resource handling; τ:time periods; p:survival; R:lifetime reproduction; r:population dynamic growth rate; h:home range; n:abundance. From Witting (2016).

It is difficult to overestimate the importance of inter-specific allometries for our understanding of evolution, as the allometric exponents reveal the correlated evolution between the life history and mass. This correlation is not restricted to well-known Kleiber scaling, where the exponent is -1/4 for the allometry between mass specific metabolism and mass. The metabolic exponent is instead increasing on a macro evolutionary scale with a decline in mass, over an apparent body mass invariance in unicellular eukaryotes, to a strongly positive value of about 0.84 in prokaryotes (Makarieva et al., 2008; Delong et al., 2010).

This change indicates a change in the mechanisms of natural selection across the tree of life. And by integrating the primary selection of metabolism into the natural selection of mass and allometries (Witting, 1995, 2008), I find that a change in the importance of mass specific metabolism for the selection of mass is explaining allometric transitions from prokaryotes over larger unicells to multicellular animals.

The study finds that mass specific metabolism is selected as the pace (speed) of the resource handling that generates net energy for self-replication, with mass being selected as a function of the average net energy in the population. The evolved mass is then a joint function of the mass specific metabolism and resource handling that generates net energy for self-replication, with the allometric exponents for mass specific metabolism across a set of species increasing with the importance of mass specific metabolism for the generation of the essential net energy.

This mechanism explains the range of exponents that are observed from prokaryotes to mammals (Table 1). A positive 5/6 exponent is predicted for prokaryotes with three dimensional ecology given body mass variation that evolves from primary variation in mass specific metabolism. A negative 1/4 exponent is predicted for multicellular animals with two dimensional ecology given body mass variation that evolves from adaptations to ecological niches. And an observed decline in the exponent (from 0.61 over 0 to -0.20) with an increase in the mass of protozoa, is predicted from a gradual decline in the importance of mass specific metabolism for the selection of mass.

It is concluded that the primary selection of metabolism and mass is the only thing that is needed to explain the broad-scale evolution of body mass allometries from prokaryotes over larger unicells to multicellular animals.

References

• 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.
• 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. εm Proceedings of the National Academy of Sciences 105:16994--16999.
• Witting, L. 1995. The body mass allometries as evolutionarily determined by the foraging of mobile organisms. Journal of Theoretical Biology 177:129--137, https://doi.org/10.1006/jtbi.1995.0231.
• Witting, L. 2008. Inevitable evolution: back to The Origin and beyond the 20th Century paradigm of contingent evolution by historical natural selection. Biological Reviews 83:259--294, https://doi.org/10.1111/j.1469--185X.2008.00043.x.
• Witting, L. 2016. The natural selection of metabolism and mass selects allometric transitions from prokaryotes to mammals. Preprint at bioRxiv https://dx.doi.org/10.1101/084624.