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Download paper Released 2016-11-22

Body mass evolution is bend by time

A new paper on bioRxiv shows how the natural selection of metabolism is bending body mass evolution in the fossil record by dilation and contraction of natural selection time.

Unconstrained population dynamic feed-back selection predicts an exponential increase in body mass on the per-generation time-scale of natural selection (Witting, 1997), in general agreement with fossil data where the maximum size of a clade tends to increase in a near-exponential manner during periods of phylogenetic radiation (e.g., Hayami, 1978; Smith et al., 2010; Okie et al., 2013).

The exponential increase generates a log-linear increase of mass over time, but the log-linearity is bend in physical time whenever the time-scale of natural selection is evolving with the evolutionary changes in mass. The potential bend is described by an allometry

d w / d t ∝ wx

where the rate of evolutionary change in mass (d w / d t) in physical time (t) is a power function of mass (w). The bending exponent (x) is one for unbend evolution, it is smaller than one when evolution is bend downward by a dilation of natural selection time, and it is larger than one when evolution is bend upward by a contraction of natural selection time.

The natural selection of metabolism and mass, that explains allometries (Witting, 2016a) and lifeforms (Witting, 2016b) across the tree of life, was then used to show that the bending exponent (x) evolves from the relative importance of metabolism for the evolution of mass, with the exponent being dependent also on the spatial dimensions (1D, 2D, 3D) of the interactive competition in the population.

When the importance of metabolism is insignificant we predict Kleiber scaling, where elephants live much longer the mice. For this we expect a biotic time dilation and a downward bend trajectory (blue in Fig. 1). Yet, the body mass trajectory of fossil horses is bend strongly upward (red) with an exponent of 1.50 (Witting, 1997). This indicates somewhat surprisingly that the lifespan of the horse has declined quite a bit while its mass increased from about 25 kg to 500 kg over 57 million years of evolution.

Fig. 1 Evolutionary bending by natural selection dilation (blue curve) and contraction (red and green curves) of natural selection time. Dots are time and mass scaled body mass data from the fossil record: red:horses; green:maximum mass for whales; yellow:maximum for all mobile organisms; blue:maximum for trunked mammals. Elaborated from Witting (2016c).

The analysis shows not only that the 3/2 exponent for the horse is explained by a body mass selection that was driven entirely by metabolic acceleration; but more generally that body mass evolution varies over a continuum of four modes of selection (four curves in Fig. 1); with each mode being confirmed by a unique bend of the relevant body mass trajectories in the fossil record.

The 3/2 (2D) exponent for the horse (red) is predicted for evolution within a niche, where resource handling is optimal and net energy can increase only by an increase in the metabolic pace of resource handling.

The exponent is declining to 5/4 (2D) or 9/8 (3D, green) for an unconstrained evolution where resource handling and pace are equally important for the increase in mass. This is expected as a base case for unconstrained evolution across ecological niches, and it is observed for the evolution of a maximum mass in four out of five mammalian clades across 30 to 64 million years of evolution.

The predicted exponent is declining further to 3/4 (2D, blue) or 5/6 (3D) for a fast body mass evolution, where evolution in resource handling is outrunning evolution in metabolic pace. This downward bend is found for the trajectories for the maximum mass of trunked, and all terrestrial, mammals.

An unbend trajectory, with a bending exponent of one (yellow) for 2D and 3D evolution, is predicted for evolution along a metabolic bound. And it is observed for the maximum mass of all heterotroph organisms across the entire span of 3.5 billion years of evolution on Earth.

The bend of body mass trajectories over millions of years in the fossil record is thus confirming the Malthusian Relativity hypothesis that allometries and major lifeforms are selected by the primary selection of metabolism and mass.


  • Hayami, I. 1978. Notes on the rates and patterns of size change in evolution. Paleobiology 4:252--260.
  • Okie, J.G., A.G. Boyer, J.H. Brown, D.P. Costa, S.K.M. Ernest, A.R. Evans, M.Fortelius, J.L. Gittleman, M.J. Hamilton, L.E. Harding, K.Lintulaakso, S.K. Lyons, J.J. Saarinen, F.A. Smith, P.R. Stephens, J.Theodor, M.D. Uhen and R.M. Sibly 2013. Effects of allometry, productivity and lifestyle on rates and limits of body size evolution. εm Proceedings of the Royal Society B 280:20131007.
  • Smith, F.A., A.G. Boyer, J.H. Brown, D.P. Costa, T.Dayan, S.K.M. Ernest, A.R. Evans, M.Fortelius, J.L. Gittleman, M.J. Hamilton, L.E. Harding, K.Lintulaakso, S.K. Lyons, C.McCain, J.G. Okie, J.J. Saarinen, R.M. Sibly, P.R. Stephens, J.Theodor and M.D. Uhen 2010. The evolution of maximum body size of terrestrial mammals. Science 330:1216--1219.
  • Witting, L. 1997. A general theory of evolution. By means of selection by density dependent competitive interactions. Peregrine Publisher, Århus, 330 pp, URL https://mrLife.org.
  • Witting, L. 2016a. The natural selection of metabolism and mass selects allometric transitions from prokaryotes to mammals. Preprint at bioRxiv https://dx.doi.org/10.1101/084624.
  • Witting, L. 2016b. The natural selection of metabolism and mass selects lifeforms from viruses to multicellular animals. Preprint at bioRxiv https://dx.doi.org/10.1101/087650.
  • Witting, L. 2016c. The natural selection of metabolism bends body mass evolution in time. Preprint at bioRxiv https://dx.doi.org/10.1101/088997.