Fossil evolution bend by natural selection time

Unconstrained natural selection predicts an exponential (i.e., log-linear) increase in body mass on the per-generation timescale of natural selection. But the log-linear trajectory is bent in physical time because the timescale of natural selection evolves with the evolutionary changes in mass.

Natural selection time evolves by the inverse of mass specific metabolism, with the selection of metabolism generating part of the net energy for the natural selection of mass. The bend of body mass evolution thus reflects the importance of metabolism for the natural selection of mass. This bend is described by an allometry

d w / d t ∝ w^x

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 increase in net energy that is selected into body mass by interactive competition is generated by the organisms handling of resources, with metabolism determining the pace of handling. During fast body mass evolution, evolution in resource handling is typically outrunning the primary selection of metabolic pace. Metabolism is then evolving mainly by a secondary mass-rescaling selection that maintains the net energy of the organisms during the selection of mass. This produces the well-known Kleiber scaling, where mass specific metabolism evolves to the negative 1/4 power of mass (given 2D interactions), generating elephants that live much longer the mice. The result is time dilation, a predicted bending exponent of 3/4, and a downward bend trajectory (blue in Fig. 1) that resembles the fossil trajectories for the maximum mass of trunked, and all terrestrial, mammals.

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).

Symmetrical selection across ecological niches is another case where resource handling and metabolic pace are equally important for the selection of net energy and mass. This increased relative importance of metabolic selection produces time contraction with bending exponents of 5/4 (2D) and 9/8 (3D, Fig. 1 green). This case is observed for the evolution of a maximum mass in four mammalian clades over 30 to 64 million years.

Evolution within a niche (red) is a special case where resource handling is selected to an optimum, and net energy is increasing primarily from the selection increase in metabolic pace. This produces strong time contraction, with a 2D bending exponent of 3/2, as observed for small horses over 54 million years of evolution.

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

References

• Witting, L. 2016. The natural selection of metabolism bends body mass evolution in time. Preprint at bioRxiv https://dx.doi.org/10.1101/088997.