Allometric intercepts evolve from primary selection on mass specific metabolism
The mass-rescaling allometries with Kleiber scaling have a mass specific metabolism that evolves only by the rescaling of the life history with the evolutionary changes in mass. This generates a time dilation, where mass specific metabolism and net energy is constant on the per generation time-scale of natural selection, while the two energetic components are declining in physical time.
Yet the intercepts of Kleiber allometries evolve by pre-mass selection on the metabolic pace that generates net energy for self-replication. This creates an additional metabolic-rescaling where the life history is evolving from correlations with pre-mass metabolism and the dependence of the selected body mass on the net energy that is generated by the pre-mass component of metabolism.
The metabolic-rescaling exponent for mass specific metabolism (ββ•) is a function of the relative importance of mass specific metabolism for the evolution of mass. This is illustrated in Fig. 1 that shows how the exponent depends on the spatial dimensionality of intra-specific interactions (2D versus 3D), and on the selected rate of increase in metabolic pace (rββ) over the selected rate of increase in resource handling (rα).
When this pre-mass increase in metabolism is combined with the life history invariance of the selected density regulation optimum, we can use the equations of the feed-back selection to solve for the metabolic-rescaling exponents of the life history. This rescaling (Table 1) includes time periods, a population density and a lifetime reproduction that are inversely proportional, and a survival that is proportional, to the pre-mass component of mass specific metabolism.
- Witting, L. 2017. The natural selection of metabolism and mass selects allometric transitions from prokaryotes to mammals. Theoretical Population Biology 117:23--42, http://dx.doi.org/10.1016/j.tpb.2017.08.005.