Malthusian Relativityι**=7/3ψ
The unfolding of population dynamic feed-back selection

Mass-rescaling with biotic time dilation

Mass-rescaling dilates natural selection time to maintain fitness with a selection increase in mass

A selection increase in mass is dependent upon a mass-rescaling, where life history traits evolve in response to the increase in mass in order to avoid a secondary decline in fitness with the increase in mass.

This mass-rescaling is induced by a metabolism that trade-offs against the time that is needed to grow an offspring when the net energy of the parent has to be allocated between the mass and the metabolism of the growing offspring. The overall process of the metabolic trade-off selection is illustrated by the following causal relationship

First we have the selection induced increase in net energy [ dε/dt>0 ] that allows for the selection increase in mass [ dw/dt>0 ]. Then, from a physiological constraint between net energy, metabolism and mass (Witting, 2016) it follows that the time that is needed to grown an offspring is increasing with mass [ dtj/dt>0 ]. And from a reproductive constraint R = tr ε / tj εj, where lifetime reproduction (R) is inversely related to the juvenile period (tj) we find a fitness decline [ dR/dt<0 ] that must be avoided by selection before the selection increased in mass can occur.

A partial solution is given by the selection of an allometric rescaling where mass specific metabolism is declining with mass [ dβ/dt<0 ]. This will shorten [ dtj/dt<0 ] the juvenile period because a larger fraction of the parental energy is then allocated to the growth of the offspring at the cost of the energy that is burned by the metabolism of the offspring.

But with net energy being ε = α β we have a decline in net energy [ dε/dt<0 ] with the decline in mass specific metabolism, and given R = tr ε / tj εj this implies a decline in lifetime reproduction and fitness because the parent will no longer have the required energy available for reproduction.

This extra conflict is solved by a reproductive period that is selected to increase proportionally with the juvenile period [ dtr/dt>0 ] and inversely proportional with mass specific metabolism. This creates an increased lifetime reproduction [ dR/dt>0 ] and a physiologically invariant fitness R = tr ε / tj εj = w0 that can be selected by the selection increase in mass.


  • Witting, L. 2016. The natural selection of metabolism and mass selects allometric transitions from prokaryotes to mammals. bioRxiv