Malthusian Relativityι**=7/3ψ
Population dynamics - the evolutionary extension

Population limitation

The population dynamic equilibrium of selection-delayed dynamics explains the exponents of body mass allometries

The population dynamic equilibrium of selection-delayed dynamics is the competitive interaction fix-point for the selection attractor on mass. This selection is optimising the home range to minimise the overall regulation [ fι fs ] of the counteracting forces of interference competition (fι) and local resource exploitation (fs). On top of this there is selection for a population density where the interference between the individuals in the optimal home ranges is matching the level of the competitive interaction fix-point that defines the selection attractor on mass (Fig. 1).

Fig. 1 The optimal home range is selected to minimise the joint regulation by interference competition and local resource exploitation (green arrows), and the population dynamic feed-back is selecting the population density where the level of interference that is generated by individuals in optimal home ranges is matching the level of the competitive interaction fix-point that defines the selection attractor on mass (red arrows). From Witting (2016b).

This selection based population dynamic equilibrium is not only part of the allometric solution for life history and ecological traits like mass, metabolism, abundance and home range. It is the very key for the allometric correlations, as it is the selected invariant density regulation

f = fe fι fs = fe(Nwβ) fι(NVH(d-1)/d) fs(βH1/d/V) ∝ w0

that determines the exponents of the body mass allometries (Witting, 1995, 2016a). Damuth's (1981, 1987) -3/4 power decline in abundance with mass is following as an essential prediction from selection-delayed dynamics in two spatial dimensions, while the corresponding exponent for three dimensional dynamics is -5/6 (see the Metabolism and Mass section of mrLife.org).

It is suggested that it is this selection constraint for population densities with invariant interference competition that generates a green world; where overexploited resources are rare because natural species have evolved intermediate growth rates with intermediate population densities. With the invariant interference being the fix-point of natural selection there is a balanced life history, where an abundance decline from increased mortality is selecting for a reallocation of energy from mass to reproduction, with the abundance increasing back towards the competitive interaction fix-point.

References

  • Damuth, J. 1981. Population density and body size in mammals. Nature 290:699--700.
  • Damuth, J. 1987. Interspecific allometry of population density in mammals and other animals: the independence of body mass and population energy-use. Biological Journal of the Linnean Society 31:193--246.
  • Witting, L. 1995. The body mass allometries as evolutionarily determined by the foraging of mobile organisms. Journal of Theoretical Biology 177:129--137.
  • Witting, L. 2016a. The natural selection of metabolism and mass selects allometric transitions from prokaryotes to mammals. bioRxiv http://dx.doi.org/10.1101/084624.
  • Witting, L. 2016b. The natural selection of metabolism and mass selects lifeforms from viruses to multicellular animals. bioRxiv http://dx.doi.org/10.1101/087650.