Allometric aspects of population dynamics: A symmetry approach

Abstract

The maximum intrinsic rate of increase (r max ) shows a −0.25 scaling with adult body weight (W) in mammals (and others). Average adult life span (1/M) and age at maturity (α) show −0.25 scalings, independent of population size; these two lead to ther max scaling, providedR o is invariant with body size in rarified populations (=R om ). Thus ther max scaling follows from the existence of two population size symmetries (i.e. 1/M and α) and one body size symmetry (R o ). The theory provides a formula to calculate the height (A 3) of the scalingr max =A 3 ·W −0.25. The theory also helps to explain ‘Fowler's Rules’, which linkR om to the relative position of the inflection point of the population growth curve.