Sizing Up Allometric Scaling Theory
Figure 7
Influence of the location of the transition between area-preserving and area-increasing branching.
The scaling exponent α is plotted against the number of levels N̅ with area-increasing branching in the network. For each N̅ the exponent was determined from a group of artificial networks that start from a smallest organism of fixed size and span eight orders of magnitude in blood volume to the largest organism, as described in section “Finite-size corrections to 3/4 allometric scaling”. N̅ is varied from 0 (pure area-preserving branching) to the entire network (pure area-increasing). Black circles: Networks with branching ratio n = 2 and a smallest organism size of N = 25 levels. Green circles: Networks with branching ratio n = 3 and a smallest organism size of N = 16 levels. These graphs capture both finite-size effects and the effects of varying the extent of the network that is built with area-increasing branching. The exponent α changes from 3/4 to 1 as N̅ grows, which is suggested by considering a composite of Figures 3B and 4. The red circles mark the prediction of the finite-size corrected WBE model (N̅ = 24 for n = 2 and N̅ = 15 for n = 3).