## Finite-size corrections for networks with both area-preserving and area-increasing branching.

(A) As in Figure 3B, we numerically determine the scaling exponent *α* by OLS regression within a group of artificial networks spanning roughly 8 orders of magnitude in body mass (blood volume). The exponent obtained from a group is plotted against the size of the smallest network in that group (as measured by the number of capillaries, *N*_{cap,S}). Many groups are built by systematically increasing the size of the smallest network, resulting in the depicted graph. In all cases the branching ratio was *n* = 2. Black circles: numerical values. Red curve: analytical approximation, Equation 23. Green curve: Best fit to the shape of Equation 23, . (B) As in (A), except that each exponent is plotted against the number of levels *N _{S}* of the smallest network in the group from which it was determined. We display results obtained for a branching ratio

*n*= 2 (black circles) and

*n*= 3 (green circles). The red circles mark the predictions of the WBE model, since

*N*= 25 for the smallest network (a shrew, meaning

_{S}*N̅*= 24 plus 1 level for pulsatile flow) in the case of

*n*= 2, and

*N*= 16 for

_{S}*n*= 3.