Table 1.

Predicted scaling exponents for physiological and anatomical variables of plant internal networks as a function of branch radius (r_ext,k) for our model and the WBE model

Internal network property	WBE model exponent for rext,k	Our model exponent for rext,k	Observed average cross-species exponent from the literature for rext,k	Observed average cross-species exponent for all measured trees for rext,k (radial and axial data combined)	Observed average cross-species exponent for all measured trees for rext,k (axial data only)
Packing (conduit frequency vs. conduit radius, rint,k, not branch radius)	n.s.	−2	−2.04 (−2.74, −1.34)	−2.16 (−3.35, −0.97)	−1.86 (−2.91, −0.81)
Conduit radius taper (rint,k)	1/6 ≈ 0.17	1/3 ≈ 0.33	0.27 (0.20, 0.34)	0.29 (0.08, 0.50)	0.34 (0.04, 0.64)
Conduits in branch segment ()	2	4/3 ≈ 1.33	n.d.	1.19 (0.86, 1.52)	1.03 (0.11, 1.95)
Fluid velocity (uk)	−1/3	0 or n.s.	n.s.	n.m.	n.m.
Conducting-to-nonconducting ratio	1/3	0 or n.s.	n.d.	0.00 (−0.88, 0.88)	0.13 (−0.66, 0.92)
Network conductance (κk)	2	1.84 (finite)	1.44 (ref. 12)	n.m.	n.m.
		2 (infinite)
Branch segment conductivity (Kk)	8/3 ≈ 2.67	8/3 ≈ 2.67	2.78 (ref. 12)	n.m.	n.m.
Leaf-specific conductivity (Kk/Nleaves)	2/3 ≈ 0.67	2/3 ≈ 0.67	2.12 (−1.38, 5.62)	n.m.	n.m.
Volume flow rate (Qk)	2	2	1.77 (1.38, 2.16)	n.m.	n.m.
Pressure gradient along branch segment ()	−2/3	−2/3	n.d.	n.m.	n.m.
Branch segment conductance (Zk/Nint,k)	2	2	n.d.	n.m.	n.m.

Observed values for average cross-species scaling exponents [mean, 95% confidence intervals using standardized major axis (SMA) regression] are shown for literature data and our measurements for oak, maple, and pine. n.d., no data found; n.m., not measured; n.s., nonsignificant.