## Does xylem follow murrays law

Given that Murray's law is applicable to xylem, we hypothesized that plants should follow the law as long as the conduits were not providing structural support. We have tested this hypothesis in compound leaves (Acer negundo, Fraxinus pensylvan-ica, Campsis radicans, and Parthenocissus quinquifolia), vine stems (C. radicans and P. quinquifolia), and shoots (Psilotum nudum) [11,14]. In leaves and Psilotum shoots, structural support of the organ is primarily from nonvascular tissues. Vines, being structural parasites, require little in the way of self-supporting tissue. When the 2r3 of the conduits in the petiolules and petioles of compound leaves were compared, they were statistically indistinguishable in four species as predicted by Murray's law (Figure 4.3). In the vine wood, one species (P. quinquefolia) complied with Murray's law and the other (C. radicans) deviated only slightly (Figure 4.4, compare y axis 2r3 ratio with Murray value of 1).

Psilotum nudum is a stem photosynthesizer, so water is transpired continuously along the length of the flow path. This means that Q (the estimated xylem flow rate) declines from the single-stemmed base of the shoot to the tips of all the branch ends. Under these conditions, Murray's law predicts that the 2r3 should diminish proportionally with Q [14]. The relative decline in Q from base to tip of Psilotum was estimated from shoot transpiration measurements, assuming steady-state conditions. Consistent with Murray's law, Q declined in direct proportion to the 2r3 from base to tip. A log-log plot gave a slope indistinguishable from the Murray's law value of 1 (Figure 4.5).

The conduit furcation numbers of the compound leaves, vines, and Ps. nudum were all between 1.12 and 1.4, meaning an average increase in conduit number of between 12 and 40% from adjacent mother to daughter ranks. To compare the relative transport efficiency of these vascular networks, we calculated their position on

0.0 0.5e+5 1.0e+6 1.5e+6 2.0e+6 2.5e+6 3.0e+6 3.5e+6 Petiolule Sr3 (|m3)

FIGURE 4.3 The sum of the conduit radii (Sr3) in petioles of compound leaves vs. the Ir3 of the petiolules they supply. Each symbol corresponds to a single leaf (Acer negundo, triangles; Fraxinus pensylvanica, circles; Campsis radicans, diamonds; and Parthenocissus quinquifolia, squares). The dashed line is a linear regression with a slope of 1.04. This is statistically indistinguishable from the Murray's law predicted slope of 1 (solid line). Data from McCulloh, K.A. et al., Nature, 421, 939, 2003.

Figure 4.2B — assuming the same "reference network" (constant volume and three bifurcating branch ranks) used to calculate the increase in the Murray optimum with F. Relative to the F = 1 value assumed by West et al., [15-17] the higher furcation numbers in leaf and vine networks show a shift toward a more efficient network (Figure 4.2B).

0.0 0.5e+5 1.0e+6 1.5e+6 2.0e+6 2.5e+6 3.0e+6 3.5e+6 Petiolule Sr3 (|m3)

FIGURE 4.3 The sum of the conduit radii (Sr3) in petioles of compound leaves vs. the Ir3 of the petiolules they supply. Each symbol corresponds to a single leaf (Acer negundo, triangles; Fraxinus pensylvanica, circles; Campsis radicans, diamonds; and Parthenocissus quinquifolia, squares). The dashed line is a linear regression with a slope of 1.04. This is statistically indistinguishable from the Murray's law predicted slope of 1 (solid line). Data from McCulloh, K.A. et al., Nature, 421, 939, 2003.

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