Does tree wood not follow murrays law

As a further test of Murray's law, we predicted that the wood of freestanding trees should deviate from the law in proportion to how much of the wood was composed of transporting conduits. Wood holds up trees, and the more this wood is made of transporting conduits, the more these conduit walls are functioning in mechanical support — violating an assumption of Murray's law. Conifer wood is made of conduits, with over 90% of its volume in tracheids [12,34], and it should deviate the most from Murray's law by hypothesis. Ring-porous angiosperms, in contrast, have relatively few, large vessels produced in a narrow annual ring composed of nearly 10% of the wood area, the rest being fibers [12]. These trees should deviate the least. Diffuse-porous angiosperms are intermediate in wood structure and should be intermediate with respect to Murray's law. Except for the conifer species, we tested this hypothesis in wood of the same trees used for the compound leaf analysis.

The results supported the hypothesis (Figure 4.4). The conifer species, Abies concolor, had the highest fraction of wood devoted to conduit area (91%) and deviated the most from Murray's law (Figure 4.4, closed triangle). The deviation cannot be attributed to some inherent limitation of a tracheid-based conducting

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Conduit furcation number (F)

FIGURE 4.4 The ratio of the sum of the conduit radii cubed (Sr3) versus the conduit furcation number (F) for branching ranks within leaves (open symbols — petiolule vs. petiole) and across the pooled means of three to four branching ranks within stems (closed symbols). The Ir3 ratio is the most distal rank 2r3*, which was the petiolule for the angiosperm species and the petiole for the conifer species, over the 2r3 of progressively more proximal ranks. The conduit furcation number (F) was standardized to account for differences in branching architecture (McCulloh et al., Nature, 421, 939, 2003) and is always the mean for adjacent ranks. The horizontal "ML optimum" line at a Ir3 ratio of 1 is for Murray law networks where Ir3 is constant across ranks. The dashed curve is for networks where the 2r2 is constant across ranks, i.e., a constant cross-sectional area of conduits. Above this line, conduit area increases from base to tip (inverted cone), while below the line, the conduit area diminishes in the same direction (upright cone). Symbols are grand means from three to four individuals. PQ = Parthenocissus quinquefolia (vine), CR = Campsis radicans (vine), FP = Fraxinus pensyl-vanica (ring-porous), AN = Acer negundo (diffuse-porous), and AC = Abies concolor (conifer). Data are from McCulloh, K.A. et al., Funct. Ecol, 18: 931-938, 2004.

system because Ps. nudum possesses tracheids and followed Murray's law quite closely (Figure 4.5). The ring-porous species F. pensylvanica had the lowest conduit area fraction (12%) and had the lowest deviation from Murray's law (Figure 4.4, closed square). When statistics were performed on the ratio of the 2r3 of the most distal to progressively more proximal ranks on a rank-by-rank basis (as opposed to overall means reported in Figures 4.2B and 4.4), the young wood of F. pensylvanica complied with Murray's law [11]. The diffuse-porous tree (A. negundo) had an intermediate conduit area fraction (24%) and was intermediate between the ring-porous and conifer tree with respect to Murray's law (Figure 4.4, closed circle).

Interestingly, the furcation numbers for wood of these self-supporting trees were generally smaller (0.98 to 1.1) than furcation numbers in vascular tissue that was not functioning in mechanical support (1.2 to 1.4) (Figure 4.4). Furthermore, when all the data are compared, a significant correlation exists between increasing conduit furcation number and increasing convergence on Murray's law (Figure 4.4, Ref. [12]). The implications for transport efficiency are evident in Figure 4.2B where the relative hydraulic conductance from the tree wood data is compared to the vine and

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FIGURE 4.5 The sum of the conduit radii cubed (2r3) vs. the estimated xylem flow rate (Q) on a log-log plot. Murray's law predicts that Q oc 2r3, indicating a slope of 1 (solid line). The pooled slope was determined using a linear mixed-effects model (slope = 1.01) and is statistically indistinguishable from this value. Symbols indicate measurements on all shoot segments from five Ps. nudum individuals. Figure modified from McCulloh, K.A. and Sperry, J.S., Am J. Bot, 92: 985-989.

FIGURE 4.5 The sum of the conduit radii cubed (2r3) vs. the estimated xylem flow rate (Q) on a log-log plot. Murray's law predicts that Q oc 2r3, indicating a slope of 1 (solid line). The pooled slope was determined using a linear mixed-effects model (slope = 1.01) and is statistically indistinguishable from this value. Symbols indicate measurements on all shoot segments from five Ps. nudum individuals. Figure modified from McCulloh, K.A. and Sperry, J.S., Am J. Bot, 92: 985-989.

leaf data for the same reference network (Figure 4.2B, compare closed tree vs. vine and leaf data points). Not only is tree wood less efficient than the other xylem types because of its deviation from Murray's law, but it is also less efficient because of its lower furcation number. This result implies a conflict between the optimization of hydraulics vs. mechanics when the two functions are performed by vascular tissue.

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