Murray's law and the hydraulic vs mechanical functioning of wood

1. Murray's law states that the hydraulic conductance per blood volume of the cardiovascular system is maximized when the sum of the vessel radii cubed (Sigma r(3)) is conserved. 2. We hypothesize that Murray's law will apply to xylem conduits as long as they only transport water and do not also help support the plant. Specifically, the less volume of wood occupied by conduits, the more the conduits should conform to Murray's law. 3. We tested the applicability of Murray's law along a continuum of decreasing conduit fraction from coniferous (91% conduits) to diffuse-porous (24% conduits) to ring-porous wood (12% conduits), using anatomical and functional tests. The anatomical test compared the Sigma r(3) conservation across branch points by direct measurements of conduit radii. The functional test compared the hydraulic conductivity between branches of different ages. 4. As predicted, Murray's law was rejected in conifer wood where hydraulic function is coupled to mechanical support. The angiosperm wood did not deviate as strongly from Murray's law, especially the ring-porous type. For comparison we report previously published results from compound leaves and vines which showed general agreement with Murray's law. 5. Deviation from Murray's law was associated with fewer, narrower conduits distally causing a decrease in Sigma r(3) distally. Although less efficient hydraulically, this configuration is not top-heavy and is more mechanically stable. With the evolution of vessels and fibres, angiosperm wood can more closely approach Murray's law while still meeting mechanical requirements.