The height of self-supporting stems ranges over six orders of magnitude, and an individual seedling may span this entire size range as it grows to old age. One obvious result is a dramatic increase in the root-to-leaf hydraulic path-length. Another is a concomitant increase in the resistance to water flow through this pathway – a feature that is illustrated, albeit too simplistically, by means of the Hagen–Poiseuille equation for capillary tubes with length *l* and radius *r* (Fig. 1a).

Assuming a constant pressure gradient, this equation predicts that the total resistance to water transport *R*_{T} is proportional to *l*/*r*^{4}. Therefore, if *r* is constant, the relationship between hydraulic resistance and path-length (a rough gauge of plant height) is linear, as predicted by the pipe-model for tree vasculature (Fig. 1b). Naturally, the biological situation is far more complex because the *l*/*r*^{4} relationship neglects other resistances (e.g. flow through bordered pits or vessel end-wall perforation plates). Nevertheless, it shows that one strategy to reduce *R*_{T} is to increase *r*.

Curiously, this is not generally observed when tracheary cell dimensions are measured along the lengths of branches or along the lengths of whole trees. For example, according to ‘Sanio's Laws’ (Sanio, 1872), tracheid length tends to increase radially (from the inside to the outside of successive annual growth rings) and distally up to some maximum height (from the base to the top of stems). Likewise, Carlquist (1975) reports that tracheary cell diameters in the most recent growth ring tend to decrease from the bottom to the top of trees. These trends likely reflect adaptive compromises to competing developmental and functional demands. For example, tracheary cell length is largely defined by the length of fusiform initals, whereas widening cell diameters to reduce hydraulic resistance can weaken mechanical tissues and increase the chances of embolism formation, particularly in branches sustaining high transpirational demands. Trade-offs between reducing hydraulic resistance and protecting against physical damage have been partially resolved by adaptive differences in the cell dimensions of early vs late wood. But the unavoidable ontogenetic extension of the hydraulic path-length, coupled with dramatic phyletic increases in plant height, undoubtedly required complex evolutionary innovations.

‘This is one of the few attempts to test some of the basic assumptions of the WBE theory.’