Our results bear on the venerable "rule" first postulated by Da Vinci that trees show area-preserving branching, meaning that the collective cross-sectional area of trunk, major branches, and minor branches is the same [27, 41]. Measurements generally confirm this rule, at least within the branches of the canopy [32,42]. Da Vinci based his rule on the explicit assumption that flow velocities were equal throughout the tree [13,41] and implicitly that branch cross-sectional area was proportional to the area of the water-conducting conduits. Neither of these assumptions must be true from first principles, nor are they true in fact. So why do trees tend to follow this rule? We suggest that trees follow Da Vinci's area-preserving branching pattern because it is the best compromise between opposing demands of hydraulics (area-increasing conduit networks) and mechanics (area-decreasing branching of wood in total).
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