Sap flow, tapering of xylem conduits and optimized distribution networks in trees: the need for an overall perspective

Water transport in trees is critically dependent on lumen diameter of xylem conduits. It has also been clearly demonstrated, in both conifers and broadleaves, that the chain of conduit elements has a general tapered shape. This means that conduits in the distal parts (leaves, branches) are smaller in diameter compared to the base of the stem and root tips. This tapering is effective in reducing the increase of water resistance that would occur when trees grow taller, thus allowing a relatively constant supply of resources to leaves (i.e. constant leaf specific conductance). Two ambitious models have tried to describe the general structure that an efficient distribution network must match: West et al. (1999), with the so-called WBE model, highlighted the importance of minimizing the whole water transport resistance, via tapering, in order to maintain a given metabolic rate with ontogenesis; Banavar et al. (1999, BMR model) demonstrated that the most efficient networks are those in which the total fluid volume is as small as possible. We developed a model in order to consider both constraints (resistance and volume). We demonstrated that is not possible to achieve a closed-form mathematical solution, so a specific software was developed to solve our model. Solutions all converged to a single stable solution of constrained optimization, demonstrating that the diameter of conduits should scale with tree height with a power of about 0.18. This tapering is very similar to that measured in tall trees, thus showing that trees converge to this optimal theoretical value.