A species-level model for metabolic scaling in trees. I. Exploring boundaries to scaling space within and across species

Metabolic scaling theory predicts how tree water flow rate (Q) scales with tree mass (M) and assumes identical scaling for biomass growth rate (G) with M. Analytic models have derived general scaling expectations from proposed optima in the rate of axial xylem conduit taper (taper function) and the allocation of wood space to water conduction (packing function). Recent predictions suggest G and Q scale with M to the ≈ 0.7 power with 0.75 as an upper bound. We complement this a priori optimization approach with a numerical model that incorporates species-specific taper and packing functions, plus additional empirical inputs essential for predicting Q (effects of gravity, tree size, heartwood, bark, and hydraulic resistance of leaf, root and interconduit pits). Traits are analysed individually, and in ensemble across tree types, to define a 2D ‘scaling space’ of absolute Q vs. its scaling exponent with tree size. All traits influenced Q and many affected its scaling with M. Constraints driving the optimization of taper or packing functions, or any other trait, can be relaxed via compensatory changes in other traits. The scaling space of temperate trees overlapped despite diverse anatomy and winter-adaptive strategies. More conducting space in conifer wood compensated for narrow tracheids; extensive sapwood in diffuse-porous trees compensated for narrow vessels; and limited sapwood in ring-porous trees negated the effect of large vessels. Tropical trees, however, achieved the greatest Q and steepest size-scaling by pairing large vessels with extensive sapwood, a combination compatible with minimal water stress and no freezing-stress. Intraspecific scaling across all types averaged Q α M0.63 (maximum = Q α M0.71) for size-invariant root-shoot ratio. Scaling reached Q α M0.75 only if conductance increased faster in roots than in shoots with size. Interspecific scaling could reach Q α M0.75, but this may require the evolution of size-biased allometries rather than arising directly from biophysical constraints. Our species-level model is more realistic than its analytical predecessors and provides a tool for interpreting the adaptive significance of functional trait diversification in relation to whole-tree water use and consequent metabolic scaling.