Fig. 1: Schematic representation of our model, underlying first principles and notation.

a, Water-transport pathway. Purple labels indicate the three hydraulic traits that determine the conductance to water flow of each of the three segments of the water-transport pathway. Water potentials are shown at various points along the pathway: ψ_s in soil, ψ_r in roots at the beginning of the xylem segment, ψ_x at the end of the xylem segment and ψ_l in leaves near the stomata. The soil-to-leaf water potential difference Δψ = ψ_s − ψ_l thus comprises the successive pressure drops along the three segments, that is, Δψ_r = ψ_s − ψ_r along the radial outside-xylem segment within the roots, \({\Delta}\psi _\mathrm{x} = \psi _\mathrm{r} - \psi _\mathrm{x}\) along the xylem and \({\Delta}\psi _\mathrm{l} = \psi _\mathrm{x} - \psi _\mathrm{l}\) along the outside-xylem segment within the leaves. b, Model-calibration pathway. The model takes as inputs three effective whole-plant hydraulic traits (K_p, ψ₅₀ and b) together with two cost parameters (the unit costs of photosynthetic and hydraulic capacities, α and γ, respectively). It predicts as outputs the optimal values (denoted by asterisks) of stomatal conductance \(g_\mathrm{s}^ \ast\), assimilation rate A^*, transpiration E^*, acclimated photosynthetic capacities \(V_{{{{\mathrm{cmax}}}}}^ \ast\) and \(J_{{{{\mathrm{max}}}}}^ \ast\), soil-to-leaf water-potential difference Δψ^* and leaf internal-to-external CO₂ ratio χ^*. Each variable is first calculated as a function of Δψ and χ, as shown by the four light-green arrows, from which the optimal combination (Δψ^*, χ^*) is then calculated by maximizing profit F according to equation (1). Blue arrows and boxes indicate the process through which the best-fit traits and unit costs for each species are calculated by minimizing the model error. Orange labels indicate the three principles and hypotheses underlying the model, displayed next to the processes they affect.