Why does leaf nitrogen decline within tree canopies less rapidly than light? An explanation from optimization subject to a lower bound on leaf mass per area.

A long-established theoretical result states that, for a given total canopy nitrogen (N) content, canopy photosynthesis is maximized when the within-canopy gradient in leaf N per unit area (N(a)) is equal to the light gradient. However, it is widely observed that N(a) declines less rapidly than light in real plant canopies. Here we show that this general observation can be explained by optimal leaf acclimation to light subject to a lower-bound constraint on the leaf mass per area (m(a)). Using a simple model of the carbon-nitrogen (C-N) balance of trees with a steady-state canopy, we implement this constraint within the framework of the MAXX optimization hypothesis that maximizes net canopy C export. Virtually all canopy traits predicted by MAXX (leaf N gradient, leaf N concentration, leaf photosynthetic capacity, canopy N content, leaf-area index) are in close agreement with the values observed in a mature stand of Norway spruce trees (Picea abies L. Karst.). An alternative upper-bound constraint on leaf photosynthetic capacity (A(sat)) does not reproduce the canopy traits of this stand. MAXX subject to a lower bound on m(a) is also qualitatively consistent with co-variations in leaf N gradient, m(a) and A(sat) observed across a range of temperate and tropical tree species. Our study highlights the key role of constraints in optimization models of plant function.