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.