Optimizing the Canopy Photosynthetic Rate by Patterns of Investment in Specific Leaf Mass

Given the total leaf mass per ground area in a laterally homogeneous vegetative canopy (of a crop, even-aged stand, or clonal plant), how should this mass be distributed with depth to maximize the canopy's photosynthetic rate? That is, how should the specific leaf mass, m (mass per unit of leaf area), vary with cumulative-leaf-area index, L? We present a formal solution using the calculus of variations, an analytical solution for simple cases, and general numerical methods. The predicted optimal gradients in m(L) are large but broadly comparable with those seen in field crops. Optimizing m(L) gives typically 5% greater photosynthesis than the best possible choice of a constant m(L). More significantly for competitive growth, optimizing m(L) upholds canopy photosynthesis down to very low average m; hence, it allows a high leaf-area index and attendant capacity to shade competitors. Photosynthetic gains from m(L) optimization are remarkably insensitive to leaf angle. Equally surprisingly, daily average canopy photosynthesis is also predicted to be insensitive to leaf angle, contrary to the predictions of earlier models. The accuracy of accounting for diffuse skylight interception appears crucial. We further analyze the ecological and agricultural significance of leaf angle, and we outline research needs for related problems of light interception, canopy developmental patterns, water-use efficiency, and nitrogen-use efficiency.