MODELING CANOPY PRODUCTION .1. OPTIMAL DISTRIBUTION OF PHOTOSYNTHETIC RESOURCES

On the basis of detailed numerical simulations, Field (1983. Oecologia 56, 341-347) stated that total canopy photosynthesis will be a maximum for a fixed total canopy leaf nitrogen provided the derivative partial derivative A/partial derivative N, where A is photosynthetic rate and N is leaf nitrogen concentration, has the same value throughout the canopy. This paper uses the calculus of variations to formally prove Field's assertion. It shows that if the single-leaf light response is a first-degree homogeneous function of both light-saturated photosynthetic rate A(max) and intensity I of photosynthetically active radiation and if A(max) is linearly related to N, then the optimal distribution of leaf nitrogen is linearly related to the decline in I with canopy depth, and A(max) is proportional to this decline. The nature of photosynthetic gains due to optimisation of canopy nitrogen distribution is illustrated numerically for a simple model canopy. It is found that, for canopies with fixed mean leaf nitrogen, canopy photosynthesis is approximately proportional to canopy leaf area index (LAI), and the gain due to canopy optimisation compared with a uniform canopy is small for shallow canopies but pronounced for deep canopies. It is also found that, for canopies with fixed total leaf nitrogen, there is a canopy LAI which maximises canopy photosynthesis, and that this LAI and the corresponding canopy photosynthesis are approximately proportional to total canopy nitrogen.