## INTRODUCTION

Based on our understanding of the biochemical and physical processes controlling photosynthesis, sophisticated models have been developed to calculate the gas exchange between a canopy of leaves and the atmosphere if stomatal conductivity, canopy properties and atmospheric conditions are known. These models have proven relatively successful for crops, where canopy properties can be monitored with handheld devices and the response of stomata to environmental variables can be modelled empirically, based on prior observations of the given species. Natural vegetation, on the other hand, is very difficult to parameterize in these models, because it often consists of a range of species whose stomatal responses are largely unknown. In addition, both species composition and canopy structure of natural vegetation can vary widely in space and time. The application of gas exchange models that use prescribed vegetation properties becomes even more problematic if the aim is to make predictions into the future, particularly with respect to changes in climate or land use.

Cowan & Farquhar (1977) showed that it may be possible to get away from simple extrapolation of past observations if the problem is approached from a different perspective. They assumed *a priori* that plants would optimize stomatal conductivity dynamically in order to maximize total photosynthesis for a given amount of transpiration. This optimality assumption allowed them to formulate how stomatal conductivity should vary in response to the rate of photosynthesis and atmospheric water vapour deficit, given a fixed amount of water available for transpiration over a period of hours to days. However, the application of this approach at larger scales in time and space (e.g. canopies, days to years) requires detailed information about canopy properties and water availability.

Biochemical properties of foliage have been observed to adapt to environmental conditions as well, not only spatially within a canopy (Kull & Niinemets 1998; Niinemets *et al.* 1999; Niinemets, Kull & Tenhunen 2004), but also seasonally (Misson *et al.* 2006). Kull (2002) reviewed a range of models that derived theoretically optimal distributions of photosynthetic capacity in the canopy, and noted that all of these models over-predicted canopy photosynthesis and the slope of the nitrogen profile through the canopy, while under-predicting the leaf area index (*L*_{AI}). The author blamed inappropriate merit functions, oversimplified photosynthesis models and the lack of consideration of whole plant processes in the acclimation of the canopy for the discrepancy between model results and reality. Kull (2002) also stated that

Poor results in optimum modelling are not proof that optimality fails; they merely imply that the function to be maximised in a natural community remains undiscovered.

If some of the self-organizing principles of vegetation could be summarized in an appropriate merit function (or ‘objective function’ in mathematical language), this would greatly improve our ability to describe how vegetation will change in a changing environment. Furthermore, the generality of such an objective function would facilitate the construction of global models and may reduce the uncertainty associated with the extrapolation of local observations, as is the case now. However, the appropriateness of the objective function and the associated constraints can only be tested by comparison of model predictions with observations in nature.

The aim of this paper was to formulate a quantitative, general concept of vegetation optimality, and to test whether it is consistent with observations. In order to test the generality of the concept, no attempt was made to ‘fit’ the parameters in this exercise.