Models of vegetation function are widely used to predict the effects of climate change on carbon, water and nutrient cycles of terrestrial ecosystems, and their feedbacks to climate. Stomatal conductance, the process that governs plant water use and carbon uptake, is fundamental to such models. In this paper, we reconcile two long-standing theories of stomatal conductance. The empirical approach, which is most commonly used in vegetation models, is phenomenological, based on experimental observations of stomatal behaviour in response to environmental conditions. The optimal approach is based on the theoretical argument that stomata should act to minimize the amount of water used per unit carbon gained. We reconcile these two approaches by showing that the theory of optimal stomatal conductance can be used to derive a model of stomatal conductance that is closely analogous to the empirical models. Consequently, we obtain a unified stomatal model which has a similar form to existing empirical models, but which now provides a theoretical interpretation for model parameter values. The key model parameter, g 1 , is predicted to increase with growth temperature and with the marginal water cost of carbon gain. The new model is fitted to a range of datasets ranging from tropical to boreal trees. The parameter g 1 is shown to vary with growth temperature, as predicted, and also with plant functional type. The model is shown to correctly capture responses of stomatal conductance to changing atmospheric CO 2 , and thus can be used to test for stomatal acclimation to elevated CO 2 . The reconciliation of the optimal and empirical approaches to modelling stomatal conductance is important for global change biology because it provides a simple theoretical framework for analyzing, and simulating, the coupling between carbon and water cycles under environmental change.

Summary• Data from 13 long-term (> 1 yr), field-based studies of the effects of elevated CO 2 concentration ([CO 2 ]) on European forest tree species were analysed using meta-analysis and modelling. Meta-analysis was used to determine mean responses across the data sets, and data were fitted to two commonly used models of stomatal conductance in order to explore response to environmental conditions and the relationship with assimilation.• Meta-analysis indicated a significant decrease (21%) in stomatal conductance in response to growth in elevated [CO 2 ] across all studies. The response to [CO 2 ] was significantly stronger in young trees than old trees, in deciduous compared to coniferous trees, and in water stressed compared to nutrient stressed trees. No evidence of acclimation of stomatal conductance to elevated [CO 2 ] was found.• Fits of data to the first model showed that growth in elevated [CO 2 ] did not alter the response of stomatal conductance to vapour pressure deficit, soil water content or atmospheric [CO 2 ]. Fits of data to the second model indicated that conductance and assimilation responded in parallel to elevated [CO 2 ] except when water was limiting.• Data were compared to a previous meta-analysis and it was found that the response of g s to elevated [CO 2 ] was much more consistent in long-term (> 1 yr) studies, emphasising the need for long-term elevated [CO 2 ] studies. By interpreting data in terms of models, the synthesis will aid future modelling studies of responses of forest trees to elevated [CO 2 ].

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The effects of elevated atmospheric CO 2 concentration on growth of forest tree species are difficult to predict because practical limitations restrict experiments to much shorter than the average life-span of a tree. Long-term, processbased computer models must be used to extrapolate from shorter-term experiments. A key problem is to ensure a strong flow of information between experiments and models. In this study, meta-analysis techniques were used to summarize a suite of photosynthetic model parameters obtained from 15 field-based elevated [CO 2 ] experiments on European forest tree species. The parameters studied are commonly used in modelling photosynthesis, and include observed light-saturated photosynthetic rates (A max ), the potential electron transport rate (J max ), the maximum Rubisco activity (V cmax ) and leaf nitrogen concentration on mass (N m ) and area (N a ) bases. Across all experiments, light-saturated photosynthesis was strongly stimulated by growth in elevated [CO 2 ]. However, significant down-regulation of photosynthesis was also observed; when measured at the same CO 2 concentration, photosynthesis was reduced by 10-20%. Wullschleger (1993) and Ryan et al. (1994), are therefore invaluable for improving model predictions.These challenges were faced by the ECOCRAFT network, a group of laboratories conducting field-based experiments on the effects of elevated [CO 2 ] on European forest tree species. The network has existed since 1991, and the experimental results up to 1995 have been compiled by Jarvis (1998). Besford, Mousseau & Matteucci (1998) reviewed observations of photosynthetic rates in the ECOCRAFT experiments, and concluded that 'both up and down-regulation of photosynthesis has been found. Downregulation appears to be associated with either poor nutrient status or accumulation of starch, occurs more often late in the growing season and in the older needles of conifers.'The group then faced the problem of quantifying these results in such a way that they could be included in models. This problem was addressed by establishing a central relational database of model parameters (Medlyn & Jarvis 1999). The parameters required, and the methods of deriving them from experimental data, were agreed upon by project working groups comprising both experimentalists and modellers. This paper reports on the photosynthesis parameters from the database, presenting them in formats useful for modelling. First, lists of photosynthesis parameters for different species, extracted from the database, are presented. This catalogue should provide a useful resource for modellers. Second, quantitative methods (i.e. meta-analysis) are used to estimate the effects of elevated [CO 2 ] on the parameters across experiments. Different hypotheses for the effects of long-term elevated [CO 2 ] on photosynthesis are examined. This analysis aids our understanding of photosynthetic responses to elevated [CO 2 ] and suggests ways in which we can improve model formulation.Photosynthesis is a key process when stu...

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