## INTRODUCTION

Leaf-level photosynthesis (*A*_{area}) is often enhanced in plants grown under long-term exposure to elevated levels of atmospheric CO_{2} ( Gunderson & Wullschleger 1994; Curtis 1996; Drake, Gonzàlez-Meler & Long 1997). This enhancement is caused by an increase in the rate of carboxylation of ribulose-1,5-bisphosphate (RuBP) catalyzed by RuBP carboxylase/oxygenase (Rubisco) ( Woodrow & Berry 1988). There are at least two fundamentally different ways in which the rate of carboxylation per unit leaf area can be modified by elevated CO_{2}. The first way, which we refer to as a ‘direct’ effect of CO_{2}, involves the biochemistry of photosynthesis. This direct effect consists of (i) a reduction in substrate limitation of Rubisco catalysis ( Farquhar, von Caemmerer & Berry 1980) (ii) competitive reduction of RuBP oxygenation ( Farquhar *et al.* 1980 ), and (iii) any adjustments in the photosynthetic apparatus (from light capture through starch and sucrose synthesis) that alter the RuBP limitation of Rubisco ( Sage, Sharkey & Seemann 1989; Sage 1990). The second way in which elevated CO_{2} may affect the rate of carboxylation per unit leaf area involves changes in leaf morphology and anatomy ( Gunderson & Wullschleger 1994; Luo, Field & Mooney 1994). These may include changes in mesophyll cell number per unit leaf area ( Vu, Allen & Bowes 1989), mesophyll thickness ( Sims, Seemann & Luo 1998), carbohydrate concentration ( Stitt 1991) and leaf mass per unit area (*LMA*) ( Curtis 1996).

During short-term exposure to elevated CO_{2}, photosynthesis is frequently limited by the capacity to regenerate RuBP. In the longer-term, the amount or activity of Rubisco may decrease, thus balancing the reduction in RuBP regeneration ( Sage 1990; Stitt 1991; Gunderson & Wullschleger 1994; Drake *et al.* 1997 ). The effect of this down-regulation of the amount or activity of Rubisco on *A*_{area} may be offset if it is associated with an increase in mesophyll tissue such that the amount of photosynthetic apparatus per unit leaf area is maintained ( Radoglou & Jarvis 1990; Luo *et al.* 1994 ). Alternatively, other changes in leaf morphology or anatomy associated with an increase in *LMA* may potentially reduce *A*_{area} since photosynthesis and *LMA* are negatively correlated at ambient CO_{2} ( Reich, Walters & Ellsworth 1997; Peterson *et al.* 1999 ). This negative correlation is independent of any effect *LMA* may have on *N*_{area} or *N*_{mass} ( Peterson *et al.* 1999 ) and may be due to a reduction in N allocation to photosynthetic versus non-photosynthetic compounds ( Evans 1989), to greater allocation of biomass to structural versus photosynthetic components ( Vitousek, Field & Mantson 1990; Lloyd *et al.* 1992 ), to reduced light penetration through the various layers of leaf tissue ( Terashima & Hirosaka 1995), or to greater limitations to internal diffusion ( Parkhurst 1994; Pachepsky *et al.* 1997 ).

While biochemical aspects of photosynthetic enhancement at elevated CO_{2} have been studied extensively, less emphasis has been placed on understanding how those enhancements interact with changes in leaf morphology and anatomy. In an important advancement, Pachepsky & Acock (1996) developed a two-dimensional model of leaf-level photosynthesis that demonstrates how leaf anatomy can have an important effect on photosynthesis. However, the general utility of this model is limited because it requires detailed maps of mesophyll cell location and information on stomatal area and density to parameterize it. Luo *et al.* (1994) developed the Photosynthetic Acclimation to CO_{2} (PAC) model which is much less data-intensive and which suggests that interactions between biochemical and morphological responses to elevated CO_{2} can have important effects on leaf-level photosynthesis. The PAC model uses the biochemical model of Farquhar *et al.* (1980) to model photosynthesis as a function of nitrogen per unit leaf area (*N*_{area}) (e.g. Harley *et al.* 1992 ). The model assumes that (i) nitrogen per unit leaf mass (*N*_{mass}) reflects the biochemical capacity for photosynthesis (e.g. Körner & Miglietta 1994) since the majority of leaf N is found in the proteins of the Calvin cycle (including Rubisco) and the thylakoid membranes ( Evans 1989) and (ii) that *LMA* summarizes aspects of leaf morphology and anatomy such as photosynthetic biomass and non-structural carbohydrate storage. The PAC model links changes in biochemical capacity and leaf morphology through the relationship *N*_{area} = *N*_{mass}×*LMA*. The model predicts that a reduction in biochemical capacity at elevated CO_{2} (estimated from a reduction in *N*_{mass}) may be counterbalanced by morphological upregulation if an increase in *LMA* is relatively greater than the reduction in *N*_{mass}. Leaf mass per unit area has been shown to be tightly correlated with leaf thickness in soybeans grown at ambient and elevated CO_{2} ( Sims *et al.* 1998 ), but there is also substantial evidence to show that increases in *LMA* at elevated CO_{2} can be caused by increased storage of non-structural carbohydrates (e.g. Roumet *et al.* 1996 ). However, if both *N*_{area} and *LMA* increase while *N*_{mass} decreases, then the increase in *LMA* must involve additional N-bearing tissue even though N concentration decreased.

The PAC model provides valuable insights into relationships between biochemical and morphological responses to elevated CO_{2} by showing how net changes in *N*_{mass} and *LMA* can interact to affect photosynthesis. However, because the PAC model focuses on net changes, it does not allow us to accurately assess the relative importance of biochemical versus morphological responses. This could be achieved by experimentally controlling *N*_{mass} or *N*_{area} in addition to *LMA*, but this is clearly impractical. An alternative approach would be to use a simple multiple regression of *A*_{area} on CO_{2} concentration, *N*_{area} and *LMA*. Since the coefficients in a multiple regression are partial derivatives, they quantify the relationship between the dependent variable (*A*_{area}) and each independent variable when the other independent variables in the equation are held constant. This allows us to statistically control both *N*_{area} and *LMA*, and to partition the response of *A*_{area} among each independent variable. Using this approach, the partial regression coefficient for CO_{2} represents an index of CO_{2} limitation of photosynthesis because it quantifies the change in *A*_{area} per unit change in CO_{2} when both *N*_{area} and *LMA* are held constant. Similarly, the partial regression coefficient for *N*_{area} represents an index of biochemical capacity per unit leaf area, and the coefficient for *LMA* represents an index of morphological regulation.

The multiple regression discussed above would provide useful information on the relative importance of the effects of CO_{2} concentration, *N*_{area} and *LMA* on photosynthesis. This model is, however, too simplistic to capture the range of interactions that are known, or that are likely to occur between these variables. To start with, both *N*_{area} and *N*_{mass} are correlated with *LMA* at ambient CO_{2} ( Reich *et al.* 1994 ; Reich & Walters 1994; Peterson *et al.* 1999 ). This lack of independence may confound parameter estimation and interpretation in the simple regression model. In addition, the response of *N*_{area}, *N*_{mass} and *LMA* to elevated CO_{2} are also likely to be correlated with each other. This complex set of correlations make it difficult to tease apart the individual responses. These correlations can, however, be dealt with using statistical control by framing the multiple regression model in the context of a structural equation model ( Hoyle 1995). A structural equation model (often referred to as path analysis or covariance structure analysis) can be specified as a system of multiple regression equations that partitions interactions among multiple dependent and independent variables (see the Methods section for details). In this paper we present a model that partitions the response of *A*_{area} to elevated CO_{2} into independent and interactive components representing changes in an index of CO_{2} limitation, an index of biochemical capacity and an index of leaf morphology. Although the model is not mechanistic, it partitions known and hypothesized relationships in a conceptually and mechanistically plausible framework based on the general concepts of the PAC model. We used this linear model to re-analyse existing data from 10 C_{3} species (three pine and seven deciduous tree species) grown at ambient and elevated CO_{2} concentrations. One aim of this study was to develop a computationally and data efficient tool for assessing the relative importance of changes in biochemical capacity and leaf morphology that could be applied to biogeochemical or biogeographic models of global change. We also compared responses across species to identify whether generalizations could be made from these data based on functional or taxonomic relatedness.