Description of the Structural Equation Modelling (SEM) approach and

modelling to investigate the networks of connections among components that contribute to leaf photosynthetic enhancement in elevated CO2 in these herbaceous plants. The

approach helped us examine complex cause-effect hypotheses about the mechanisms driving this photosynthetic enhancement. Photosynthetic enhancement in eCO2 was

examined both as an enhancement ratio and as an absolute difference, with very similar results between these two focal variables.

I specified a formal model that included two environmental inputs (any pair of precipitation, temperature and soil water content) and several physiological variables associated with the regulation of gas exchange of leaves. Following conventional understanding of how stomatal conductance and photosynthesis are regulated (Farquhar & Sharkey, 1982) and first-order theory of how elevated CO2 would affect photosynthesis

(Pearcy & Björkman, 1983), I formulated an initial path diagram hypothesizing the causal relationships among these variables (Fig. S2.6). Following the structural equation modelling approach (Grace, 2006, Lamb et al., 2011) we set up a set of linear equations that establish an expected pattern to the variance-covariance matrix in the actual data. Using the Lavaan package in R (Rosseel, 2012), I applied the maximum likelihood approach to then minimize deviations between the observed data and the covariances appropriate for our initial model. Standardized path coefficients were expressed in terms of standard deviations so they could be compared. I then used the Chi-square test to determine whether the covariances implied by the model adequately fit the actual covariance structures of the data. I also formulated variations on the basic model in Fig. S2.6 to examine whether new variables (difference in Ci, or Ci/Ca ratio rather than Slim)

were more relevant than the ones chosen for the initial, basic model.

In the simple core model depicted in Fig. S2.6 and Fig. 2.7, precipitation provides soil moisture, which in turn affects gs in ambient CO2. There is a direct pathway from gs to the

absolute enhancement in Anet in eCO2. Also there is an indirect pathway from gs in ambient

CO2 to the absolute Anet enhancement in eCO2, which is mediated by relative stomatal

limitation in aCO2, Ci/Ca ratio in aCO2 or increase in Ci in eCO2.Other variables could be

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involving Vcmax or leaf Narea yielded poor fits to the model, invalidating the overall model

(Lamb et al., 2011). Based on the core model in Fig. S2.6, I evaluated the hypothesis that temperature rather than precipitation would drive both available soil water as well as photosynthetic enhancement by eCO2. In this case, all other relationships were identical

to the core model. I also substituted the Slim by Ci/Ca ratio in the theoretical model in Fig.

S2.6 (Fig. S2.7). Other aspects of the model are same as given in Fig. S2.6. The arrow width is proportional to the size of the standardized coefficients. The overall Chi-square of 6.45 was not significant (P = 0.26), indicating an adequate fit to the data. Based on results in Fig. 2.7, Slim provided stronger descriptors for the Anet enhancement than Ci/Ca

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Fig. S 2.6 The basic structure of the core SEM model used to examine the multivariate regulation of photosynthetic enhancement by eCO2 for

herbaceous species at the EucFACE site.

The arrows denote a causal relationship where a change in the variable at the tail is a direct cause of changes in the variable at the head. The object ΔAnet denotes the absolute

enhancement of Anet by eCO2. Model results were very similar when Anet enhancement

ratio for eCO2 was used instead.

Fig. S2.6 The basic structure of the core SEM model used to examine the multivariate regulation of photosynthetic enhancement by eCO2 for herbaceous species at the

EucFACE site.

The arrows denote a causal relationship where a change in the variable at the tail is a direct cause of changes in the variable at the head. The object ΔAnet denotes the absolute

enhancement of Anet by eCO2. Model results were very similar when Anet enhancement ratio

for eCO2 was used instead.

Soil water content

ΔA

S

Precipitation

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Fig. S 2.7 An alternative fitted SEM model based on the original theoretical one in Fig. S 2.6, but including the measurement temperature instead of precipitation.

Other aspects of the model are same as given in Fig. S2.6. Temperature was not significant in this model. The overall Chi-square of 6.2 was not significant (P = 0.18), indicating an adequate fit to the data.

Fig. S2.7 An alternative fitted SEM model based on the original theoretical one in Fig. S2.6, but including the measurement temperature instead of precipitation.

Other aspects of the model are same as given in Fig. S6. Temperature was not significant in this model. The overall Chi-square of 6.2 was not significant (P = 0.18), indicating an adequate fit to the data.

ns

Temperature

ΔA

S

in aCO

g

in aCO

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Fig. S 2.8 Another alternative SEM model similar to the theoretical model in Fig. S2.6, but replacing Slim with Ci/Ca ratio.

The results are substantially similar to those in Fig. 2.7, except that there is a negative rather than positive interaction between Ci/Ca ratio and Δ Anet.

Soil water content ΔAnet

Ci/Ca in aCO2 Precipitation ns 0.31 0.45 - 0.39 gsin aCO2 0.49

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Fig. S 2.9 Atmospheric [CO2] measured at EucFACE at 21 m above-ground for

aCO2 (gray symbols) and eCO2 (blue symbols) plots during the first three years

of CO2 fertilisation. Data are 1-min means for [CO2]. Smoothed regressions

with 95% confidence intervals (gray areas) are shown for aCO2 (black dashed

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