Comparison of the A C

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1 Plant, Cell and Environment (009) 3, doi: /j x Comparison of the A C c curve fitting methods in determining maximum ribulose 1 5-bisphosphate carboxylase/oxygenase carboxylation rate, potential light saturated electron transport rate and leaf dark respiration ZEWEI MIAO 1, MING XU 1,, RICHARD G. LATHROP JR. 1 & YUFEI WANG 1 1 Grant F. Walton Center for Remote Sensing & Spatial Analysis, Rutgers University, 14 College Farm Road, New Brunswick, NJ , USA and Institute of Geographical Sciences and Natural Resources Research, Chinese Academy of Sciences, 11A Datun Road, Beijing , China ABSTRACT A review of the literature revealed that a variety of methods are currently used for fitting net assimilation of CO chloroplastic CO concentration (A C c) curves, resulting in considerable differences in estimating the A C c parameters [including maximum ribulose 1 5-bisphosphate carboxylase/oxygenase (Rubisco) carboxylation rate ( cmax), potential light saturated electron transport rate (J max), leaf dark respiration in the light (R d), mesophyll conductance (g m) and triose-phosphate utilization (TPU)]. In this paper, we examined the impacts of fitting methods on the estimations of cmax, J max, TPU, R d and g m using grid search and non-linear fitting techniques. Our results suggested that the fitting methods significantly affected the predictions of Rubisco-limited (A c), ribulose 1,5- bisphosphate-limited (A j) and TPU-limited (A p) curves and leaf photosynthesis velocities because of the inconsistent estimate of cmax, J max, TPU, R d and g m, but they barely influenced the J max : cmax, cmax : R d and J max : TPU ratio. In terms of fitting accuracy, simplicity of fitting procedures and sample size requirement, we recommend to combine grid search and non-linear techniques to directly and simultaneously fit cmax, J max, TPU, R d and g m with the whole A C c curve in contrast to the conventional method, which fits cmax, R d or g m first and then solves for cmax, J max and/or TPU with cmax, R d and/or g m held as constants. Key-words: A C i curve; chloroplastic CO concentration; grid search; leaf photosynthesis; New Jersey Pinelands; non-linear fitting. INTRODUCTION Process-based ecosystem models have been widely used to quantify major ecosystem functions and their response Correspondence: M. Xu. Fax: ; mingxu@ crssa.rutgers.edu to climate change. Most of the models use Farquhar s photosynthesis model (Farquhar et al. 1980; von Caemmerer & Farquhar 1981) in calculating gross primary productivity (GPP). The Farquhar s photosynthesis model requires several critical parameters: the maximum ribulose 1 5- bisphosphate carboxylase/oxygenase (Rubisco) carboxylation rate ( cmax); the potential light saturated electron transport rate (J max); leaf dark respiration in the light (R d); and mesophyll conductance (g m). These parameters can be obtained from the leaf-level measurements of gas exchange, namely the net assimilation of CO chloroplastic CO concentration (A C c) or net assimilation of CO intercellular CO concentration (A C i) curves. The A C i model proposed by Farquhar et al. (1980) and later modified by Sharkey, Berry & Raschke (1985) and Harley et al. (199a,b) has been incorporated as the mechanistic basis for the photosynthetic response to acclimation across a range of scales and complexity from cellular to global levels (Harley & Sharkey 1991; de Pury & Farquhar 1997; Bernacchi et al. 00; Medlyn, Dreyer & Ellsworth 00; Manter & Kerrigan 004; Monti et al. 006). For example, a number of ecosystem models, including the dynamic global vegetation model (DGM) (Cramer, Bondeau & Woodward 001), the Biome Geochemical Cycles (Biome-BGC) (Thornton, Law & Gholz 00), the Lund Potsdam Jena dynamic global vegetation model (LPJ) (Sitch, Smith & Prentice 003), the Local Terrestrial Ecosystem Carbon (LoTEC) model (Hanson, Amthor & Wullschleger 004), the MAESTRA (Hanson et al. 004) and the CANOAK model (Hanson et al. 004), employ the Farquhar et al. (1980) A C i model or A C c model with stomatal and/or mesophosyll conductance to estimate plant photosynthetic rates at current or projected future climate. According to Farquhar et al. (1980), plant carboxylation rates are limited by the slowest of one of three processes: (1) the maximum rate of Rubisco-catalysed carboxylation (Rubisco-limited), i.e. cmax; () the regeneration of ribulose biphosphate (RuBP) controlled by electron transport rate (RuBP-limited), i.e. J max; or (3) the regeneration of RuBP controlled by the rate of triose-phosphate utilization (TPU) Journal compilation 008 Blackwell Publishing Ltd 109

2 110 Z. Miao et al. (TPU-limited) (Farquhar et al. 1980; Harley et al. 199a,b; Wullschleger 1993, Long & Bernacchi 003; Sharkey et al. 007). Dark respiration in the light (R d), i.e. CO evolution from mitochondria under lighted conditions, is also a significant part of the carbon lost by plants. Therefore, the major parameters, cmax, J max, TPU and R d, are central to the prediction of plant photosynthesis capacity with the Farquhar s photosynthesis model. Accurate predictions of cmax, J max, TPU and R d are required in the projection of ecosystem productivity, because potential bias or errors of these parameters may be exacerbated when these variables are scaled up from a single leaf (or canopy level) to ecosystem level or from short-term field measurement (minute to hour scales) to long-term ecosystem process predictions (daily to decadal scales) (Harley & Baldocchi 1995; Hanson et al. 004). There are large numbers of J max and cmax databases for various plant species found around the world as well as numerous publications discussing the A C i (or A C c) theoretical models and fitting practices (Harley & Sharkey 1991; Wullschleger 1993; Medlyn et al. 1999, 00; Long & Bernacchi 003; Ethier & Livingston 004; Dubois et al. 007; Rodeghiero, Niinemets & Cescatti 007; Sharkey et al. 007). However, the methods for fitting the A C c parameters are not yet consistent in the literature. So far, at least five methods are commonly used in Farquhar s photosynthesis model to estimate the cmax, J max, TPU, R d and g m values, and these include: (1) fitting cmax, R d and/or g m using a portion of the A C i data where C i is below a transition point (generally 0 5 Pa), then use the remaining A C i data to fit J max, TPU and/or g m by holding the mentioned cmax and R d value as constants (Manter & Kerrigan 004; Onoda, Hikosaka & Hirose 005; Monti et al. 006; Flexas et al. 007); () fitting the A c curve (i.e. cmax and R d) using a portion of the A C i data where C i is below a transition point (generally 0 5 Pa), then using the whole A C i data to fit the entire A C i curve by holding the mentioned cmax, R d and/or g m values as constants to determine J max and TPU (Harley et al. 199a; Wullschleger 1993; Curtis et al. 1995); (3) solving for cmax and R d first using a portion of the A C c data,then fitting cmax, J max, TPU and g m by holding R d as a constant (Harley et al. 199b; Long & Bernacchi 003); (4) fitting cmax, J max, TPU, R d and g m simultaneously using the whole data points of A C i curve (Parsons et al. 1997; Medlyn et al. 00; Photosynthesis Assistant 1.1., Dundee Scientific, UK; Dubois et al. 007; Sharkey et al. 007); and (5) fitting the A C c parameters simultaneously or separately with the quadratic equations reported by Ethier & Livingston (004). For example, a commonly used software package called Photosynthesis Assistant 1.1. (for Windows by Parsons and Ogston, Dundee Scientific, UK) initially estimates cmax and R d using the first half of the A C i data, then estimates initial J max and TPU with the initial cmax and R d held as constant; finally re-fitting all the three parameters simultaneously using the entire data set by inputting the initial cmax, J max, TPU and R d values. It is noted that most non-linear fitting techniques are sensitive to initial values, suggesting the results are local optima rather than global optima. The fixed initial values as determined by the segment fitting may bias the non-linear optimization results, especially when the segment fitting for Jmax and TPU are poor because of small sample size. Previous studies have shown that fitting cmax, J max, TPU, R d and g m either simultaneously or separately can result in significantly different estimates for these parameters. ariable C i transition points (C i,t) at which the A C c curve switches between the Rubisco- and RuBP-limited curves may affect the estimations of the A C c parameters significantly (Harley et al. 199b; Long & Bernacchi 003; Ethier & Livingston 004; Manter & Kerrigan 004; Dubois et al. 007). Therefore, the objective of this study was to investigate how different fitting methods influence the estimation of cmax, J max, TPU, R d, g m and, thus, leaf photosynthesis, and to find a proper method for determining the A C c parameters. In the study, we also analysed the influences of fitting practices on the J max : cmax, cmax : R d and J max : TPU ratios, three important relationships commonly used in terrestrial ecosystem models. MATERIALS AND METHODS Description of the A C c model and fitting methods The A C c curves were fitted based upon the mechanistic model of CO assimilation originally published by Farquhar et al. (1980), then later modified and developed by Sharkey (1985), Harley et al. (199a,b) and Wullschleger (1993). According to the biochemical model, net CO assimilation rate (mmol CO m - s -1 ) can be expressed as: A c Rd min { Ac, Aj, Ap} (1) with O cmaxcc Ac R C τ C + K ( 1 + O K ) c c c o O JCc Aj R C τ 4( C + O τ ) c c A 3 TPU R (4) p d Cc Ci A gm (5) J αi I + α 1 J max θj ( αi + J ) J + αij d d () (3),or (6) max max 0 (7) τ cmax K K c o omax (8)

3 Comparison of A C c curve fitting methods 111 Γ * 05. O, τ where A is the net CO assimilation rate (mmol CO m - s -1 ); c and o are rates of carboxylation and oxygenation of Rubisco (mmol CO m - s -1 ); C c and O are the partial pressures of CO and O at Rubisco (Pa); R d is the rate of CO evolution in the light resulting from processes other than photorespiration (mmol CO m - s -1 ); t is the specificity factor for Rubisco; and min{} denotes the minimum of ; A c, A j and A are the net CO assimilation rate limited by Rubisco, RuBP and TPU, respectively (mmol CO m - s -1 ); cmax is the maximum rate of carboxylation (mmol CO m - s -1 ); K c and K o are Michaelis Menten constants for carboxylation and oxygenation, respectively; C i is the partial pressures of CO in the intercellular air space (Pa); g m is mesophyll conductance (mmol CO m - s -1 Pa -1 ); J is the potential rate (mmol m - s -1 )of electron transport that is dependent upon incident light irradiance [i.e. photosynthetically active radiation (PAR)] I; the factor 4 in Eqn 3 indicates that the transport of four electrons will produce sufficient ATP and NADPH for the regeneration of RuBP in the Calvin cycle (Farquhar et al. 1980); a is the efficiency of light energy conversion on an incident light basis (mol electrons/mol photons); J max is the light saturated rate of electron transport; and TPU is the rate of phosphate release in triose phosphate utilization (starch and sucrose production) (Farquhar et al. 1980; von Caemmerer & Farquhar 1981; Harley, Weber & Gates 1985; Harley, Tenhunen & Lange 1986; Harley et al. 199a,b; Medlyn et al. 1999, 00; Ethier & Livingston 004; Sharkey et al. 007). In this study, after comparing Eqns 6 and 7 (i.e. the equations of potential rate of electron transport), we found that there were no significant differences in fitting the A C c curves between the two equations. Hereinafter, we used Eqn 6 in the following simulations. Based on our literature review, we designed and tested six different methods in fitting A C c curves (Table 1). Specifically, both methods I and II solved cmax, J max, TPU, R d and g m simultaneously using the whole A C c curve data points. Method I directly fitted the A C c curve, and method II used quadratic equations cited from Ethier & Livingston (004) to fit the A C c parameters. Methods III I, which were the so-called segment methods, fit the A c curve with a portion of the gas-exchange measurement data points (C i 0 Pa) to get cmax, R d and/or g m.thea j and A p curves or the whole A C c curve (i.e. Eqn 1) are then fit independently with a portion (C i > 0 Pa) or the whole range of gas-exchange data points with cmax, R d and/or g m held as constants. The details of fitting methods were listed in Table 1. The temperature dependences of K c, K o, R d and t are described by the Arrhenius equation: Parameter (K c, K o, R d, T) exp[c -DH a/(rt k)], where c is a sealing constant, DH a is an activation energy, R is the gas constant and T k is leaf temperature (K) (Harley et al., 199b; Wullschleger 1993). In keeping with recent efforts to model CO assimilation, these parameters were directly cited from Harley et al. (9) (199b), Wullschleger (1993), Bernacchi et al. (001), Medlyn et al. (00), Long & Bernacchi (003) and Ethier & Livingston (004), and were applied equally to all species (Table ). We set the g m up-limit to 30 mmol m - s -1 Pa -1 according to Sharkey et al. (007). Study area The study was conducted in the McDonalds Branch basin of the Brendan Byrne State Forest, an undisturbed watershed that drains into the Rancocas River, located in the New Jersey Pinelands, USA. The Brendan T. Byrne State Forest (formerly the Lebanon State Forest) is a complex mosaic and combined gradients of the New Jersey Pine Barrens communities (Forman 1979). Our field experimental sites were allocated along four transects that spanned hydrological gradients of wetland communities from pitch-pine lowland (the drier end of the gradient) to cedar swamp community (the wetter end). We measured leaf gasexchange on four shrubby indicator species, including highbush blueberry (accinium corymbosum L.), dangleberry [Gaylusaccia frondosa (L.)Torr.&A.Gray.], coastal fetterbush (Eubotrys racemosa L.) and sweet pepperbush (Clethra alnifolia L.). Leaf gas-exchange on-site measurements Using a portable LI-6400 system (Li-Cor Inc., Lincoln, NE, USA), we measured leaf gas-exchange (A C i curves) on 654 plants (leaves) over two growing seasons (June September) of 004 and 005. To eliminate potential effects of species and community types, we randomly selected 160 A C i curves out of the total samples to examine the influences of fitting methods on the A C c parameters. During the field measurements, ambient CO concentration of the cuvette (C a) in the open gas-exchange chamber reduced from 370 to 00, 100 and 50 mmol CO mol -1, then increased from 50 to 300, 450, 600 and 800 mmol CO mol -1 at a constant saturating light intensity of 1500 mmol photosynthetic photon flux density m - s -1. The gas exchange properties including photosynthesis rate, C i, leaf temperature and internal leaf PAR were logged at each C a once the system had reached a pre-determined stability point (coefficient of variation 1%). Model fitting techniques and statistical analysis We combined the grid search and non-linear two-stage least square regression technique to fit the A C c curves and estimate global optimum of cmax, J max, TPU, R d and g m. With the grid search including five-tier DO-END loops, we initialized cmax parameter from 0 to 160 mmol CO m - s -1, J max from 0 to 40 mmol m - s -1 with an increase of every 0 mmol m - s -1, and initialized TPU from to 8 mmol m - s -1 ; R d from1to8mmol m - s -1 with a step of mmol m - s -1 ; and g m from1to10mmol m - s -1 Pa -1 by a step of mmol m - s -1 Pa -1, respectively. That is, for every A C c curve, we iteratively fit 7680 times with 7680 initial

4 Table 1. Methods and equations used to fit A Cc curves in the current study cmax Rd Jmax gm Method Analysis steps Equation a Selected points b Equation Selected points Equation Selected points Equation Selected points References c I Estimate cmax, Jmax, TPU, Rd and gm simultaneously II Estimate cmax, Jmax, TPU, Rd and gm simultaneously III (i) Estimate cmax, Rd and gm; and (ii) estimate Jmax and TPU with cmax, Rd and gm held constant I (i) Estimate cmax, Rd and gm; and (ii) estimate Jmax, TPU and gm with cmax and Rd held constant (i) Estimate cmax, Rd and gm; and (ii) estimate Jmax, TPU and gm with cmax and Rd held constant I (i) Estimate cmax, Rd and gm; and (ii) estimate cmax, Jmax and TPU with Rd and gm held constant a b b ac Eqn -1: A c( or A j) OJ 4 RO d c JCi RC d i + τ τ for Aj. Eqn 1 All Eqn 1 All Eqn 1 All Eqn 1 All Parsons & Ogston 1999; Sharkey et al. 007 Eqn -1 All Eqn -1 All Eqn -1 All Eqn -1 All Ethier & Livingston 004; Warren & Dreyer 006; Flexas et al. 007 Eqn Ci 0 Pa Eqn Ci 0 Pa Eqn 3 Ci > 0 Pa Eqn Ci 0 Pa Manter & Kerrigan 004; Onoda et al. 005 Eqn Ci 0 Pa Eqn Ci 0 Pa Eqn 1 Ci > 0 Pa Eqn 1 Ci > 0 Pa Manter & Kerrigan 004; Onoda et al. 005 Eqn Ci 0 Pa Eqn Ci 0 Pa Eqn 3 All Eqn 3 All Harley et al. 199b; Wullschleger 1993 Eqn 1 All Eqn Ci 0 Pa Eqn 1 All Eqn All Long & Bernacchi 003 cmax Rd, where a -1/gm, b C + K ( 05O i c 1 + O Ko)+ and c Rd[ Ci + Kc( 1 + O Ko) ] cmax C g ( i τ ) m 4O J R for Ac; a -4/gm, b 4 C τ g All TPU values were estimated by Eqn 4: Ap 3TPU - Rd. The definitions of the variables in above equations were seen in the section of description of the A Cc model. b Selected points: all, entire portion of the A Cc curve data points used; Ci 0 Pa or Ci > 0 Pa, a portion of data points where Ci 0 Pa or Ci >0 Pa of each A Ci curve used. c The methods analysed in the table may not be exactly same as those used in the studies in the references, because some of thesereferences were for A Ci curve and do not include gm and TPU. Ac, ribulose 1 5-bisphosphate carboxylase/oxygenase-limited; Aj, ribulose 1,5-bisphosphate-limited; Ci, intercellular CO concentration; Ci,t, intercellular CO concentration transitional points; gm, mesophyll conductance; Jmax, potential light saturated electron transport rate; Rd, leaf dark respiration in the light; TPU, triose-phosphate utilization; cmax, ribulose 1 5-bisphosphate carboxylase/oxygenase carboxylation rate. m d and.. i 11 Z. Miao et al.

5 Comparison of A C c curve fitting methods 113 Table. Model parameters used to fit the A C i curves in the current study Parameters Description of parameters Units alues c(k c) The scaling constant for K c Dimensionless DH a(k c) The constant of activation energy for K c kj mol c(k o) The scaling constant for K o Dimensionless 9.59 DH a(k o) The constant of activation energy for K o kj mol c(t) The scaling constant for t Dimensionless DH a(t) The constant of activation energy for t kj mol O The partial pressures of O in the intercellular air space Pa A The efficiency of light energy conversion on an incident light basis mol electrons/mol photons 0.4 for Eqn for Eqn 5 Q The curvature of the light response of electron transportation curve Dimensionless 0.90 R The gas constant kj K( F) -1 mol C The conversion coefficient from ppm to Pa Dimensionless T The thermodynamic temperatures at 0 C K value combinations of cmax, J max, TPU, R d and g m, respectively.we obtained the global optimum of cmax, J max, TPU, R d and g m based on the minimum of the root mean square error (RMSE) of each curve. In the study, leaf temperature and light intensity were input to the model as independent variables to calculate the temperature dependence of K c, K o, R d, t and J, respectively. In other words, we used leaf temperature and incident PAR at every C i level rather than the more commonly used method of using only the first leaf temperature and incident PAR (Wullschleger 1993; Parsons et al. 1997; Dubois et al. 007; Sharkey et al. 007). Multiple levels were used to be able to account for the small fluctuation of leaf temperature during the leaf-gas-exchange measurements. To ensure our fitting programs worked correctly, we compared our estimates of A C c and A C i parameters by method I with the results from Photosynthesis Assistant (version 1.1. for Windows by Parsons and Ogston, Dundee Scientific, UK) and Sharkey et al. s Microsoft EXCEL spreadsheet-based software (Sharkey et al. 007). By comparison, our grid search plus non-linear, two-stage least square regression technique produced significantly lower RMSE values than the above software packages (at the confidence level of 98.6% by F-test). With method I, we tested sensitivity of the A C c parameters to the C i cut-off points (C i,t) by setting the C i cut-off points to 0, 5 and 30 Pa. The program was developed on a basis of SAS MACRO and Proc Model module (SAS Institute Inc 9.1, Cary, NC, USA). Relationships among cmax, J max, TPU, R d and g m were analysed by using the PROC CORR, PROC GLM, PROC ANOA and PROC TTest modules of SAS, respectively. RESULTS Differences among the fitting methods in estimating cmax, J max, TPU, R d and g m By Student s t-test, differences in cmax between method I and methods II I were significant at the confidence level of 95.0% (P < 0.05) (Fig. 1). cmax estimates from method I ranged from to 9.64 mmol CO m - s -1 with a lower standard deviation than the other methods (Table 3). One should note that the cmax (and/or R d) estimates were the same for methods III- because cmax and R d (or g m) were fitted with the data points of C i 0 Pa at first and then held as constants. There were significant differences at the confidence level of 95% (P < 0.01) in J max and TPU estimates between methods I and II-I (Figs & 3).The average and standard deviation of J max estimated from method I were mmol m - s -1, which were lower than those from methods II-I, respectively (Table 3). TPU predictions by method I were generally lower than that from method II, but higher than that from methods III I (Fig. 3). For methods III I (the segment methods), 75, 76, 67 and 19 data sets out of the 160 leaves failed to converge cmax (µmol m s 1 ) by methods II I I II 0 III I cmax (µmol m s 1 ) by method I Figure 1. Differences in ribulose 1 5-bisphosphate carboxylase/oxygenase carboxylation rate ( cmax) estimates (mmol CO m - s -1 ) between methods I and II I. cmax estimates were the same for methods III. n 17, 17, 85, 84, 141 and 93 for methods I, II, III, I, and I, respectively, because some data sets failed to converge in fitting the A C c curve.

6 114 Z. Miao et al. Table 3. Mean and standard deviation of the A C c parameters Method a cmax (mmol m - s -1 ) J max (mmol m - s -1 ) TPU (mmol m - s -1 ) R d (mmol m - s -1 ) g m (mmol m - s -1 Pa -1 ) I II III I I a n (number of leaf gas-exchange data sets) 17, 17, 85, 84, 141 and 93 for methods I, II, III, I, and I, respectively, as some data sets failed to converge in fitting A C c curve. g m, mesophyll conductance; J max, potential light saturated electron transport rate; R d, leaf dark respiration in the light; TPU, triose-phosphate utilization; cmax, ribulose 1 5-bisphosphate carboxylase/oxygenase carboxylation rate. J max (µmol m s 1 ) by methods II I J max (µmol m s 1 ) by methods &I (a) (b) J max (µmol m s 1 ) by method I J max (µmol m s 1 ) by method I I II III I I I Figure. Differences in potential light saturated electron transport rate (J max) estimates (mmol m - s -1 ) between methods I and II I. n 17, 17, 85, 84, 141 and 93 for methods I, II, III, I, and I, respectively. in solving J max, TPU and g m, respectively, whereas for methods I and II, 33 leaves out of 160 data sets failed to fit the A C c curve. In other words, using methods III I (i.e. the segment methods), more data sets could not find optimal solutions for the A C c parameters than methods I and II (i.e. the simultaneously whole curve fitting methods). Differences in R d estimates were significant among method I and methods II I at the confidence level of 99.99% by Student s t-test (P < ) (Fig. 4). The mean and standard deviation of R d from method I were 1.60 and 0.50 mmol m - s -1, respectively, which were lower than the counterparts from methods II I and I, but the mean of R d from method I is higher that in method (Table 3). For example, R d estimates ranged from to.930 mmol m - s -1 for method I, which were significantly lower than that the R d values from method II [i.e. Ethier & Livingston (004) s method] (Fig. 4). Unlike cmax, J max, TPU and R d, g m estimates had relatively large variations among methods I and II I. Differences in g m estimates between methods I and II I TPU (µmol m s 1 ) by methods II I TPU (µmol m s 1 ) by method I I II III I and I Figure 3. Triose-phosphate utilization (TPU) estimates (mmol m - s -1 ) by methods I I. n 17, 17, 85, 84, 141 and 93 for methods I, II, III, I, and I, respectively.

7 Comparison of A C c curve fitting methods 115 R d (µmol m s 1 ) by methods II I R d (µmol m s 1 ) by method I I II III I Figure 4. Leaf dark respiration in the light (R d) estimates (mmol m - s -1 ) by methods I I. n 17, 17, 85, 84, 141 and 93 for methods I, II, III, I, and I, respectively. were significant at the confidence level of 99.99% (P < ) (Fig. 5). For example, the means and standard deviations of g m estimates varied from mmol m - s -1 Pa -1 for method I, which was higher than those in methods II and, but lower than those in methods III, I and I (Table 3). The C i cut-off point (C i,t) considerably affected predictions of the A C c parameters. For example, for method I, with the C i cut-off points of 0, 5 and 30 Pa, the mean and standard deviation of cmax estimates were , and , respectively (not shown). The mean and standard deviations of J max estimates varied from , to , whereas the average and standard deviations of R d estimates ranged from , to , respectively. When the C i cut-off point equalled 30 Pa, more data sets failed to solve the A C c parameters than with a C i cut-off point of 0 Pa. Effects of the fitting methods on relationships among cmax, J max, TPU, R d and g m estimates Fitting methods considerably affected the relationships among cmax, J max, TPU and R d (Table 4). Although cmax estimates significantly correlated to J max and R d at the confidence of 99.99% (P < ) for all of the fitting methods, the correlations between cmax and R d and between J max and R d differed among the fitting methods (Table 4). For example, correlation coefficients between cmax and J max varied from for methods to for method I. The correlation coefficients between cmax and R d and between J max and R d ranged from for method I to for method II,and from for method to for method III, respectively. The correlations between cmax and TPU slightly differed among the fitting methods. Correlations between g m and cmax, J max and R d were not statistically significant at the confidence of 95%, because for many data sets, g m estimates reached the upper limit of 30 mmol m - s -1 Pa -1, i.e. + in the present study. The fitting methods had little effect on the ratios of J max to cmax, cmax to R d and cmax to TPU in spite of significant differences in estimating cmax, J max, TPU, R d and g m (Table 5). For example, the J max : cmax ratio ranged from for method II to for method I. The cmax : R d and cmax : TPU ratios varied slightly from for method II to for method I, and from for method I to for method II. Differences among the fitting methods in projecting A c and A j curves Differences in projecting A c and A j curves were substantial among the fitting methods because of the inconsistent cmax, J max, R d and g m estimates. The impact of fitting methods on A c and A j curves increased with the increase of C i (Fig. 6). Because of the diverging A c and A j curves, the intersection points between the A c and A j curves (i.e. the CO assimilation rate at which the A C c curve switches between the Rubisco- and RuBP-limited curves) were significantly different between methods I and II-I, though we set the preliminary C i,t value to 0 Pa for methods III-I. For example, for Eubotrys racemosa measured on 10 June 005, the C i,t values were 8.18, 60.4 and Pa for methods I, and I, and the A c (or A j) values at C i,t were 6.19, and 9.65 mmol m - s -1 for methods I, and I (Fig. 6a), respectively. Figure 6b indicated that for Gaylusaccia frondosa measured on 11 September 005, the C i,t values were 53.6, and Pa for methods I, II and I, respectively. The variations in A c and A j curves and differences in intersection points of the two curves produced a large bias (or error) in estimating leaf photosynthetic velocity for a given leaf. DISCUSSION Fitting methods versus C i transition point (C i,t) between the A c and A j curves According to Farquhar s photosynthesis model, the C i transitional points (C i,t) between the A c and A j curves are critical to accurately predict the A C c parameters. on Caemmerer & Farquhar (1981) noted that the C i transition points (C i,t) from A c to A j consistently occurred between 00 and 50 mbar in Phaseolus vulgaris when measurements were performed at ambient O concentration and high irradiance. Since then, it has become established practice to use the mbar transition zone of P. vulgaris as the cut-off point for fitting the lowest portion of A C c curve performed under standard conditions for many species (Harley et al. 199a,b; Wullschleger 1993; Medlyn et al. 00; Ethier & Livingston 004; Manter & Kerrigan 004; Onoda et al. 005; Monti et al. 006; Sharkey et al. 007).

8 116 Z. Miao et al. Table 4. Correlation coefficients among cmax, J max and R d estimates (mmol m - s -1 ) cmax versus J max cmax versus R d J max versus R d cmax versus TPU Method a,b Correlation coefficient P Correlation coefficient P Correlation coefficient P Correlation coefficient P I < < < < II 0.91 < < < < III < < < I < < < < < < < < I < < < < a n (number of leaf gas-exchange data sets) 17, 17, 85, 84, 141 and 93 for methods I, II, III, I, and I, respectively. b Correlations between g m and cmax, J max and R d were not statistically significant at the confidence of 95%. g m, mesophyll conductance; J max, potential light saturated electron transport rate; R d, leaf dark respiration in the light; TPU, triose-phosphate utilization; cmax, ribulose 1 5-bisphosphate carboxylase/oxygenase carboxylation rate. Previous studies have demonstrated that C i,t may significantly affect the A C i parameters when C i,t is set too high or too low, and the constant or variable C i,t may strongly affect cmax, J max and leaf photosynthetic rate (Manter & Kerrigan 004; Dubois et al. 007). Theoretically, we calculated C i,t as A c A j at C c,t. Replacing A c and A j by Eqns and 3, the previously mentioned relationship becomes cmaxcc,t JCc,t C + K ( 1+ O K ) 4( C + O τ ), (10) i.e. C c,t c o c,t c,t 4cmaxO τ JKc( 1+ O Ko ). (11) ( J 4 ) gm (µmol 1 m 1 s 1 Pa 1 ) by methods II I cmax 8 I II III and I I gm (µmol 1 m 1 s 1 Pa 1 ) by method I Figure 5. Mesophyll conductance (g m) estimates (mmol m - s -1 Pa -1 ) by methods I I. n 17, 17, 85, 84, 141 and 93 for methods I, II, III, I, and I, respectively. Substituting J with Eqn 6, then Eqn 11 can be rewritten as: C C c,t 4O τ Jmax + ( αi) αi( Jmax cmax ) Kc( 1+ O Ko ). αi( Jmax cmax ) 4 Jmax + ( αi) So, i,t At O JCc,t Cc,t + Cc,t + Rd gm C c ( Cc,t + O ) τ 4 τ (1) g m, (13) where A t is the net CO assimilation rate (mmol CO m - s -1 )atc i transition point (C i,t). Therefore, C i,t is a function of cmax, J max, J max/ cmax, R d and g m given high light irradiance, ambient O and constant temperature for a given plant. This is supported by the previous studies that noted that C i,t depends on the ratio of J/ cmax when g m (von Caemmerer & Farquhar 1981; Dubois et al. 007). The C i,t values from method I varied from 1.91 to 56.0 Pa with the mean of 38.4 Pa, which was Table 5. Ratios of cmax to J max, cmax to R d,and cmax to TPU Method a J max a cmax cmax a R d b J max a TPU b I b II III I I a n (number of leaf gas-exchange data sets) 17, 17, 85, 84, 141 and 93 for methods I, II, III, I, and I, respectively. b Regression coefficient. All of linear regressions were significant at the confidence level of 99.99% (P < ). J max, potential light saturated electron transport rate; R d, leaf dark respiration in the light; TPU, triose-phosphate utilization; cmax, ribulose 1 5-bisphosphate carboxylase/oxygenase carboxylation rate.

9 Comparison of A C c curve fitting methods 117 A c and A j curves (µmol m s 1 ) A c and A j curves (µmol m s 1 ) (a) A c I A c A c I A j I A j A j I C i (Pa) (b) A c I A c III A c I A j I A j III A j I Furthermore, we found that the C i,t value differed among individuals of the same species, as was found by several earlier studies (Ethier & Livingston 004; Manter & Kerrigan 004; Onoda et al. 005). For example, Ethier & Livingston (004) found that the C i,t values ranged from 300 to 400 mbar for shoots of 50-year-old Douglas fir trees. Unfortunately, this large variation of C i,t has not been carefully considered in previous studies, which may have introduced large biases to the reported A C c curve parameters in the literature (Ethier & Livingston 004; Manter & Kerrigan 004; Dubois et al. 007). Methods I and II automatically determined the C i,t values in the process of fitting the A C c curve parameters through min{a c, A j, A p} in Eqn 1. When RuBP carboxylation limits photosynthesis (A c < A j), A c will be used to estimate leaf photosynthetic rate, otherwise, for RuBP regeneration (A j < A c), A j is used. Therefore, methods I and II are applicable to most of our leaf gas-exchange data sets. On the contrary, methods III I (the segment methods) may require more gas-exchange measurement data points to ensure sufficient C i range for fitting the A j curve, especially Ci,t (Pa) C i (Pa) Figure 6. Rubisco-limited (A c) and ribulose 1,5-bisphosphate-limited (A j) curves projected by methods I I: (a) Eubotrys racemosa L. measured at 09:09:4 h, 10 June 005, and (b) Gaylusaccia frondosa (L.) measured at 10:6:47 h, 11 September 005. A c and A j I, III, and I refer to A c and A j curves projected by methods I, III, and I, respectively. The A c and A j curves projected by methods II and I were not shown Clethra alnifolia Eubotrys racemosa Galusaccia frondosa accinium corymbosum much higher than the empirical cut-off point of 0 5 Pa between A c and A j curves and the 0 Pa as we used in methods III I. This difference will inevitably introduce biases (or errors) to the estimates of A C c parameters and leaf photosynthetic velocity as indicated by the four woody shrub species in the New Jersey Pinelands. With the C i,t of 0 Pa, even when we combined the non-linear technique with grid search, the segment methods (methods III I) failed to find an optimal solution of above 40% of A C c data sets we measured. In fact, we found that the C i,t parameter was species and season dependent (Fig. 7). For example, Eubotrys racemosa L. had a higher C i,t value than other species. For the 004 and 005 growing seasons, the C i,t values in September were higher than other months. Ci,t (Pa) June July Months August September Figure 7. Means and standard deviations of the intercellular CO concentration transitional points (C i,t) (Pa) between the Rubisco-limited and ribulose 1,5-bisphosphate-limited curves predicted by method I.

10 118 Z. Miao et al. for the 40% of leaf A C i curves with which we failed to solve J max, TPU, R d and/or g m. From Eqn, da cmax [ Γ * + Kc( 1 + O Ko )] f ( cmax, Cc ). (14) dc [ C + K ( 1 + O K )] c c o When C c 0 mmol mol -1, da cmax [ Γ * + Kc( 1 + O Ko )] maximum. (15) dc [ K ( 1 + O K )] At leaf temperature of 5 C, c da << cmax. (16) dc Therefore, whatever fitting methods are used, it is of vital importance to accurately estimate cmax with more data points and small intervals at lower C i end (e.g. 50, 75 and 15 mmol mol -1 ) rather than the current coarse steps of 50, 100 and 00 mmol mol -1. Fitting methods versus estimate errors in fitting A C c curves Our results indicate that fitting methods affected not only the estimation of the A C c curve parameters but also leaf photosynthesis velocity. Using the cmax, J max, TPU, R d and g m predictions from methods I I, we projected the A C i curves of each individual leaf and calculated RMSE in comparison with field photosynthetic measurements. The average RMSEs of the 160 A C i curves (n 17, 17, 85, 84, 141 and 93 for methods I I, respectively) were lowest for method I (Fig. 8). In other words, method I is the most accurate in estimating leaf photosynthesis and A C c parameters. It is worth noting that although method II [Ethier & Livingston s (004) method] is mathematically o identical with method I, from the viewpoint of fitting practice, method I is better than the quadratic equation approach. Methods III I (the segment methods), which used the empirical C i,t to split gas-exchange sample data into A c and A j curves, increased the uncertainty in estimating J max, TPU and g m. For methods III I, sample sizes for fitting J max, TPU and/or g m were smaller than other methods because of the splitting of the A C i curves. The fewer data points available for fitting J max, TPU and/or g m increase errors and the probability of failing to fit J max, TPU and/or g m, particularly when fitting J max, TPU and/or g m simultaneously. As described earlier, 40% of the 160 A C i curves failed to solve optimal solutions for methods II. Therefore, a large sample size in A C i curve measurements, especially at the high C i end, is necessary to estimate J max, TPU and/or g m accurately when using the segment methods (methods III I). Long & Bernacchi (003) suggested that one should ensure a minimum of five points for all of Rubisco-limited A c, RuBP-limited A j and TPU-limited A p curves; that is, each A C i curve should have at least 10 or 15 gas-exchange measurement data points, particularly for data points at low and high C i ends, rather than the traditional measurements of 8 or 9 data points for most A C i curves reported in the literature. In short, method I has three advantages over the other methods. Firstly, method I has the lowest RMSE and thus the best accuracy in fitting the A C c curves. Secondly, method I is the least sensitive to the sample size of the A C c curve among the six methods and features the highest degree of freedom for a given A C c curve. Finally, method I is technically easy to implement because it fits cmax, J max, TPU, R d and g m directly and simultaneously and does not need to theoretically transform Eqns and 3 to quadratic functions (i.e. Eqn -1) as in method II [Ethier & Livingston s (004) method] or empirically split the A C c curve as in methods III I. RMSEs of A C c curves I II III I I Fitting methods Figure 8. Means and stand deviations of the root mean square errors (RMSEs) between gas-exchange measured photosynthetic rate and model predictions by methods I I. n 17, 17, 85, 84, 141 and 93 for methods I, II, III, I, and I, respectively. A C c, net assimilation of CO chloroplastic CO concentration curve. Fitting methods versus the ratios of J max to cmax, cmax to R d and J max to TPU The J max : cmax ratio is important to analyse plant photosynthetic processes. As cmax and J max limit the photosynthetic rate at low and high concentrations, respectively, the J max : cmax ratio reveals the ratio of photosynthetic rate at high CO to that at low CO concentrations. This indicates that a change in the J max : cmax ratio may change the CO stimulation of photosynthesis. Onoda et al. (005) reported that elevated CO concentration (700 mmol mol -1 ) tended to reduce both cmax and J max without changing the J max : cmax ratio. Additionally, in terrestrial ecosystem models, J max is often derived from cmax by using a linear relationship, e.g. J max b cmax or J max a + b cmax (Thornton et al. 00). However, little attention has been paid to the influence of fitting methods on the relationship

11 Comparison of A C c curve fitting methods 119 between J max and cmax. Similar to the calculation of C i,t in Eqn 13, we theoretically deduced the ratio of J max/ cmax as follows. Replacing J with Eqn 6, Eqn 10 can be rewritten as: αi αi 1 + J max Then, we get J max cmax cmax 4( Cc,t + O τ ). C + K ( 1 + O K ) c,t c o 4( Cc,t + O τ) Jmax + ( αi) [ Cc,t + Kc( 1 + O Ko )] αi At 4 Ci,t + O J I τ g max + ( α ) m. At Ci,t + Kc( + O Ko) 1 αi gm (17) (18) Thus, the J max : cmax ratio is a function of J max, C i,t and g m given high light irradiance (I) and ambient atmosphere O and temperature for a specific species. Assuming T 5 C, I 1500 mmol m - s -1, O Pa, K c 7.85 Pa CO, K o Pa O, t and ai 360 mmol m - s -1 (Table ), we can simplify Eqn 15 as J Ratio of J max to cmax max cmax J max 40 (µmol m s 1 ) J max 90 (µmol m s 1 ).0 J max 140 (µmol m s 1 ) Ci,t (Pa) Figure 9. Potential light saturated electron transport rate (J max) : ribulose 1 5-bisphosphate carboxylase/oxygenase carboxylation rate ( cmax) ratios along with intercellular CO concentration transitional points C i,t (Pa) at various J max levels. At 4 Ci,t +. Jmax g m. (19) At Ci,t g 360 m The J max : cmax ratio increased non-linearly with C i,t at different J max values (Fig. 9). In this study, we find that the J max : cmax ratio ranges from 1.45 to Most of the fitting methods have minor influence on the J max : cmax ratio because we set C i,t to a constant of 0 Pa and light irradiance (I) was relative stable, ranging from 1498 to 1501 mmol m - s -1 (Table 5). The range of the ratio for our four shrub species was similar to the combined ratio of 1.67 used for a number of crop, broadleaf and coniferous species (Medlyn et al. 00), but lower than the ratio values for various woody and C 3 crop species obtained in previous studies (Farquhar et al. 1980; Wullschleger 1993; Xu & Baldocchi 003; Ellsworth et al. 004; Manter & Kerrigan 004; Yin, an Oijen & Schapendonk 004; Onoda et al. 005; Warren & Dreyer 006). For example, these values were in line with.09, a ratio of mean J max to mean cmax of 109 C 3 plant species (Wullschleger 1993), and for rice, wheat, barley, common bean and soybean (Yin et al. 004), but lower than the ratio of.5 averaged over 19 woody species fitted with variable C i,t transition points (Manter & Kerrigan 004). It is important to note that many ecosystem models, such as Biome-BGC (Thornton et al. 00), set the J max : cmax ratio to.1 according to the results by Wullschleger (1993), but our results showed that the J max : cmax ratio may simply change with the C i transition point in fitting the A C i curves. In addition, the J max : cmax ratio is also dependent upon the models used in estimating J max : cmax, TPU and R d, i.e. the A C c curve or conventional A C i curve (i.e. g m ). With the conventional A C i curves, our J max : cmax ratio was very close to the results by Wullschleger (1993). R d is often calculated from cmax in some ecosystems models, by using the linear relationship of R d b cmax or R d a + b cmax (Collatz et al. 1991). The ratio of cmax to R d represents the ratio of leaf photosynthetic rate at low CO concentration to leaf day respiratory CO production. Theoretically, we derived the cmax : R d ratio as follows. At the C i compensation point (C i,0), A c 0, so C i,0 C c,0. Eqn can be rewritten as O 0 Wc Rd, (0) τc c,0 i.e O cmaxcc,0 + ( 1 + ) R d. (1) C C K O K R i.e. τ c,0 Then, cmax d R cmax d c,0 c o τ [ Cc,0 + Kc( 1 + O Ko )], () τc 05. O c,0 τ [ Ci,0 + Kc( 1 + O Ko) ] fc ( i,0 ). (3) τc 05. O i,0 Thus, the cmax : R d ratio is a function of the C i compensation point (C i,0), which depends upon leaf nitrogen, Rubisco activity, mitochondrial enzymes activity, etc. (Osmond & Grace 1995; Guo et al. 005). Assuming T 5 C, O Pa, K c 7.85 Pa CO, K o Pa O, t in Table, and the mean C i, Pa for method I in our data set, the cmax : R d ratio is equal to 3.34.

12 10 Z. Miao et al. Fitting methods do not significantly influence the cmax : R d ratio. For example, for methods I I, our mean cmax : R d ratio varied from 3.43 for method II to 7.33 for method I (Table 5). These values were slightly higher than the ratio values reported for the Mediterranean evergreen species Quercus ilex L. that ranged from to.5 (Rodeghiero et al. 007), but were lower the ratio value of 35 reported for an unknown species (Long & Bernacchi 003) and the ratio values of 66.7 and 90.9 reported in other earlier studies (Farquhar et al. 1980; Collatz et al. 1991; Harley et al. 199b). TPU limitations can significantly affect J max and cmax predictions. The relation between J max and TPU can be calculated by A j A p at the C c transit points (C c,tpu) between the A j and A p curves. Replacement by Eqns 3 and 4, respectively, then 05. O 1 τc So, TPU J C c,tpu J Cc,TPU 3 4( + ) TPU. C O τ c,tpu O Cc,TPU C τ c,tpu 1( Cc,TPU + O τ) Cc,TPU Γ * when c,tpu 1( C + *) < 1 C Γ 1. Similarly, i,tpu c, TPU ( 1TPU J) O τ 3TPU R + J 1TPU g m d (4) (5) Γ *. (6) Thus, the relationship between J max and TPU is a function of C c,tpu (the C c transitional points between the A j and A p curves). Fitting methods do not significantly affect the ratios of J max to TPU. For a given A C c curve, J max predictions will be significantly affected without considering TPU limitations if C c,tpu is not too high (Fig. 10). In previous studies, TPU limitations have often not been taken into account in the fitting process because of the rare occurrence of TPU limitations under natural conditions. During the A C i curve measurements, however, TPU limitations may occur under high C i concentration in the Li-Cor chamber. For example, for our data sets, the mean C i,tpu value of 17 leaves was 53.7 Pa, which was considerably higher than natural ambient CO concentration (370 mmol mol -1 ). TPU limitations indeed occur in approximately 80% of our data sets. One way to diminish TPU impacts on cmax and J max is to remove TPU-limited data points (usually one to three data points at high C i end in our data). However, C c,tpu values varied from plant to plant. One may not be certain of data points of TPU limitation for a specific A C c curve. Theoretically, the function of min{a c, A j, A p} in Eqn 1 can automatically determine TPU values if TPU limitations occur, particularly for methods I and II (the whole curve simultaneously fitting methods). From the prospective of fitting practices of A C c curves, if the degree of freedom of an A C c curve is high enough, we J max (µmol m s 1 ) without TPU limitations cmax (µmol m s 1 ) without TPU limitations recommend that A C c parameters should include TPU limitation regardless of occurrence of TPU limitation in natural conditions. CONCLUSIONS J max _TPU J max _no_tpu J max (µmol m s 1 ) with TPU limitations cmax _TPU cmax _no_tpu cmax (µmol m s 1 ) with TPU limitations Figure 10. Influences of triose-phosphate utilization (TPU) limitations on potential light saturated electron transport rate (J max) and ribulose 1 5-bisphosphate carboxylase/oxygenase carboxylation rate ( cmax) predictions from method I. In comparing six commonly employed fitting methods, we have shown that the fitting method chosen can significantly affect the estimations of the A C c parameters ( cmax, J max, TPU, R d and g m) in Farquhar s photosynthetic model. The J max : cmax, cmax : R d and J max : TPU ratios were less sensitive to the fitting methods than those A C c parameters. We found that our method I, which integrated grid search and non-linear two stage least square techniques in fitting cmax, J max, TPU, R d and g m dirctly and simultaneously with the entire range of A C c data points, is superior to the other methods examined in terms of fitting accuracy, the highest

13 Comparison of A C c curve fitting methods 11 degree of freedom for a given A C c curve, and simplicity of the fitting skill and procedure. Regardless of fitting method employed, increasing the number of data points at low C i end will significantly improve the fitting and estimation of cmax. ACKNOWLEDGMENTS The research was supported by the Kirkwood Cohansey project of the New Jersey Pinelands Commission. The authors would like to thank Drs Erik Hamerlynk and Allison Brown for their help with field measurements. The National Science Foundation partially supported this study with the grant number We are also grateful to the constructive comments of three anonymous reviewers and subject editor of the journal on the earlier manuscript. REFERENCES Bernacchi C.J., Singsaas E.L., Pimentel C., Portis A.R. Jr. & Long S.P. (001) Improved temperature response functions for models of Rubisco-limited photosynthesis. Plant, Cell & Environment 4, Bernacchi C.J., Portis A.R., Nakano H., von Caemmerer S. & Long S.P. (00) Temperature response of mesophyll conductance: implications for the determination of Rubisco enzyme kinetics and for limitations to photosynthesis in vivo. Plant Physiology 130, von Caemmerer S. & Farquhar G.D. (1981) Some relationships between the biochemistry of photosynthesis and the gas exchange of leaves. Planta 153, Collatz G.J., Ball J.T., Grivet C. & Berry J.A. (1991) Physiological and environmental regulation of stomatal conductance, photosynthesis and transpiration: a model that includes a laminar boundary layer. Agricultural and Forest Meteorology 54, Cramer W., Bondeau A., Woodward F.I., et al. (001) Global response of terrestrial ecosystem structure and function to CO and climate change: results from six dynamic global vegetation models. Global Change Biology 7, Curtis P.S., ogel C.S., Pregitzer K.S., Zak D.R. & Teeri J.A. (1995) Interacting effects of soil fertility and atmospheric CO on leaf area growth and carbon gain physiology in Populus x euramericana (Dode) Guinier. New Phytologist 19, Dubois J.J.B., Fiscus E.L., Booker F.L., Flowers M.D. & Reid C.D. (007) Optimizing the statistical estimation of the parameters of the Farquhar von Caemmerer Berry model of photosynthesis. New Phytologist 176, Ellsworth D.S., Reich P.B., Naumburg E.S., Koch G.W., Kubiske M.E. & Smith S.D. (004) Photosynthesis, carboxylation and leaf nitrogen responses of 16 species to elevated pco() across four free-air CO enrichment experiments in forest, grassland and desert. Global Change Biology 10, Ethier G.J. & Livingston N.J. (004) On the need to incorporate sensitivity to CO transfer conductance into the Farquhar von Caemmerer Berry leaf photosynthesis model. Plant, Cell & Environment 7, Farquhar G.D., von Caemmerer S. & Berry J.A. (1980) A biochemical model of photosynthetic CO assimilation in leaves of C3 species. Planta 149, Flexas J., Diaz-Espejo A., Galmés J., Kaldenhoff R., Medrano H. & Ribas-Carbo M. (007) Rapid variations of mesophyll conductance in response to changes in CO concentration around leaves. Plant, Cell & Environment 30, Forman R.T.T. (1979) Pine Barrens: Ecosystem and Landscape. Academic Press, New York, USA. Guo S., Schinner K., Sattelmacher B. & Hansen U.P. (005) Different apparent CO compensation points in nitrate- and ammonium-grown Phaseolus vulgaris and the relationship to non-photorespiratory CO evolution. Physiological Plantarum 13, Hanson P.J., Amthor J.S., Wullschleger S.D., et al. (004) Oak forest carbon and water simulations: model intercomparisons and evaluations against independent data. Ecological Monograph 74, Harley P.C. & Baldocchi D.D. (1995) Scaling carbon dioxide and water vapour exchange from leaf to canopy in a deciduous forest. I. leaf model parameterization. Plant, Cell & Environment 18, Harley P.C. & Sharkey T.D. (1991) An improved model of C3 photosynthesis at high CO: reversed O sensitivity explained by lack of glycerate reentry into the chloroplast. Photosynthesis Research 7, Harley P.C., Weber J.A. & Gates D.M. (1985) Interactive effects of light, leaf temperature, CO and O on photosynthesis in soybean. Planta 165, Harley P.C., Tenhunen J.D. & Lange O.L. (1986) Use of an analytical model to study limitation on net photosynthesis in Arbutus unedo under field conditions. Oecologia 70, Harley P.C., Loreto F., di Marco G. & Sharkey T.D. (199a) Theoretical consideration when estimating the mesophyll conductance to CO flux by analysis of the response of Photosynthesis to CO. Plant Physiology 98, Harley P.C., Thomas R.B., Reynolds J.F. & Strain B.R. (199b) Modelling photosynthesis of cotton grown in elevated CO. Plant, Cell & Environment 15, Long S.P. & Bernacchi C.J. (003) Gas exchange measurements, what can they tell us about the underlying limitations to photosynthesis? Procedures and sources of error. Journal of Experimental Botany 54, Manter D.K. & Kerrigan J. (004) A Ci curve analysis across a range of woody plant species: influence of regression analysis parameters and mesophyll conductance. Journal of Experimental Botany 55, Medlyn B.E., Badeck F.W., De Pury D.G.G., et al. (1999) Effect of elevated CO on photosynthesis in European forest species: a metal analysis of model parameters. Plant, Cell & Environment, Medlyn B.E., Dreyer E., Ellsworth D., et al. (00) Temperature response of parameters of a biochemically based model of photosynthesis. II. A review of experimental data. Plant, Cell & Environment 5, Monti A., Brugnoli E., Scartazza A. & Amaducci M.T. (006) The effect of transient and continuous drought on yield, photosynthesis and carbon isotope discrimination in sugar beet (Beta vulgaris L.). Journal of Experimental Botany 57, Onoda Y., Hikosaka K. & Hirose T. (005) Seasonal change in the balance between capacities of RuBP carboxylation and RuBP regeneration affects CO response of photosynthesis in Polygonum cuspidatum. Journal of Experimental Botany 56, Osmond C.B. & Grace S.C. (1995) Perspectives on photoinhibition and photorespiration in the field: quintessential inefficiencies of the light and dark reactions of photosynthesis? Journal of Experimental Botany 46, Parsons R. & Ogston S. (1999) Photosyn Assistant er Dundee Scientific, Dundee, UK.