Parameterization and testing of a biochemically based photosynthesis ...

Tree Physiology 19, 481--492 © 1999 Heron Publishing----Victoria, Canada

Parameterization and testing of a biochemically based photosynthesis model for walnut (Juglans regia) trees and seedlings XAVIER LE ROUX,1,3 SANDRINE GRAND,1 ERWIN DREYER2 and FRANÇOIS-ALAIN DAUDET1 1

U.A. Bioclimatologie-PIAF (INRA-Université Blaise Pascal), Site de Crouel, 234 Avenue du Brezet, 63039 Clermont-Ferrand Cedex 02, France

2

Unité d’Ecophysiologie Forestière INRA, 54280 Champenoux, France

3

Author to whom correspondence should be addressed

Received October 28, 1998

Summary The biochemically based leaf photosynthesis model proposed by Farquhar et al. (1980) and the stomatal conductance model proposed by Jarvis (1976) were parameterized for walnut. Responses of photosynthesis to CO2 and irradiance were used to determine the key parameters of the photosynthesis model. Concurrently, stomatal conductance responses to leaf irradiance (Q), leaf temperature (Tl ), water vapor pressure deficit at the leaf surface (D), and air CO2 concentration at the leaf surface (Cs) were used to parameterize the stomatal conductance model. To test the generality of the model parameters, measurements were made on leaves from a 20-year-old tree growing in the field, and from sunlit and shaded greenhouse-grown seedlings. The three key parameters of the photosynthesis model (maximum carboxylation rate Vcmax, electron transport capacity Jmax, and dark respiration rate Rd ) and the key parameter of the conductance model (reference stomatal conductance, gsref ) were linearly correlated with the amount of leaf nitrogen per unit leaf area. Unique relationships could be used to describe nitrogen effects on these parameters for leaves from both the tree and the seedlings. Our data allowed separation of the effects of increasing total photosynthetic apparatus per unit leaf area from the effects of partitioning nitrogen among different pools of this apparatus for foliage acclimation to leaf irradiance. Strong correlations were found between stomatal conductance gs and Q, D and Cs, whereas the relationship between gs and Tl was weak. Based on these parameterizations, the model adequately predicted leaf photosynthesis and stomatal conductance when tested with an independent set of data obtained for the tree and seedlings. Total light-driven electron flows derived from chlorophyll fluorescence data obtained at different leaf temperatures were consistent with values computed by the model. The model was also tested with branch bag data acquired from a three-year-old potted walnut tree. Despite a relatively large variance between observed and simulated values, the model predicted stomatal conductance and photosynthesis reasonably well at the branch scale. The results indicate that the photosynthesis--conductance model developed here is robust and can be applied to walnut trees and seedlings under various environmental conditions where water is non-limiting.

Keywords: carbon dioxide, chlorophyll fluorescence, leaf gas exchange, nitrogen, stomatal conductance, temperature, transpiration, water vapor pressure deficit.

Introduction During the last decade, process-based simulation models have been increasingly used to deepen our understanding of tree growth and development (Isebrands et al. 1989). In particular, several mechanistic, carbon-based models have been developed to simulate the growth of juvenile poplar clones (Rauscher et al. 1990), peach trees (Grossman and DeJong 1994), young red pine trees (Zhang et al. 1994) or Pinaceae branches (Ford and Ford 1990), among many other examples. Of the processes controlling tree growth and yield represented in these models, photosynthetic capacities are always of prime importance, because they determine (along with foliage distribution) potential tree carbon gains. Furthermore, environmental variables largely control actual photosynthetic rates. Thus, developing a process-based model of tree growth for a given species calls for reliable and comprehensive information on functional relationships between leaf CO2 assimilation and plant and environmental variables (e.g., Host et al. 1990). Along with other valuable hardwood tree species, common walnut (Juglans regia L.) is grown as a plantation species in temperate and Mediterranean regions for both fruit and stemwood production. In particular, walnut cropping or intercropping helps mitigate the problems of farm surpluses and timber shortages in Europe. However, appropriate, biologically based management techniques still need to be developed for this species. Recently, we constructed an ecophysiological model for simulating common walnut tree growth processes (Le Dizès et al. 1997). The model takes into account the 3-D tree structure, and computes radiation absorption, photosynthesis, respiration, carbon allocation, reserve dynamics and tree growth and development. Its ultimate goal is to help define pruning practices in walnut. However, ecophysiological traits of this species are still poorly documented. In particular, information on photosynthesis and stomatal conductance is meager

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(Dean et al. 1982, Tombesi et al. 1983, Parker and Pallardy 1991, Girona 1993). Furthermore, as for many other tree species, comprehensive information on the effects of environmental variables and plant nutrient status on photosynthesis is still lacking for walnut. This is a major impediment for simulating and predicting the response of walnut tree growth to various environments. The objective of this study was to develop a photosynthesis-stomatal conductance model for common walnut under nonlimiting water conditions that would allow us to (i) assess photosynthetic carbon gain of individuals ranging from several-month-old seedlings to several-year-old trees, (ii) simulate the spatial variability of photosynthesis within the foliage of individual trees, and (iii) predict the influence of the major environmental (i.e., light, air humidity and CO2 concentration) and plant (leaf temperature and nitrogen status) variables on leaf photosynthetic rates. These objectives required the parameterization of a process-based leaf photosynthesis model that accounts for the influence of both leaf physiological characteristics and local microclimate. Leaf gas exchange measurements were used to estimate values of the key parameters of a version (Harley et al. 1992) of the C3 photosynthesis model originally proposed by Farquhar et al (1980). Because the amount of leaf nitrogen on an area basis (Na in g N m −2) and photosynthetic capacity are generally highly correlated (Field and Mooney 1986, Evans 1989a), the relationships between key model parameters and Na were investigated. Concurrently, an empirical stomatal conductance model (Jarvis 1976) was parameterized for common walnut. To improve the generality of the model parameters, measurements were made on sunlit and shaded leaves within the crown of a 20-year-old tree growing in the field, and on leaves of greenhouse-grown seedlings. The model was tested against (i) independent measurements of leaf stomatal conductance and photosynthesis, and (ii) total light-driven electron flow derived from chlorophyll fluorescence data. In addition, the model was tested against branch bag data obtained from a three-year-old walnut tree.

Materials and methods Plant material During summer 1996, leaf gas exchange measurements were made in a common walnut (Juglans regia) orchard at Plauzat, France (45°30′ N, 3°04′ E). Trees, which were planted in 1976 at a density of 100 ha −1, were around 7.5 m high. The tree selected for the study was 7.7 m high and was located in the middle of a 1.5-ha orchard. The tree crown had a maximal diameter of 6 m (North--South) and was 5 m deep. Total leaf area was 144 m2 for a 95 m3 crown volume (Sinoquet et al. 1997). A scaffolding erected around the tree gave access to branches in several directions and to the top of the tree. A platform gave access to the center of the tree crown. All measurements were made from early July to early August 1996. Six LVDTs (linear variable displacement transducers; Solartron Metrology, Bognor, U.K.) were used to monitor variations in the diameter of the trunk and five branches. Measurements revealed no stem or branch shrinkage, indicat-

ing the absence of water stress during gas exchange measurements (data not shown). Insect control was maintained during the study period. During early July 1997, leaf gas exchange measurements were made on five-month-old seedlings of Juglans regia. During mid-January, seeds were soaked in water for 48 h and planted in 18 dm3 pots filled with vermiculite (two individuals per pot). Seedlings were grown in a greenhouse under semicontrolled conditions (air temperature ranging from 16 to 35 °C) and automatically watered twice a day with a complete nutrient solution (Le Blevennec 1986). Half the seedlings were maintained under full light conditions (i.e., maximum Q around 1000 µmol m −2 s −1 on clear days), whereas the others were shaded by a green screen (maximum Q around 125 µmol m −2 s −1) from the end of February until July. For model testing, branch-bag data acquired during summer 1995 on a three-year-old common walnut tree were used. The tree was grown outdoors in a 200 dm3 container filled with a 1:2 (v/v) mixture of peat and clay soil. The container was irrigated daily and supplemented with 20 g NH 4NO3 per year. Model description The overall model consists of (i) a leaf photosynthesis submodel that simulates the effects of environmental variables (radiation, air water vapor pressure deficit and CO2 concentration) and leaf properties (temperature and nitrogen status) on the CO2 assimilation rate, and (ii) a stomatal conductance submodel simulating the effects of the same environmental and leaf characteristics on stomatal conductance. The amount of leaf nitrogen on an area basis is used as a key input parameter for scaling photosynthetic capacities and stomatal conductance between leaves. Both submodels are combined analytically. Water restriction is not considered in the present version of the model. Leaf photosynthesis submodel Leaf photosynthesis is simulated according to Farquhar et al. (1980). The version of the model proposed by Harley et al. (1992) was used, but without including the potential limitation arising from triose phosphate utilization. Net CO2 assimilation rate (A, µmol CO2 m −2 s −1) is expressed as: A = [1 − (0.5O ) / (τCi)] min (W c,W j) + Rd ,

(1)

where Wc (µmol CO2 m −2 s −1) is the carboxylation rate limited by the amount, activation state or kinetic properties of Rubisco, Wj (µmol CO2 m−2 s −1) is the carboxylation rate limited by the rate of RuP2 regeneration, τ is the specificity factor for Rubisco (Jordan and Ogren 1984), Rd (µmol CO2 m −2 s −1) is the rate of CO2 evolution in light that results from processes other than photorespiration, and O and Ci (Pa) are the partial pressures of O2 and CO2 in the intercellular air spaces, respectively. Rubisco activity is likely to restrict assimilation rates under conditions of high irradiance and low Ci. Regeneration of RuP2 is likely to be limiting at low irradiance and high Ci. Parameter Wc obeys competitive Michaelis-Menten kinetics with respect to O2 and CO2:

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W c = Vcmax C i / (Ci + K c(1 + O / K o)),

(2)

where Vcmax (µmol CO2 m −2 s −1) is the maximum rate of carboxylation, and K c and K o (Pa O2 and Pa CO2) are Michaelis constants of Rubisco for carboxylation and oxygenation, respectively. Parameter Wj is controlled by the rate of electron transport J (µmol m −2 s −1):

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Table 1. Values, units and sources of the parameters used in the photosynthesis--stomatal conductance model for walnut (Equations 1 to 14). Input variables are leaf irradiance, leaf temperature, air CO2 concentration and water vapor pressure deficit at the leaf surface, and amount of leaf nitrogen per unit leaf area. Parameter

Value

Unit

Source1

gs submodel

(3)

aN bN

30.6 82.9

mmol m −2 s −1 mmol g −1 s −1

meas. meas.

Parameter J depends on photosynthetically active photon flux density Q (µmol m −2 s −1):

aQ bQ

0.0310 −8.1

µmol −1 m2 s µmol m −2 s −1

meas. meas.

aD bD

1.18 −0.19 × 10 −3

− Pa −1

meas. meas.

aT bT cT

−2.03 0.242 −4.8 × 10 −3

− C ° −2 C

meas. meas. meas.

a Cs b Cs c Cs

2.07 −4.02 × 10 −2 2.32 × 10 −4

− Pa−1 Pa −2

meas. meas. meas.

α

0.24

mol mol −1

H92

a N−Rd b N−Rd

−32.85 −1.027

− g −1

meas. meas.

a N−Vcmax b N−Vcmax a N−Jmax b N−Jmax

47.42 1.118 36.11 0.993

− g−1 − g−1

meas. meas. meas. meas.

c(K c) c(K o ) c(τ)

35.79 9.59 −3.9489

− − −

H92 H92 H92

80.47 × 103 14.51 × 103 −28.99 × 103 84.45 × 103 109.5 × 103 79.5 × 103 199.5 × 103 201 × 103 650 650

J mol −1 J mol −1 J mol −1 J mol −1 J mol −1 J mol −1 J mol −1 J mol −1 J K−1 mol −1 J K−1 mol −1

H92 H92 H92 H92 meas. H92 meas. H92 H92 H92

W j = JCi / (4(Ci + O / τ)).

J = αQ / (1 + α2Q2 / J2max )0.5 ,

(4)

where Jmax (µmol m −2 s −1) is the light-saturated rate of electron transport, and α is the apparent efficiency of light energy conversion on an incident light basis (mol electrons per mol photons). The temperature dependence of Rd, τ, K c, and K o is described by: Parameter (Rd , τ, Kc, Ko) = exp(c -- ∆ H a) / (RTl),

(5)

where ∆Ha (J mol −1) is the activation energy of the given parameter, R (8.3143 J K −1 mol −1) is the gas constant, Tl (K) is leaf temperature, and c is the dimensionless, scaling constant of the given parameter. Similarly, the temperature dependence of Vcmax and Jmax is described by: Parameter (Vcmax, Jmax ) = exp(c − ∆H a / RTl) + exp((∆STl − ∆ Hd) / (RTl)),

(6)

where ∆S (J K −1 mol −1) is an entropy term, and ∆Hd (J mol −1) is the deactivation energy of the given parameter. To account for the linear relationships commonly observed between leaf photosynthetic capacities and Na (g N m −2) (e.g., Field 1983, Leuning et al. 1991, Harley et al. 1992) and considering that these capacities are a function of exp(c), the scaling factors c for Vcmax, Jmax, and Rd are linearly related to ln(Na) as: c = aN + bNln(Na).

(7)

° −1

A submodel

T effect ∆Ha (Kc) ∆Ha (K o) ∆Ha (τ) ∆Ha (R d) ∆Ha (V cmax) ∆Ha (J max ) ∆Hd(V cmax) ∆Hd (Jm a x ) ∆S (V cmax ) ∆S (J max )

A complete list of the parameters is given in Table 1. Stomatal conductance submodel The empirical stomatal conductance model proposed by Jarvis (1976) was used. The model assumes that stomatal conductance, gs, is affected by non-synergistic interactions between plant and environmental variables. Thus, gs (mmol H2O m −2 s −1) is computed as: gs = gsref f (Q) f (Tl) f (D) f (Cs ),

(8)

where D is the air water vapor pressure deficit at the leaf surface (Pa), Cs is the air CO2 concentration at the leaf surface (Pa), and gsref is the reference stomatal conductance (defined

1

Sources: meas. = measured; H92 = Harley et al. (1992).

as the value observed under standard conditions, i.e., Q = 1600 µmol m −2 s −1, Tl = 25 °C, D = 1000 Pa, and Cs = 35 Pa). The magnitude of each scaling function f indicates the relative importance of its control on gs. The original functions of f proposed by Jarvis (1976) for Q and D are used, whereas the effects of Tl and Cs are represented by second-order polynomials: f (Q) = aQ (Q − bQ ) / (1 + aQ(Q − bQ )),

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(9)

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LE ROUX, GRAND, DREYER AND DAUDET

f (D) = aD + bD D,

(10)

f (Tl) = aT + bT Tl + cTT2l ,

(11)

f (Cs ) = acs + bcs Cs + ccs C2s ,

(12)

where a, b and c are parameters. To account for the linear relationship observed between the reference stomatal conductance and photosynthetic capacity (e.g., Osmond 1983, Dang et al. 1997c), gsref is allowed to vary as a function of Na (i.e., the index of photosynthetic capacity in the photosynthesis submodel): gsref = aN + bNNa.

(13)

The limitations of this empirical relationship are discussed later. Coupling the photosynthesis and stomatal conductance submodels Parameter Ci is a driving variable of the photosynthesis submodel, and it is linked to A and stomatal conductance according to: A = gsCO 2(Cs − Ci) / P,

(14)

where P is atmospheric pressure (Pa), and gsCO 2 (= gs 1000/1.6) is leaf stomatal conductance for CO2 (µmol CO2 m −2 s −1). An analytical solution is used to couple the photosynthesis and stomatal conductance submodels. Combining Equations 1, 2 or 3, and 14, A can be expressed as the solution of a quadratic equation, where the variable gsCO 2 is used instead of Ci (see Wang and Jarvis 1993). Determination of the parameters of the photosynthesis submodel Gas exchange was measured with an infrared gas analyzer-leaf chamber system (LI-6400, Li-Cor, Inc., Lincoln, NE) that allowed control of environmental variables within the leaf cuvette. Net CO2 assimilation and transpiration rates, stomatal conductance, and CO2 mole fraction in the substomatal spaces were calculated according to von Caemmerer and Farquhar (1981). Measurements were made on 17 leaves within the mature tree crown in the field (encompassing full sunlight and shade conditions), and on five sunlit and five shaded greenhouse-grown seedlings (one leaf per seedling). All measurements were performed on fully expanded leaves. For each leaf, an A−Ci response curve measured at high irradiance (Q = 1500 µmol m −2 s −1) was used to infer the best fit Vcmax value by nonlinear least squares regression. Only data collected for Ci values below 25 Pa were used. On the same leaf, an A−Q response curve performed at high CO2 (Ca = 100 Pa) was used to infer the best fit Jmax value by the same nonlinear regression technique. For each response curve, eight to nine measurements were acquired (Ca = 100, 35, 30, 20, 15, 10, 7.5 and 5 Pa, and Q = 1800, 1500, 1000, 500, 200, 100, 50, 20 and 0 µmol m −2 s −1). A 20 to 30 min equilibration time was allowed before any measurement. Based on a posteriori simu-

lations, we made sure that CO2 assimilation was always limited by Rubisco activity for Ci values less than 25 Pa during A−Ci responses, and by regeneration of RuBP for all the conditions encountered during A−Q responses. Values of Rd were estimated by measurements of the CO2 evolution rates at the end of a night (from 0400 to 0600 h) for leaves of the mature tree only. For A−Ci and A−Q responses, leaf temperature and D in the leaf chamber were maintained at 25 ± 0.2 °C and 1 ± 0.1 kPa, respectively. The same conditions were used for Rd measurements. For two leaves of the mature tree for which Vcmax was determined at 25 °C, A−Ci responses were also performed at leaf temperatures of 18 and 31 °C. In all cases, a 4-day minimum interval was allowed between two successive observations (i.e., A−Ci or A−Q curves) on the same leaf to avoid effects of stress resulting from measurements. After the last gas exchange measurement series, each leaf was collected and fresh leaf area was measured with a leaf area meter (Delta T Devices, Hoddesdon, U.K.). Leaves were frozen in liquid nitrogen and lyophilized, and their dry mass measured. Total nitrogen concentration (i.e., on a dry mass basis) of each leaf was determined with an elemental analyser (Carlo Erba Instruments, Milan, Italy). Our data also allowed analysis of potential variations in leaf nitrogen investment in two different pools of the photosynthetic system. Niinemets and Tenhunen (1997) recently proposed a model to determine coefficients for leaf nitrogen partitioning into Rubisco, Pr , bioenergetic pools, Pb, and thylakoid light-harvesting components, Pl , based on estimated values of Vcmax, Jmax and chlorophyll content. In this model, Pr defines the overall light-saturated photosynthetic capacity (i.e., influences Vcmax ), whereas Pb determines the protein content limiting the capacity for electron transport and photophosphorylation (i.e., influences Jmax ). We computed Pr (g N in Rubisco per g total leaf N) and Pb (g N in cytochrome f, ferredoxin NADP reductase, and coupling factor per total leaf N) as proposed by Niinemets and Tenhunen (their Equations 4 and 5 and Table A1). Lack of information on leaf chlorophyll content prevented us from computing Pl. Determination of the parameters of the stomatal conductance submodel The reference stomatal conductance gsref was measured under standard conditions (i.e., Q = 1600 µmol m −2 s −1, Tl = 25 °C, D = 1000 Pa, and Cs = 35 Pa) on 22 leaves within the mature tree crown in the field, and on five sunlit and five shaded greenhouse-grown seedlings (one leaf per seedling). The specific leaf area and total nitrogen concentration of each leaf were determined as described above. In addition, the responses of gs to Q, Tl, D, and Cs were studied for leaves of the fieldgrown tree, fixing the three other variables to their reference values. The response of gs to decreasing Q was assessed on six leaves, using nine Q values (from 1600 to 0 µmol m −2 s −1). The effect of Tl on gs was studied on four leaves. For each leaf, measurements were made at three Tl values (17−21, 25, and 29−31 °C). The response of gs to increasing D (six steps from 1 to 3.5 kPa) was observed on four leaves. The response of gs

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to decreasing Cs was assessed on eight leaves, using eight Cs values (from 100 to 3 Pa). All measurements were made on illuminated leaves (i.e., stomata were open at the beginning of each response curve). A 20 to 30 min equilibration time was allowed before any measurement. Additional measurements for model testing Measurements of total light-driven electron flow at the leaf scale The variation in chlorophyll fluorescence with increasing Q was measured with a portable fluorometer (PAM 2000, Walz, Effeltrich, Germany). Measurements were made on five leaves of the mature tree and on leaves from two sunlit and one shaded seedling for which the parameters of the photosynthesis submodel had been determined. The total light-driven electron flow, J, was derived from (i) the chlorophyll fluorescence ratio ∆F/Fm′ (∆F = Fm′ − Fs, where Fs and Fm′ denote steady state fluorescence during photosynthesis and during a saturating flash, respectively) and is a reliable estimate of ΦII, i.e., the quantum yield of energy conversion by photosystem II, PSII, (Genty et al. 1989) and (ii) incident Q: J = kQΦII .

(15)

Parameter k depends on the absorptance of the leaves and the fraction of PSII. To calibrate k, we compared ΦII and the apparent quantum yield of carboxylation (ΦCO 2 ) obtained as described by Valentini et al. (1995) or Roupsard et al. (1996) by measuring CO2 assimilation under very low O2 (O2-free humidified nitrogen was supplied to the leaf cuvette) as: ΦII = (4 / k)ΦCO2 = (4 / k)(A + Rd) / Q .

(16)

Figure 1 displays the relationship observed on leaves from five shaded and five sunlit seedlings. The estimated k value was used at ambient O2 to derive J values from fluorescence data, and to compare them to values computed by the photosynthesis submodel (Equation 4) using previously determined Jmax values or Na as inputs. Complementary measurements of stomatal conductance and photosynthesis at the leaf scale To test the model against an independent data set, complementary gas exchange measurements were carried out on eight leaves of the 20-year-old tree and six seedling leaves. Measurements were performed at two irradiances (around 60 and 1000 µmol m −2 s −1) for the leaves of the mature tree (D and Tl ranges: 1000−1750 Pa and 22−28 °C, respectively), and at five irradiances (from 75 to 1300 µmol m −2 s −1) for the seedling leaves (D and Tl ranges : 1700−2650 Pa and 28.5−30 °C, respectively). In all cases, Cs was about 35 Pa. Measured stomatal conductance and photosynthesis values were compared with values computed by the photosynthesis--stomatal conductance model using as inputs Q, Tl, D and Cs values measured in the leaf cuvette along with the leaf nitrogen concentrations and specific leaf areas determined after the measurements.

Figure 1. Relationship between the quantum yield of energy conversion by PSII (ΦII = ∆F/Fm′) measured by fluorescence and the apparent quantum yield of carboxylation (ΦCO 2 ) as measured on leaves of sun and shade seedlings at < 1% O2. Values were obtained during the determination of light response curves at 100 Pa CO2 (m) and CO2 response curves at 360 µmol m −2 s −1 Q (n).

Measurements of bulk stomatal conductance and photosythesis at the branch scale To test the ability of the model to predict photosynthesis and stomatal conductance at the branch scale, branch bag data obtained earlier on two branches of a threeyear-old walnut tree were used. A detailed description of the branch bag technique is given in Daudet (1987). Briefly, the branch bags were made of polyethylene film (30 µm) with low Q absorption (about 10%). Electrovalves were used for automatic air sampling at three different locations for each circuit. Improved software was developed to measure gas exchange on several chambers simultaneously with a differential IRGA (Mark III, ADC Bioscience, Ltd., Hoddeston, U.K.) and a dew point meter (1100 DP, General Eastern, Woburn, MA) for CO2 and water vapor determinations, respectively. Cyclic injection at the entry of each chamber of a flow of pure CO2 controlled by a mass flow regulator (FC 260, Tylan Corporation, Torrance, CA) allowed computation of air flow rate (about 0.25 m3 min −1). Net CO2 assimilation and transpiration rates were computed by mass balance equations. Because leaf temperature was not measured, it was assumed to be equal to air temperature, and heterogeneities in leaf gas exchange rates were neglected when computing the bulk stomatal conductance at the branch scale gs (mmol H2O m −2 s −1) as: gs = E / (es − ea),

(17)

where E is the branch transpiration rate (mmol H2O m −2 s −1), ea is the mole fraction of water vapor in bulk air and es is the mole fraction of water vapor for saturated air at leaf temperature. Continuous determinations of transpiration and photosynthetic rates were made independently on two branches of the tree at 1-h intervals in summer 1995. Gas exchange data obtained during a sunny and hot day (July 24, 1995, 29 MJ m −2 global irradiance, 32 °C maximal air temperature, 3 kPa maximal water vapor pressure deficit) are presented here for comparison with the model. After gas exchange measurements, the two branches of the tree were digitized according to Sinoquet

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and Rivet (1997). The location, orientation and area of each leaf was measured. The total leaf area of the upper and lower branches was 0.27 and 0.19 m2, respectively. Using the parameter values derived from measurements made on seedlings and within the mature tree crown, the photosynthesis--stomatal conductance model was applied on each branch of the three-year-old tree. Using the digitized tree aboveground structure and measured direct and diffuse incident Q values as inputs, the radiation transfer model of the walnut tree model INCA (Le Dizès et al. 1997) was applied to compute individual leaf irradiance. This model accounts for both diffuse and direct incident radiation. Then, simulated individual leaf irradiances, air temperature and D measured inside the branch bag, and the measured bulk Na (a single value was obtained for the whole leaf material) were used as input variables for the photosynthesis--stomatal conductance model. Carbon dioxide effects on gs were neglected, because CO2 concentration was always about 35 Pa (± 2 Pa) in the branch bags.

Results Parameterization of the photosynthesis submodel In leaves from either the mature tree or seedlings, the amount of leaf nitrogen expressed on an area basis, Na, was roughly proportional to the leaf mass to area ratio, Wa (Figure 2), indicating that leaf nitrogen concentration remained largely constant between light treatments. However, mean leaf nitrogen concentration was higher in seedling leaves (3.4%) than in leaves of the mature tree (2.3%). Nevertheless, the response of Na to irradiance was similar in leaves from seedlings and from the tree (Figure 2). Photosynthetic capacities of leaves measured in standard conditions varied sharply between shade and sun seedlings, and even more among locations within the mature tree crown. Values of Vcmax, Jmax, and Rd ranged from 20 to 69 µmol CO2 m −2 s −1, 45 to 178 µmol electrons m −2 s −1, and −0.29 to −0.98 µmol CO2 m −2 s −1, respectively (Figure 3). Most of the variability in these parameters was correlated with the concurrent variability in Na (Figure 3). A unique linear relationship adequately described the dependence of Vcmax or Jmax on Na for leaves from both the tree crown and seedlings (Figure 3). This could not be checked for Rd because this parameter was not determined for seedling leaves. The computed values of Pr and Pb were not correlated to Na (P = 0.31 and 0.09, respectively) (Figure 4). The mass fraction of nitrogen in Rubisco Pr was 0.2, whereas the mass fraction of nitrogen in cytochrome f, ferredoxin NADP reductase, and coupling factor Pb was about 0.05. Estimated Vcmax increased fourfold as leaf temperature increased from 18 to 31 °C (Figure 5). Based on the original values of ∆Ha and ∆Hd derived by Harley et al. (1992) for cotton, Vcmax values were overestimated for leaf temperatures above about 27 °C (Figure 5). Better estimations of Vcmax for walnut in the range 18 to 31 °C resulted from computing ∆Ha and ∆Hd by regression (Figure 5; see values in Table 1).

Figure 2. Relationship between (top) amount of leaf nitrogen per unit leaf area, Na, and leaf mass to area ratio, Wa, and (bottom) Na and daily intercepted photosynthetically active radiation, Qi, for leaves sampled within the tree crown in the field (d) and leaves of shade and sun seedlings (s). Parameter Qi is the mean irradiance computed over a two-week period before sampling (from measurements for seedling leaves, and from model simulations for tree leaves, see Le Roux et al. 1999).

Figure 3. Relationships between the three key parameters of the photosynthesis model (maximum rate of carboxylation Vcmax, lightsaturated rate of electron transport, J max, and dark respiration rate, Rd ) and amount of leaf nitrogen per unit leaf area, Na. Measurements were performed on leaves within a 20-year-old tree crown (d) and leaves of greenhouse-grown seedlings (s) at a leaf temperature Tl = 25 °C. Measurements of Rd were performed on leaves of the mature tree only. The values of fitted parameters corresponding to Equation 7 are given in Table 1.

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Figure 4. Relationship between the coefficients for leaf nitrogen partitioning into Rubisco, Pr, and into bioenergetic pools, Pb, and amount of leaf nitrogen per unit leaf area, Na, for leaves from the mature tree (d) and seedlings (s).

487

Figure 6. Relationship between the reference stomatal conductance gsref (Tl = 25 °C, Cs = 35 Pa, D = 1 kPa and Q = 1500 µmol m −2 s −1) and amount of leaf nitrogen per unit leaf area, Na. Measurements were performed on leaves within a 20-year-old tree crown (d) and leaves of greenhouse-grown seedlings (s). The best fit line and parameters correspond to Equation 13.

relationship was obtained between gs and Tl. However, gs measured at leaf temperatures around 20 or 30 °C was always lower than at 25 °C. The values of the parameters of the photosynthesis--stomatal conductance model are presented in Table 1. Model testing at the leaf scale

Figure 5. Relationship between the maximum rate of carboxylation, Vcmax (expressed as the ratio V cmax (T) / Vcmax (25), i.e., the rate observed at actual temperature to the rate observed at 25 °C), and leaf temperature, Tl. Measurements were performed at three temperatures on two leaves (m and n) of the 20-year-old tree. The best fit line and parameters correspond to Equation 6. The relationship proposed by Harley et al. (1992) for cotton (dotted line) is presented for comparison.

Both for leaves of the mature tree and the seedlings, the total light-driven electron flow J computed by the model (Equation 4) was consistent with values derived from chlorophyll fluorescence data using either Jmax values or Na values determined on the same leaves as inputs (Figure 8). However, the accuracy of model predictions was lower when using Na values as inputs (root mean square error (RMSE) = 7.2 µmol m −2 s −1) than when using Jmax values as inputs (RMSE = 3.9 µmol m −2 s −1). The ability of the model to simulate stomatal conductance at the leaf scale was reasonably good despite a relatively high

Parameterization of the stomatal conductance submodel Reference stomatal conductance values measured on seedlings and within the mature tree crown ranged from 66 to 318 mmol H2O m −2 s −1. Reference stomatal conductance was correlated to leaf Na (Figure 6). A unique linear relationship adequately described this correlation for leaves from both the mature tree crown and seedlings. Stomatal conductance was correlated to changes in Q, D or Cs (Figure 7). The original function proposed by Jarvis (1976) adequately described the increase in gs with increasing Q. However, the accuracy of gs values at low irradiance derived from the fitting procedure was low. A linear decrease in gs with increasing D was observed in the 1 to 3.5 kPa D range. At D = 3.5 kPa, gs values were half those observed at 1 kPa. A second order polynomial adequately described the decrease in gs with increasing Cs. The response of gs to Cs was particularly marked in the 0 to 50 Pa range (Figure 7). In contrast, no strong

Figure 7. Variations of stomatal conductance, gs, as a function of leaf irradiance, Q, water vapor pressure deficit at the leaf surface, D, leaf temperature, Tl, and CO2 concentration at the leaf surface, Cs. Best fit lines and parameters correspond to Equations 9 to 12.

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Figure 10. Comparison of leaf photosynthetic rate measured in situ and simulated by the photosynthesis model. Measurements were performed for leaves of a 20-year-old tree (d) and for leaves of greenhouse grown seedlings (s). The RMSE and the 1/1 line are indicated. Figure 8. Relationship between the total light driven electron flow, J (µmol m −2 s −1), computed from chlorophyll fluorescence data, J fluorescence , and simulated by the photosynthesis model, J simulated . Simulation results are presented when Jmax values are either directly obtained from previous measurements on the same leaf (upper panel) or estimated from amount of leaf nitrogen per unit leaf area, Na (lower panel). Measurements were performed on five leaves of a 20-year-old tree and three leaves of greenhouse-grown seedlings.

residual variance (Figure 9). The model underestimated gs for the highest gs values measured on seedlings. Concurrently, the model adequately predicted leaf photosynthetic rates for both the leaves of the mature tree and seedlings (Figure 10). The RMSE was 44.9 mmol H2O m −2 s −1 and 1.6 µmol CO2 m −2 s −1 for stomatal conductances and photosynthetic rates, respectively. Model testing at the branch scale When the model parameterized from data acquired on seedlings and the mature tree was compared with the branch bag data obtained on the three-year-old tree (Figure 11), simulated and observed stomatal conductance values were significantly correlated (P < 0.001). However, the model tended to overestimate stomatal conductance. Furthermore, the residual vari-

Figure 9. Comparison of leaf stomatal conductance measured in situ and simulated by the conductance submodel. Measurements were performed on leaves of a 20-year-old tree (d) and on leaves of greenhouse-grown seedlings (s). The root mean square error (RMSE) and the 1/1 line are indicated.

ance in the gs determination was relatively high (RMSE = 30.3 mmol H2O m −2 s −1). It should be noted that, during the testing period, air D and temperature in the branch bags reached 3.4 kPa and 32 °C, respectively. Thus, simulated gs values were largely determined by values of the f(Tl ) and f(D) scaling functions (Equations 10 and 11). Concurrently, simulated photosynthetic rates were generally consistent with measured rates (Figure 12). Carbon dioxide assimilation rates were slightly overestimated at high irradiances. The RMSE for the photosynthetic rate at branch scale was 1.53 µmol CO2 m −2 s −1. Discussion Parameterization and testing of the stomatal conductance submodel Among the different stomatal conductance models presently available (e.g., Jarvis 1976, Farquhar and Wong 1984, Ball et al. 1987), we selected the phenomenological model proposed by Jarvis (1976). This model offers a simple, convenient framework within which to identify the relative importance of each variable on gs. Use of the Jarvis model requires documentation of the stomatal responses to Q, D, Tl and Cs. In the

Figure 11. Comparison of stomatal conductance simulated by the model and deduced from branch-bag measurements performed on a 3year-old tree. Each symbol corresponds to one of two branches of the tree. The RMSE and the 1/1 line are indicated.

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Parameterization and testing of the photosynthesis submodel

Figure 12. Comparison of photosynthetic rate simulated by the model and deduced from branch-bag measurements performed on a 3- yearold tree. Each symbol corresponds to one of two branches of the tree. The RMSE and the 1/1 line are indicated.

present study, we directly measured stomatal response to variations of single environmental variables. A typical response to Q (e.g., Leverenz, 1995) was obtained, with f(Q) reaching 0.75 and 0.90 for Q equal to 90 and 280 µmol m −2 s −1, respectively. Stomatal conductance decreased linearly with increasing D over the 1 to 3.5 kPa range. Such a linear decrease has been reported for several species of herbs and trees (e.g., Aphalo and Jarvis 1991, Bunce 1996). However, such linear relationships are not common for all tree species (e.g., Dang et al. 1997b, Maroco et al. 1997). Stomatal conductance was found to be highly sensitive to Cs in the 0 to 50 Pa range (Figure 6). In contrast to results obtained for other environmental variables, the relationship between leaf temperature and gs was weak (Figure 6). Similar, weak gs responses to Tl have frequently been reported for trees (e.g., Berryman et al. 1994). Following Jarvis (1976), we did not attempt to document potential effects of synergistic interactions between plant and environmental variables on gs. Further work is needed to test the basic assumption of the Jarvis model. Nonetheless, the model predicted stomatal conductance reasonably well in a range of environmental conditions, at both leaf and branch scales (Figures 9 and 11). A limitation of the Jarvis model is that it does not account for the correlation commonly encountered between maximum stomatal conductance and photosynthetic capacity (e.g., Osmond 1983, Mitchell and Hinckley, 1993, Dang et al. 1997c) (which is different from a correlation between actual gs and actual photosynthetic rate). In the present study, the original model proposed by Jarvis (1976) was slightly modified. In accordance with observations, gsref was varied as a function of Na (which is also used as an index of leaf photosynthetic capacity in the photosynthesis submodel). The relationship between gsref and Na has no causal basis and has only been used so that the model can adequately account for the relationship between maximum stomatal conductance and photosynthetic capacity. Such a relationship would need to be calibrated before applying the model to another tree species or under other climatic conditions.

In the present study, photosynthetic responses to CO2 at high irradiance, and photosynthetic responses to irradiance at high CO2 concentration were used to determine Vcmax and Jmax, respectively. The same method was used by Porté and Loustau (1998) in Pinus pinaster Ait. Because the least squares regression technique generally leads to poor estimates of Rd (Harley et al. 1992, Loustau and Porté, INRA, Bordeaux, France, personal communication), we measured leaf respiration at night directly. As it is currently unclear to what extent dark respiration (Rd ) is inhibited in the light (e.g., Azcón-Bieto and Osmond 1983, Brooks and Farquhar 1985, Villar et al. 1995), we assumed that Rd was equal to the values of nighttime respiration. Because Rd may decrease asymptotically with increasing Q (Brooks and Farquhar 1985, Villar et al. 1995), this assumption could lead to an overestimation of Rd, particularly at high irradiance. However, this is likely to have only a small effect on diurnal and daily photosynthetic carbon gains simulated by the model. At a given irradiance, photosynthetic rates were determined by leaf nitrogen concentration on an area basis and leaf temperature. For both the mature tree and seedlings, most variability in leaf photosynthetic capacity observed at a given temperature was explained by the concurrent variability in Na. The three key parameters of the photosynthesis submodel increased linearly with increasing Na. Such linear relationships have been reported for the chaparral shrub Lepechinia calycina (Benth.) Epl. (Field 1983), Eucalyptus grandis W. Hill ex Maiden trees (Leuning et al. 1991), cotton (Harley et al. 1992), the understorey tree Tetrorchidium rubrivenium Poepp & Endl. (Anten et al. 1996), a Nothofagus fusca (Hook. f.) Ørst. canopy (Hollinger 1996), and Pinus radiata D. Don (Walcroft et al. 1997), among others. Introducing a dependency of Vcmax and Jmax on Na in the leaf photosynthesis submodel is straightforward because these parameters are expected to be strongly correlated with the amount of leaf protein (e.g., Field and Mooney 1986, Evans 1989a) and because, generally, more than half the leaf nitrogen is associated with the photosynthetic apparatus in C3 plants (Evans and Seemann 1989). The value of Rd was also correlated with Na. This is consistent with the relationships between leaf photosynthetic capacity and dark respiration rate that have been reported for several tree species (e.g., Ceulemans and Saugier 1991). Unique linear relationships adequately described the dependence of Vcmax and Jmax to Na for leaves from both the mature tree crown and seedlings. A similar result was recently obtained for Pinus radiata trees and seedlings (Walcroft et al. 1997). This supports the idea that the present relationships are robust and could be applied to individual walnut trees ranging in age from several months to several years. This was confirmed by the ability of the model to predict stomatal conductance and photosynthesis at the branch scale for a three-year-old walnut tree (Figures 11 and 12). Applying the model requires accurate documentation or simulation of the spatial distribution of Na within the tree crown. This is particularly critical if the spatial distribution of carbon gain is to be simulated within the large crowns of old trees (e.g., Le Roux et al. 1999).

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Although several relationships have been proposed to describe the effects of leaf temperature on the Farquhar model parameters (e.g., Farquhar et al. 1980, Kirschbaum and Farquhar 1984, Harley et al. 1992), experimental tests of these relationships are scarce. Harley et al. (1985) and Harley et al. (1992) determined model parameters at five temperatures for soybean and at three temperatures for cotton, respectively. Reanalysis of databases describing branch gas exchange of Picea abies (L.) Karst. were used by Falge et al. (1996) to describe the temperature dependence of these parameters in the range 10−20 °C. Walcroft et al. (1997) provided comprehensive information on the response of photosynthetic model parameters to temperature in Pinus radiata. In all cases, a marked influence of leaf temperature on photosynthetic capacities was observed. In the present study, a fourfold increase in Vcmax values was observed when leaf temperature increased from 18 to 31 °C. Such a temperature effect is larger than that reported for Eucalyptus pauciflora Sieber ex A. Spreng. (Kirschbaum and Farquhar 1984), Picea abies (Falge et al. 1996) and Pinus radiata (Walcroft et al. 1997), lower than that observed for cotton (Harley et al. 1992), and similar to that observed for soybean (Harley et al. 1985). Most often, modeling exercises performed to assess CO2 assimilation within vegetation canopies assume a uniform leaf temperature (generally taken to be equal to air temperature). However, leaf temperature gradients of several degrees can be expected in relation to irradiance gradients. Our results, along with temperature dependence relationships reported elsewhere, show that the heterogeneity in leaf temperature within the foliage must be taken into account if the spatial variation of carbon gain within tree foliage is to be accurately simulated. Effect of long-term radiation regime on the amount of total leaf nitrogen, Na , and leaf nitrogen investment into Rubisco and bioenergetic pools Most photosynthesis models presently available directly relate variation in the biochemical potential of foliage to variations in Na (e.g., Hirose and Werger 1987, Harley et al. 1992, Kull and Jarvis 1995, Leuning et al. 1995). However, as suggested by Niinemets and Tenhunen (1997), variability of Na could be largely attributable to variability of leaf anatomy (Niinemets 1995, Le Roux et al. 1999). Thus it can be argued that traditional model analyses of nitrogen effects on photosynthesis have only poorly improved theoretical analyses based on investment in leaf mass per unit leaf area (e.g., Gutschick and Wiegel 1988). Furthermore, high biochemical potentials per unit leaf area required to ensure high photosynthetic capacities under high light regimes can be achieved either by increasing the amount of total leaf nitrogen on an area basis (by increasing nitrogen concentration or the leaf mass to area ratio, or both) or by changing leaf nitrogen investment in various pools of the photosynthetic system (Sukenik et al. 1987, Ögren 1993). In the present study, a marked increase in Na was observed with increasing time-integrated leaf irradiance (Figure 2). For a given plant material (i.e., greenhouse-grown seedlings or field-growing tree), variations in Na were essentially caused by variations in Wa, whereas leaf nitrogen concentration remained

constant. However, at a given irradiance, leaf nitrogen concentration and Wa were higher and lower, respectively, for seedling leaves than for leaves from the mature tree. This was probably explained by the high nutrient availability that characterized seedlings. Furthermore, for a given light regime, the high leaf nitrogen concentration and high specific leaf area observed in seedling leaves resulted in Na values similar to values observed for leaves from the field-grown tree. This demonstrates that both light availability and nutrient availability determine the way Na is modulated via changes in nitrogen concentration and specific leaf area in walnut. The computed values of Pr (about 0.2) and Pb (about 0.05) were close to values reported for Acer saccharum Marsh. leaves experiencing Q higher than 5 mol m −2 day −1 (about 0.18 and 0.045 for Pr and Pb, respectively) (Niinemets and Tenhunen 1997).Values of Pr and Pb were not correlated to Na. This is consistent with results obtained for Cucumis sativus L. (Evans 1989b) and Alocasia and Colocasia (Sims and Pearcy 1989). Applying the model proposed by Niinemets and Tenhunen (1997) to these data shows that Pr and Pb remained largely constant between different irradiance treatments. In contrast, both Pr and Pb decreased with increasing light availability in Flindersia brayleyana F. Mell. (Thompson et al. 1988), whereas Pb was found to increase significantly with increasing irradiance in Spinacia (Terashima and Evans 1988) and Pisum (Evans 1987). In Acer saccharum, Niinemets and Tenhunen (1997) found that Pr and Pb increased with increasing integrated quantum flux density for Q lower than 5 mol m −2 day −1, whereas Pr and Pb remained quite constant for higher values of Q. The authors pointed out that photosynthesis acclimation to high light was dominated by adjustments in leaf anatomy (i.e., in Wa) rather than in foliar biochemistry, whereas acclimation to low light was due to adjustments in both leaf biochemistry and leaf anatomy. In walnut, under the conditions experienced during our study (Q ranging from 5 to 25 mol m −2 day −1), variations of leaf photosynthetic capacities were thus mainly the result of (i) adjustments in Wa, and (ii) variations in total leaf nitrogen concentration, whereas changes in leaf nitrogen investment in Rubisco and bioenergetic pools were secondary. The balance between changes in Wa and nitrogen concentration emerged as the resulting effects of both light and nutrient availabilities. A limitation of this analysis is that the resistance to CO2 transfer within leaves is not taken into account. Because this resistance can be large in trees (Lloyd et al. 1992, Epron et al. 1995, Roupsard et al. 1996) and can vary with leaf features (Syvertsen et al 1995), Vcmax values can be underestimated (see Epron et al. 1995). Thus, actual nitrogen investment in Rubisco is larger than, and possibly not strictly proportional to, values assessed from gas exchange measurements. Determination of the leaf internal resistance to CO2 transfer in walnut under different light regimes is thus needed. Conclusions A biochemically based, leaf gas exchange model that accounts for various environmental effects was developed for walnut. Such comprehensive information on the response of stomatal

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function and photosynthesis to environmental variables is still scarce for tree species (but see Dang et al. 1997a). The model was parameterized and tested for walnut seedlings and trees over a range of leaf mass to area ratios and leaf nitrogen concentrations. The simulation results showed that the model is robust and can be applied to walnut individuals ranging in age from several months to several years. With further information on aging and drought effects on photosynthetic processes and stomatal conductance, this model will be of particular use as part of the physiologically based model of walnut tree growth developed in our laboratory (Le Dizès et al. 1997). Our data allow us to understand better the acclimation of leaf photosynthetic capacities to local light regimes. It was shown that adjustments in Wa play a major role in driving variations in leaf photosynthetic capacities, whereas changes in leaf nitrogen investment into Rubisco and bioenergetic pools are secondary in walnut. Acknowledgments The authors are greatly indebted to D. Loustau and A. Porté (INRA Bordeaux, France) for valuable suggestions during experiment planning, to S. Le Dizès for help in running the model INCA, and to H. Sinoquet for providing leaf irradiance data. We also thank R. Mège, S. Ploquin and M. Vandame (INRA Clermont Ferrand, France) for technical assistance, and F. Ewers (Michigan State University, East Lansing, USA) for reviewing the English. References Anten, N.P.R., R. Hernandez and E.M. Medina. 1996. The photosynthetic capacity and leaf nitrogen concentration as related to light regime in shade leaves of a montane tropical forest tree, Tetrorchidium rubrivenium. Funct. Ecol. 10:491--500. Aphalo, P.J. and P.G. Jarvis. 1991. Do stomata respond to relative humidity? Plant Cell Environ. 14:127--132. Azcón-Bieto, J. and C.B. Osmond. 1983. Relationship between photosynthesis and respiration: The effects of carbohydrate status on the rate of CO2 production by respiration in darkened and illuminated wheat leaves. Plant Physiol. 71:574--581. Ball, J.T., I.E. Woodrow and J.A. Berry. 1987. A model predicting stomatal conductance and its contribution to the control of photosynthesis under different environmental conditions. In Progress in Photosynthesis Research. Ed. J. Biggins. Martinus Nijhoff, Dordrecht, pp 221--224. Berryman, C.A., D. Eamus and G.A. Duff. 1994. Stomatal responses to a range of variables in two tropical tree species grown with CO2 enrichment. J. Exp. Bot. 45:539--546. Brooks, A. and G.D. Farquhar. 1985. Effect of temperature on the CO2/O2 specificity of ribulose-1,5-bisphosphate carboxylase/oxygenase and the rate of respiration in the light. Estimates from gas-exchange measurements on spinach. Planta 165:397--406. Bunce, J.A. 1996. Does transpiration control stomatal responses to water vapor pressure deficit? Plant Cell Environ. 19:131--135. Ceulemans, R. and B. Saugier. 1991. Photosynthesis. In Physiology of Trees. Ed. A.S. Raghavendra. Wiley & Sons, New York, pp 21--50. Dang, Q.L., H.A. Margolis and G.J. Collatz. 1997a. Parameterization and testing of a coupled photosynthesis--stomatal conductance model for boreal trees. Tree Physiol. 18:141--153. Dang, Q.L., H.A. Margolis, M.R. Coyea, M. Sy and G.J. Collatz. 1997b. Regulation of branch-level gas exchange of boreal trees: roles of shoot water potential and vapor pressure difference. Tree Physiol. 17:521--535.

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TREE PHYSIOLOGY VOLUME 19, 1999