Leaf photosynthetic light response: a mechanistic model for scaling photosynthesis to leaves and canopies

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1 Functional Ecology 1998 ORIGINAL ARTICLE OA 000 EN Leaf photosynthetic light response: a mechanistic model for scaling photosynthesis to leaves and canopies O. KULL* & B. KRUIJT *Institute of Ecology, Riia 181, EE2400 Tartu, Estonia and Institute of Ecology and Resource Management, The University of Edinburgh, Darwin Building, Mayfield Road, Edinburgh EH9 3JU, UK Summary 1. The response of photosynthesis to radiation is an often-studied but poorly understood process, represented empirically in most photosynthesis models. However, in scaling photosynthesis from leaf to canopy, predictions of canopy photosynthesis are very sensitive to parameters describing the response of leaves to Photosynthetic Photon Flux Density (PPFD). 2. In this study, a mechanistic, yet still simple, approach is presented that models the degree of light saturation in leaves explicitly, assuming a heterogeneous environment of PPFD and chlorophyll. 3. Possible mechanisms determining the ratio of chlorophyll to nitrogen are considered, including a direct dependence on PPFD, a mechanism involving the red/far-red ratio of light in the canopy, and an approach based upon maximizing photosynthesis. 4. Comparison of model predictions with two data sets of light, nitrogen and chlorophyll from canopies of Populus and Corylus suggests that the red/far-red mechanism is the most realistic. The data also show that the trees studied do not always optimize their nitrogen partitioning to maximize photosynthetic yield. 5. We then apply the model to the data sets, to predict the shape of light response curves of leaves within canopies and assess the applicability of simple scaling schemes, in which full acclimation of photosynthesis to PPFD justifies the use of bigleaf models. We conclude that, at least for the data used, basic assumptions of such schemes do not hold. Key-words: Acclimation, chlorophyll, leaf nitrogen, photosynthetic photon flux density Functional Ecology (1998) Ecological Society Introduction Integration of photosynthesis to whole plant canopies should account for spatial variation of photosynthetic responses with at least one environmental variable. A number of environmental variables vary throughout plant canopies but the most important one with respect to photosynthesis as well as the most variable is the Photosynthetic Photon Flux Density (PPFD). It is somewhat curious that in the majority of photosynthetic scaling models the leaf photosynthetic light response is the most empirical part of these models. In the simpler cases, photosynthetic light response is described by a rectangular or non-rectangular hyperbola (Hirose & Werger 1987; Kull & Jarvis 1995). In other cases, this response is described partly mechanistically with limitations from different components of the photosynthetic apparatus but, even then, two key points heavily influencing the resulting shape of the photosynthetic light response curve are described empirically. In particular, parameters describing an empirical smoothing of the transition from one limitation to another (e.g. Collatz et al. 1991) and an empirical function, describing the relationship between actual (J) and maximum (J max ) rates of electron transport, using an initial slope (α) and a convexity (θ) are widely used (e.g. von Caemmerer & Farquhar 1981). The latter, non-rectangular hyperbola function, suffers from severe interdependencies between the two parameters (Leverenz 1987). If we scale up photosynthesis from leaf to canopy using a modelling approach, usually the resulting canopy photosynthesis shows strong sensitivity to the convexity parameter of single-leaf photosynthetic light response curves (Sands 1996). Many simple canopy photosynthesis models rely on the assumption that the shape of the photosynthetic light response (i.e. convexity) does not change throughout the canopy and that all leaves on average operate at the same relative position along the response curves (e.g. Sellers et al. 1992; Kull & Jarvis 1995). It has often been shown that, in reality, the convexity parameter does change depending on the PPFD environment, so these 767

2 768 O. Kull & B. Kruijt assumptions are unlikely to be correct for real canopies (Leverenz 1987; Ögren & Evans 1993). To understand when and why the shape of response curves varies, we need to replace empirical light response models with mechanistic ones. There have been several attempts to describe light response curves mechanistically (Gutschick 1984; Terashima & Saeki 1985; Badeck 1995). In all these cases it has been shown that leaf photosynthetic light response curves can be explained and described taking into account the heterogeneity of the PPFD distribution inside the leaf. Such heterogeneity has been considered in several studies (Ögren & Evans 1993; Vogelmann 1993; Terashima & Hikosaka 1995) and it has also been shown that some properties of the photosynthetic apparatus, mainly those related to light harvesting, are distributed unevenly within the leaf (Terashima & Hikosaka 1995). The heterogeneity of the PPFD profile inside a leaf leads to a mismatch of the light environment and CO 2 fixation inside the leaf because often part of the photosynthetic apparatus close to the illuminated surface is PPFD saturated while the rest of the leaf is not (Nishio, Sun & Vogelmann 1993; Evans 1995). Badeck (1995) describes the only model known to us where the consequences of leaf heterogeneity on total canopy photosynthesis have been analysed. He also showed that modelling spatial heterogeneity of PPFD and photosynthetic properties across leaves, compared to homogeneous leaf models, leads to different conclusions about the way resources are partitioned between different functional components of the photosynthetic apparatus. Optimization of resource partitioning, especially of nitrogen, between different parts of the photosynthetic apparatus is commonly used to explain photosynthetic acclimation (Field 1983; Evans 1989; Chen et al. 1993; Badeck 1995; Terashima & Hikosaka 1995). However, nothing is known about an optimization mechanism and it is useful to formulate more mechanistic models that are also more easily testable than evolutionary arguments. The first objective of this study is to construct a leaf photosynthesis model that includes spatial heterogeneity of the PPFD environment and photosynthetic properties inside the leaf to allow a mechanistic description of the photosynthetic light response, including a parameterization of the acclimation of the light harvesting apparatus. We ignore evolutionary cost benefit analyses of nitrogen partitioning and instead evaluate a few alternative mechanisms that could be responsible for shifts in relative share of different functional components in the overall leaf photosynthetic apparatus. The direct influence of stomata is not included in our analysis. The second objective of this study is to predict, on the basis of model calculations and field observations, whether and how the shape of response curves and operating point of leaves vary with local PPFD in canopies. This analysis will shed light on the validity of basic assumptions in simple photosynthesis scaling models. Apart from application to our second objective, the resulting model will be used as a basic element in a more general model of the acclimation of photosynthetic properties to the PPFD distribution in plant canopies, to be presented in a companion paper (Kull & Kruijt 1998). The model In current biochemical models of leaf photosynthesis three basic limitations are considered explicitly: the amount of the Rubisco enzyme, electron transport capacity and an inorganic phosphate limitation (Sharkey 1985; Collatz et al. 1991; Evans & Farquhar 1991; Harley et al. 1992). The latter is of importance when there is a high level of photosynthetic products, a situation that may occur under elevated CO 2 conditions and is not considered in this study. The electron transport limitation actually consists of two different steps: a limitation by light harvesting, usually expressed as the amount of light absorbed by the photosystems, and a limitation by the maximum electron transport capacity (J max ). It seems useful to separate these two limitations in electron transport explicitly when acclimation to PPFD is the object of study. Recent studies of acclimation to PPFD have shown that during the process of acclimation the maximum potential carboxylation (V cmax ) and J max are changing in parallel and show good correlation with changes in leaf nitrogen content. Changes in the amount of light harvesting components in a leaf are quite different as can be concluded from data on the chlorophyll a/b ratio or total chlorophyll to leaf nitrogen ratio (Evans 1993; Pons & Pearcy 1994; Kull & Niinemets 1998). The Farquhar model of leaf photosynthesis allows for temporal heterogeneity of photosynthesis, such that photosynthesis is sometimes limited by V cmax and at other times limited by the electron transport rate, J (von Caemmerer & Farquhar 1981). In this study, whilst retaining the basic Farquhar equations, we extend the model by accounting for spatial heterogeneity of the process across a leaf. Where the PPFD is highest, the photosynthetic apparatus may be lightsaturated and limited only by either V cmax or by the maximum electron transport rate, J max. Along the light path in the leaf PPFD decreases as it is absorbed by chlorophyll. Beyond a certain amount of cumulative absorption and associated chlorophyll, photosynthesis may become limited only by the absorption of photon quanta, I a, in the light harvesting complex. Thus, in our model we consider the total photosynthetic apparatus as spatially separated into two components, limited by different variables, and the relative contributions of these components depend on the rate of PPFD absorption and the total incident PPFD avail-

3 769 Photosynthetic light response able. The two components are modelled separately but we will show that in certain conditions the total leaf photosynthesis can still be computed analytically. LIGHT SATURATED PHOTOSYNTHESIS Very much like in the Farquhar model, in light saturated conditions, we express the carboxylation rate as the minimum of two potential rates, A j and A v. Electron transport capacity limited carboxylation, A j, is given by: A j = J max m 1 /a, eqn 1 where a is the number of electrons required to fix one molecule of CO 2, if for the factor m 1 we assume: C i m 1 =, eqn 2 C i + 2Γ * where C i is the intercellular CO 2 concentration and Γ * is the CO 2 compensation point in the absence of dark respiration. C i is assumed constant throughout this study and no effects of stomatal conductance are analysed. J max is proportional to leaf nitrogen content N p : J max = n 1 N p eqn 3 a and n 1 is a proportionality constant. We are assuming that the Rubisco limited rate of photosynthesis, A v, is given by: A v = V cmax m 2, eqn 4 where V cmax is the maximum catalytic capacity of Rubisco and m 2 equals: C i m 2 =, eqn 5 C i + k c (1+O i /k o ) where O i is the intercellular partial pressure of O 2, and k c and k o are Michaelis Menten constants for CO 2 and O 2, respectively. V cmax is proportional to leaf nitrogen content: V cmax = n 2 N p, eqn 6 where n 2 is a proportionality constant. Thus we may identify a nitrogen-normalized rate of light saturated carboxylation: m sat = min(m 1 n 1,m 2 n 2 ), eqn 7 which is a constant throughout a leaf if the CO 2 concentration is assumed homogeneous. LIGHT HARVESTING LIMITED PHOTOSYNTHESIS We assume that the light harvesting limited rate of carboxylation can be written as: A h = I a αm 1, eqn 8 where α is the intrinsic quantum efficiency for CO 2 uptake. The amount of quanta absorbed by the light harvesting complex, I a, is a function of incident PPFD, I 0, and chlorophyll content, assuming exponential PPFD extinction: I a = (1 r r ) I 0 (1 e kacchl ), eqn 9 where r r is leaf reflectance and k a is the coefficient of PPFD extinction on chlorophyll (C chl ). The chlorophyll concentration in a leaf usually is a fairly constant fraction of N p, modulated by the local light environment. We will present modelling approaches for C chl below, but let us assume for now that: C chl = n 3 N p, eqn 10 where n 3 can be either a constant or a variable. Because in this way carboxylation in both light saturated and unsaturated conditions are defined as functions of nitrogen content, we can use cumulative nitrogen as a co-ordinate along the light path in the leaf. At the point at which light harvesting begins to limit photosynthesis we may assume: da h = m sat eqn 11 dn If we assume n 3 in eqn 10 to be a constant, then substituting eqns 8, 9 and 10 into eqn 11, gives the value of nitrogen N lim where eqn 11 holds: ln {(m sat )/[α (1 r r ) I 0 k a n 3 m 1 ]} N lim = eqn 12 k a n 3 If N lim calculated in this way is negative, then incident PPFD is not enough to saturate any part of the leaf photosynthetic apparatus. If N lim is larger than total leaf nitrogen N p, then the whole photosynthetic apparatus is light saturated. Thus, we can evaluate the cumulative leaf nitrogen N sat at which limitation by light harvesting will take over from limitation by Rubisco or maximum electron transport capacity as follows: if N lim < 0, then N sat =0 if N lim > N p, then N sat = N p eqn 13 otherwise N sat = N lim. Thus, for a given I 0, total photosynthesis of the leaf equals: Γ * N sat N p P = (1 )( [N m sat ] dn + A h dn) eqn 14 C i 0 Nsat or evaluating using all three limitations Γ * N sat N p P = (1 ){ [ Min (A j, A v )]dn + A h dn}. C i 0 Nsat eqn 15 If the C chl :N ratio is constant, substitution of eqn 12 in eqn 14 gives an analytical solution for total leaf photosynthesis: Γ * A = (1 ) [ m sat N sat + αm 1 (1 r r ) I 0 C i (e kan 3N sat e kan 3N p )]. eqn 16

4 770 O. Kull & B. Kruijt If the chlorophyll distribution is heterogeneous with respect to nitrogen inside the leaf (n 3 is not a constant in eqn 10), eqn 12 cannot be solved analytically for N lim and numerical methods are required. The basic set of parameters used in our calculations, given in Table 1, is based on measurements by Kull & Niinemets (1998) on Populus tremula, Corylus avellana and Tilia cordata. LIGHT HARVESTING To complete the model the relationship between leaf nitrogen and chlorophyll has to be established. Many studies have shown that the whole leaf chlorophyll to nitrogen ratio depends on the light environment of the leaf. In general, in shaded conditions, chlorophyll concentrations are higher relative to the nitrogen concentration than in full sunlight (Vapaavuori & Vuorinen 1989; Evans 1993; Kull & Niinemets 1998). However, detailed investigations of photosynthetic properties and structure of the photosynthetic apparatus along the leaf cross-section have shown that similar gradients in the photosynthetic apparatus occur along the light gradient inside the leaf (Terashima & Hikosaka 1995). In this study, we are analysing two different patterns of acclimation. In the simplest case we assume that chlorophyll acclimation occurs only at the whole leaf level and that the chlorophyll to nitrogen ratio (n 3 in eqn 10) is constant throughout each leaf. We will also analyse a situation where n 3 inside the leaf varies according to the local micro light environment. The mechanism responsible for such a distribution of chlorophyll is unknown and usually it has been explained in terms of optimal partitioning of resources between different parts of the photosynthetic apparatus (Evans 1989; Badeck 1995). We will investigate three alternative hypotheses for the mechanism of chlorophyll acclimation. The first assumes a dependence on PPFD alone. The second hypothesis involves the red/far-red ratio of the light, whilst the third assumes that photosynthesis is maximized. Hypothesis 1: PPFD as the responsible factor Data on the chlorophyll to nitrogen ratio in different tree species growing in similar environments show that there was no difference between species in the relationship of this ratio with the average absorbed PPFD and that this relationship can be empirically approximated with a power function (Kull & Niinemets 1998). Thus the simplest model would just use this empirical relationship, but to have meaningful parameters we are introducing a hypothetical mechanism that could lead to the measured relationship. Let us assume that the amount of chlorophyll is in equilibrium with the total of resources that can be used to build up the photosynthetic apparatus, measured as the amount of nitrogen. Let us assume that chlorophyll is continuously built up with rate constant n 4 and broken down with rate constant n 5 and that there is additional breakdown of chlorophyll increasing with absorbed PPFD, with a rate constant n 6. According to this hypothetical model changes in chlorophyll content can be written as: dc chl = n 4 N n 5 C chl n 6 I g C chl, eqn 17 dt where I g is the average absorbed PPFD. In steady state this results in: C chl n 4 = eqn 18 N n 5 + n 6 I g This function has only two independent parameters: n 5 /n 4 and n 6 /n 4. Three parameters are only needed for calculations of dynamics. Hypothesis 2: light quality as the responsible factor There is ample evidence that the chlorophyll content is not controlled by light intensity but by the red/far-red ratio (hereafter: R:FR or ξ) through a phytochrome mechanism. This has been shown in experiments with isolated chloroplasts and with phytochrome mutant plants (Eskins, Westhoff & Beremand 1989; Table 1. Basic set of parameters used in calculations Symbol Meaning Unit Value a Number of electrons required to fix one molecule of CO 2 4 α Intrinsic quantum efficiency mol [CO 2 ] (mol quanta) n 1 Proportionality coefficient between J max and N p µmol [CO 2 ] (mmol N) 1 s n 2 Proportionality coefficient between V m and N p µmol [CO 2 ] (mmol N) 1 s C i Partial pressure of CO 2 in the intercellular air space Pa 24 0 O i Partial pressure of O 2 kpa 20 9 Γ* CO 2 partial pressure for the compensation of oxygenation and carboxylation reactions Pa 4 0 k c Michaelis Menten constant for CO 2 Pa 30 k o Michaelis Menten constant for O 2 kpa 30 k a PPFD extinction on chlorophyll k f FR extinction on chlorophyll k L PPFD extinction on leaves in a canopy 1 0 r r Leaf reflection coefficient 0

5 771 Photosynthetic light response Smith, Samson & Fork 1993; Virgin 1993; Mohr & Schopfer 1995). In particular Masoner & Kasemir (1975) have shown that chlorophyll synthesis is accelerated by pretreatment with far-red light when phytochrome is low. Thus, we can assume that a high level of active phytochrome suppresses chlorophyll formation. In this hypothesis we assume that chlorophyll formation is inversely proportional to the equilibrium phytochrome ratio, φ, which has a hyperbolic relationship with ξ (Smith & Holmes 1977), and that its destruction is proportional to amount of chlorophyll: dc chl n 7 N = n 9 C chl, eqn 19 dt n 8 + φ where ζφ max φ =, eqn 20 n 10 + ζ where n 7 /n 8 represents the maximum chlorophyll synthesis rate, φ max is the saturated equilibrium phytochrome ratio and ξ is the R:FR ratio. In steady-state the chlorophyll to nitrogen ratio is: C chl n 7 = eqn 21 N ζφ max n 9 n 8 + ( n 10 + ζ) We have found coefficients for the relationship in eqn 21 through fitting with measured data for Populus tremula and Corylus avellana. We assumed that the R:FR ratio at full sunlight, ξ 0, is equal to 1 2, and that ξ is declining with PPFD as: k L k f ζ = ζ 0 (I/I 0 ) kl, eqn 22 where k L is the canopy light extinction coefficient in the PAR region and k f in the FR region. Although both hypotheses 1 and 2 are not proven by experimental evidence, from an empirical point of view the main difference between them is that hypothesis 1 describes the C chl :N ratio with a two parameters function and hypothesis 2 with a three parameters function. chlorophyll concentration, by fitting it to some measured photosynthetic light response curves. The light response data are from birch (Betula pendula) grown in open-top chambers within the context of an elevated CO 2 impact (A. Rey & P. G. Jarvis, unpublished data). The data were collected using a photosynthesis system with an adapted light source (6200, LICor, Lincoln, NE, USA). Leaf temperature and stomatal conductance were not kept constant, but their values were recorded. The fitting procedure, using the model in eqn 16, accounted for variable C i and also for variable temperature because in the fitting procedure (a simple non-linear least squares method), Γ*, k o and k c were temperature-dependent functions according to Harley et al. (1992). We have selected just one set of curves, recorded in July 1994 on leaves of trees grown in ambient CO 2 (350 p.p.m. average). In the same period, leaf nitrogen and chlorophyll content were determined for the same trees, enabling us to fit the model to the data whilst floating the quantum efficiency and the sensitivity of J max and V cmax to leaf nitrogen (α, n 1 and n 2 ). The measured concentrations were 0 44 mmol m 2 for chlorophyll and 90 mmol m 2 for nitrogen. As shown in Fig. 1a the fit is good. The fitted values found are mol mol 1 for α, 0 25 µmol mmol 1 s 2 for n 1 and 0 65 µmol mmol 1 s 2 for n 2. In this fit, dark respiration was set to zero (being small in the light anyway), although floating its value did not significantly change the results. Hypothesis 3: maximization of photosynthesis In many studies it has been assumed that the relative share of different functional parts of the photosynthetic apparatus is such that photosynthesis is maximized. Although nothing is known about the underlying mechanism, we have also calculated the C chl :N ratios at which leaf photosynthesis is maximized for a given amount of leaf nitrogen and PPFD. Results MODEL FIT TO MEASURED LIGHT RESPONSE We have tested the photosynthesis model, for the homogeneous case with a known nitrogen and Fig. 1. Fit of the photosynthesis model to measured light response data for birch (Betula pendula) grown in open-top chambers. The measured curve is an average for several leaves. The model was run in its simplest from, assuming a homogeneous chlorophyll distribution: (a) comparison of measured and fitted curves; (b) residuals of the fit.

6 772 O. Kull & B. Kruijt THE CHLOROPHYLL BALANCE MODEL The parameters of the two models for the chlorophyll balance have been fitted to observations on Populus tremula and Corylus avellana described in Kull & Niinemets (1998). Values for n 4 and n 7 in the range of µmol [Chl] mmol 1 [N] s 1 lead to adjustment of leaf chlorophyll content over a few weeks, which is in accordance with transfer experiments (Osmond, Björkman & Anderson 1980; Pons & Pearcy 1994) and has no influence on the fitting procedures if steady-state is assumed (eqns 18 and 21). Fitted parameters are shown in Table 2. Using these parameter values for the chlorophyll model and the basic set of other model parameters (Table 1) we calculated photosynthesis PPFD response curves for several combinations of average PPFD and leaf nitrogen content (Figs 2,3,4,5). Hypothesis 1 If we assume PPFD as the controlling factor of the C chl :N ratio and a homogeneous chlorophyll distribution, the resulting light response curves are quite realistic (Fig. 2). At low average light and low nitrogen content convexity is higher than at high light and high leaf nitrogen content, as is often observed within canopies. However, when the same mechanism is also assumed to control the C chl :N ratio inside the leaf, i.e. if we allow the leaf to be heterogeneous, a light response curve close to a Blackman response is the result (Fig. 3). This is because all leaf photosynthetic apparatus becomes saturated at almost the same value of incident PPFD at the top of the leaf, as shown in Fig. 2b and Fig. 3b. Comparison of this model with data shows that this PPFD-driven mechanism underestimates leaf chlorophyll content at low light even though the parameters have been found with the best fit (Fig. 6). This is because a two parameter curve does not allow enough bending to describe C chl :N ratio correctly at low PPFD. There appears to be another indirect argument against such a light intensity-driven chlorophyll control mechanism. When we consider the meaning of the parameters n 4, n 5 and n 6 ( eqn 18) Fig. 2. (a) Instantaneous photosynthetic light response curves for leaves with two nitrogen contents (210 mmol m 2 and 50 mmol m 2 ) grown at different light environments (PPFD = 300 µmol m 2 s 1 and 50 µmol m 2 s 1 ); (b) relationship between instantaneous light and amount of potentially saturated nitrogen N sat. The C chl :N ratio is controlled by PPFD according to Hypothesis 1 but is homogeneous inside the leaf. and the fact that there is heavy diurnal fluctuation in PPFD, the leaf chlorophyll content would have to fluctuate substantially and this seems unrealistic (Fig. 7). Alternatively, slowing down the process through changing these parameters slows down the total acclimation response too much. Because assuming heterogeneity of chlorophyll inside a leaf leads to unrealistic near-blackman response curves, we may also conclude that there is probably no full acclimation to PPFD inside the leaf. Table 2. Parameters for the chlorophyll balance model found with a non-linear regression procedure Parameter n 5 /n 4 n 6 /n 4 R Variance explained (a) PARAMETERS FOR eqn 18 Units mmol [N] µmol 1 [Chl] s 1 m 2 µmol 1 [PPFD]mmol [N] µmol 1 [Chl] % Homogeneous leaf Heterogeneous leaf Parameter n 8 n 9 /n 7 n 10 R Variance explained (b) PARAMETERS FOR eqn 21 Units mmol [N] µmol 1 [Chl] % Homogeneous leaf Heterogeneous leaf

7 773 Photosynthetic light response Because an increase in chlorophyll content at a given amount of nitrogen increases the initial slope of the photosynthetic light response curve (although not very much over a realistic range of nitrogen and chlorophyll contents) but decreases convexity, for a given average light environment there exists a chlorophyll content at which photosynthesis is maximized. Such a maximum is not always very pronounced, as shown in Fig. 8. We have calculated this optimal chlorophyll content for Populus tremula and Corylus avellana leaves at measured leaf nitrogen and light conditions assuming heterogeneous leaves (Fig. 6). These results show that, while at high average PPFD these values match quite well with real data, at low light leaves contain substantially less chlorophyll than required for maximizing photosynthesis. SCALING THE PPFD RESPONSE CURVE FROM LEAF TO CANOPY Fig. 3. Same as Fig. 2 but the C chl :N profile inside the leaf is also controlled by PPFD according to Hypothesis 1. Hypothesis 2 If we assume that light quality controls the C chl :N ratio then the photosynthetic apparatus does not saturate as abruptly with increasing light as is the case if PPFD controls the C chl :N ratio, even in the heterogeneous case. This results in light response curves with a relatively smaller convexity. Figure 4 shows that if leaf nitrogen content is high, typical for leaves grown at high PPFD, a high R:FR ratio and hence a low C chl :N ratio results in relatively more photosynthesis at high PPFD. This is because the leaf saturates more rapidly (convexity is higher) with PPFD if there is less chlorophyll. If the leaf nitrogen content is low and R:FR is low and hence C chl :N high, the initial slope of the photosynthetic light response curve is substantially steeper, relatively increasing photosynthesis at low PPFD. The benefit in terms of photosynthesis from such a pattern in the C chl :N ratio is even more substantial in the case of a heterogeneous leaf (Fig. 5). If the shape of all leaf response curves in a canopy is similar and if the leaves are operating at the same relative position along those curves, then a spatial relationship of photosynthesis with PPFD as it varies through the canopy should also have the same shape as leaf scale PPFD response curves. Such a spatial function can be defined as a long-term photosynthesis PPFD response curve, where the physiological short-term photosynthesis PPFD response curves are averaged. We have modelled the daily average photosynthesis of the Populus tremula and Corylus avellana leaves sampled by Kull & Niinemets (1998) at different positions along the PPFD gradient inside the canopy (Fig. 9a). We used the heterogeneous leaf model where the R:FR ratio is the driving force for the C chl :N ratio, and the parameters were derived from the measured Chl:N and PPFD relationships described above. We imposed a sinusoidal PPFD time function Hypothesis 3 Fig. 4. Same as Fig. 2 but C chl :N ratio is controlled by R:FR ratio according to Hypothesis 2 but is homogeneous inside the leaf. (R:FR ratio = 1 2 and 0 35, nitrogen contents as Fig 2.)

8 774 O. Kull & B. Kruijt Fig. 5. Same as Fig. 4 but C chl :N profile inside the leaf is also controlled by R:FR ratio according to Hypothesis 2. with 12 h night and with a maximum PPFD at noon at the top of the canopy equal to 1000 µmol m 2 s 1 and R:FR ratio at the top of the canopy equal to 1 2. Measured leaf nitrogen contents were used and PPFD attenuation inside the canopy was taken according to attenuation of the measured global site factor (K sum ) at the sampled leaves. Qualitative variation in the PPFD frequency distribution was ignored. In Fig. 9a, we show the daily average photosynthesis rate for these leaves as a function of the relative average PPFD expressed as K sum. Figure 9b shows that at the average PPFD conditions, the operating points of leaves are not everywhere on the same relative position (expressed as the relative light saturation of photosynthesis) on their photosynthetic response curves. The main points we will address in this discussion are heterogeneity of leaves and the amount of material in the light-harvesting complex relative to the total photosynthetic apparatus. Our study emphasizes the importance of considering intra-leaf heterogeneity of PPFD in a model that relates (average) photosynthesis to (average) PPFD. This is because in a fluctuating PPFD environment, the limitations to photosynthesis shift frequently and photosynthesis is operating in the range where non-linearity of the light response is highest. Differences between predictions for homogeneous and heterogeneous leaves are also largest in this range. The relative share of the light harvesting complex in the total photosynthetic apparatus can vary substantially within and between leaves depending on the average light conditions (Pons & Pearcy 1994). In all models which purport to consider this variation, it has been described with an optimality approach, maximizing photosynthesis at a particular PPFD value, indirectly implying that PPFD is the responsible factor for shifts in photosynthetic apparatus. We included this as a first hypothesis into our analyses. Our analysis shows that this hypothesis does not agree with observed patterns of the C chl :N ratio in canopies, especially at low values of PPFD, and that it predicts unrealistically large fluctuations in chlorophyll content when PPFD fluctuates. If PPFD is responsible for shifts in chlorophyll to nitrogen ratio then the mechanism has to be more complex than in Hypothesis 1 to smooth out short-term fluctuations in PPFD, perhaps having some PPFD averaging mechanism, although we do not know of any. Our analysis further shows that exact acclimation of chlorophyll to PPFD inside a HOMOGENEOUS VS HETEROGENEOUS LEAVES Finally, Fig. 10 shows a comparison of daily average photosynthesis simulations assuming homogeneous and heterogeneous chlorophyll distributions. The difference is a constant 8% showing that there is a small benefit for a leaf to have a heterogeneous distribution of the photosynthetic apparatus. Discussion Fig. 6. Dependence of the C chl :N ratio on incident relative PPFD measured as global site factor, K sum, in Populus tremula and Corylus avellana leaves and calculated C chl :N ratios for the same leaves when described by Hypothesis 1 and Hypothesis 2, assuming homogeneous leaves. We also show the C chl /N ratios that would be required to maximize photosynthesis according to Hypothesis 3.

9 775 Photosynthetic light response Fig. 7. Dynamics of leaf chlorophyll adjustment according to Hypothesis 1 (eqn 17) at constant leaf nitrogen content of 300 mmol m 2 and fluctuating PPFD with 12 h dark period and with a maximum intensity 1000 µmol m 2 s 1 at noon. Parameter n 4 was set 10 5 or 10 6, other parameters as in Table 1. the hypothesis that the phytochrome mechanism is responsible for changes in proportions of functional parts of photosynthetic apparatus. This can only be carried out with proper experiments. However, we have shown that the proposed mechanism can certainly explain real data. It can also be concluded that concentrations of chlorophyll in low average PPFD are less than required to maximize photosynthesis, thus undermining hypotheses based upon optimization theory. However, including a nitrogen balance into a leaf level cost benefit analysis may explain this conclusion because a substantial amount of leaf nitrogen is involved in chlorophyll protein complexes (Evans 1989; Pons & Pearcy 1994). leaf leads to an unrealistically high convexity of the light response curve. Other evidence in the literature shows that neither chlorophyll synthesis (Mohr & Schopfer 1995) nor destruction (Björkman 1981) depend directly on the PPFD absorbed by chlorophyll. It seems likely that the mechanism responsible for changes in C chl :N relationship is much more non-linear in respect to PPFD than the mechanism represented by Hypothesis 1, to allow for increased photosynthesis in low-light environments. There are very few ecologically orientated studies where the relationship between R:FR ratio and leaf chlorophyll content has been studied. Bradburne, Kasperbauer & Mathis (1989) have shown explicitly that a low R:FR ratio is associated with a relatively high leaf chlorophyll content. However, manipulations with the light regime may also lead to changes in the total amount of photosynthetic apparatus. Tinoco- Ojanguren & Pearcy (1995) concluded that light quality had no effect on leaf chlorophyll content. Meanwhile, according to their data, values of maximum photosynthesis, A max, differed between light treatments. If we assume a correlation between leaf nitrogen content and A max, it is likely that light quality influenced the C chl :N ratio substantially in their experiment. In several studies (e.g. Bradburne et al. 1989; Casal & Aphalo 1989; Aphalo, Gibson & Di Benedetto 1991; Virgin 1993) attempts have been made to relate R:FR ratio with the total leaf chlorophyll but not with the amount of chlorophyll in relation to rest of the photosynthetic apparatus and this makes comparison difficult. Compared to a PPFD dependent mechanism, a phytochrome based mechanism such as the one proposed here is also more stable, because the R:FR ratio fluctuates much less in time than PPFD (Gilbert et al. 1995). Our model analysis does not allow verification of Fig. 8. Dependence of leaf photosynthesis on leaf chlorophyll content in heterogeneous leaves with different combinations of nitrogen content and growth light environment. Fig. 9. (a) Calculated daily average photosynthesis for Populus tremula and Corylus avellana leaves from different positions in the canopy. Fluctuating light with maximum at noon equal to 1000 µmol m 2 s 1 corresponding to K sum = 1 0. Leaves are assumed to have a heterogeneous chlorophyll distribution; (b) ratio of daily average photosynthesis to light saturated photosynthesis of the same leaves.

10 776 O. Kull & B. Kruijt Fig. 10. Relationship between calculated average daily photosynthesis in heterogeneous and homogeneous leaves of Populus tremula and Corylus avellana. Including PPFD heterogeneity into a photosynthesis model allows a better description of some qualitative properties of the photosynthetic light response curve compared to using a (non-rectangular) hyperbola. Real light response curves usually have a completely linear section at low values of PPFD and this cannot be described with a hyperbola (Leverenz 1987), whereas our model does predict such a section. Also, according to our model the light response saturates completely at finite values of PPFD and this seems more realistic than saturation at infinity as predicted by a hyperbola. It has often been shown that photosynthetic structures differ in different parts of a leaf and that acclimation occurs within a leaf similarly to acclimation within a canopy. Several characteristics of photosynthetic structures show similar changes in PPFD gradients within a leaf and a canopy (Nishio et al. 1993; Terashima & Hikosaka 1995; Sun, Nishio & Vogelmann 1996). Some difficulties in quantifying these relationships may arise because the PPFD profile within a leaf may be more uniform than predicted by an exponential model owing to reflections and specific leaf anatomy (Sharkey 1985; Vogelmann 1993; DeLucia et al. 1996). Nevertheless, as shown by our calculations, within leaf acclimation to the microenvironment is of minor quantitative importance and perhaps may be neglected if computing time has to be optimized (Fig. 10). We have calculated ecological light response curves, plots of average photosynthesis against average PPFD of leaves throughout a canopy, and shown that they differ substantially from proportionality (Fig. 9a). The shapes of light response curves of leaves from different light environments differ and the relative position of the operational point on the instantaneous light response curve is also different in leaves from different positions in the canopy (Fig. 9b). This is in conflict with bulk canopy photosynthesis models which assume a perfect acclimation of the photosynthetic apparatus to local PPFD. The consequence of such acclimation is that all leaves are operating at the same relative point at their response curves and this leads to simple big leaf formulations of canopy photosynthesis (Sellers et al. 1992; Kull & Jarvis 1995). We show here that this is not the case for the Populus and Corylus canopies studied in Kull & Niinemets (1998) and we also show that the ecological response differs between the two species because distribution of leaf photosynthetic apparatus in respect to PPFD environment differs among species, although the main photosynthetic parameters per unit of leaf nitrogen are similar (Kull & Niinemets 1998). In this study we have developed a photosynthesis scheme which allows scaling from chloroplast and leaf to the canopy, and relies less on either empirical parameters or evolutionary reasoning. The scheme predicts leaf photosynthetic parameters in dependence of leaf nitrogen content but it does not predict the absolute amount and distribution of nitrogen over canopies. The disagreement of our model results with simple scaling schemes is partly based upon measurements. 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