Acclimation of photosynthesis to light: a mechanistic approach

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1 Functional Ecology , ORIGINAL ARTICLE OA 000 EN Acclimation of photosynthesis to light: a mechanistic approach O. KULL* and 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. We developed a mechanistic model to explain acclimation of photosynthesis to the radiation distribution within plant canopies. The model predicts the amount of photosynthetic apparatus in any leaf from the balance between supply of carbohydrates by photosynthesis and the demand for resources by enzyme synthesis and turnover and export to sinks elsewhere in the plant. 2. The turnover of the photosynthetic apparatus is assumed to depend on the amount of available resources: nitrogen and carbohydrates. Leaves export carbohydrates into a common pool of carbohydrates and take nitrogen from the common nitrogen pool. All leaves of one plant are assumed to share these common pools. 3. The model allows description of the dynamics of the acclimation process known to occur within weeks after changes in the environment. The model also adequately explains measured leaf nitrogen distributions and total leaf area in a multispecies canopy. 4. According to our model, differences between species in leaf nitrogen distribution with respect to PPFD can be explained with differences in plant common pools of carbohydrates and nitrogen. 5. Although canopies cannot be treated as a big leaf in a simple way because mechanisms predicting amount of photosynthetic apparatus in a single leaf and in entire canopy are different, total canopy nitrogen can be used as an estimate for canopy total photosynthesis. Key-words: Canopy, labile carbohydrates, leaf nitrogen, model, photosynthetic photon flux density Functional Ecology (1999) 13, British Ecological Society Introduction The awareness of global change phenomena has led to an increasing need to understand the carbon balance of ecosystems at stand, regional and even global scales. Primary production, one of the most important components of that balance, has to be modelled at those scales, yet, most knowledge of photosynthesis is at the leaf scale. Increasing efforts are being undertaken to measure ecosystem-scale carbon exchange directly but for a comprehensive modelling of most ecosystems on earth we will have to rely on understanding the physiology of those systems as composed of a number of components (Norman 1993). The relationship between photosynthesis at the leaf scale on one hand and canopy scale on the other, will remain a key to general understanding of large-scale carbon balances. During the last decade, several scaling models have emerged. Some of them are based on simplified leaf photosynthesis models (Hirose & Werger 1987a; Kull & Jarvis 1995), but many of them are based upon the widely accepted biochemical leaf photosynthesis model by Farquhar, von Caemmerer & Berry (1980) as the basis (Sellers et al. 1992; Kruijt, Ongeri & Jarvis 1997). In these models, photosynthetic production of a plant canopy, at time scales of days to weeks, depends on several external factors like the photosynthetic photon flux density (PPFD), water availability, CO 2 concentration and temperature. It is widely agreed that the key point in scaling photosynthesis from leaf to canopy is to understand and model the way leaf photosynthesis acclimates to the local environment inside a canopy, especially the amount and distribution of photosynthetic apparatus (Field 1983; Hirose & Werger 1987a; Schieving et al. 1992; Terashima & Hikosaka 1995). There is much evidence that the PPFD profile inside the canopy is the main predictor for the distribution of leaf photosynthetic properties (Chazdon & Field 1987; Ellsworth & Reich 1993; Pearcy & Sims 1994). In general, PPFD, leaf photosynthetic capacity and leaf nitrogen content all decrease with depth into a canopy. This phenomenon has up to now been 24

2 25 Photosynthesis acclimation in canopy 1999 British Ecological Society, Functional Ecology, 13, explained from the evolutionary notion that an exactly parallel distribution of these properties maximizes total canopy production. Several optimization schemes have been proposed (Field 1983; Givnish 1988; Hilbert, Larigauderie & Reynolds 1991; Wu 1993). Although such an optimality approach often allows a qualitative description of the real distribution of photosynthetic properties within plant canopies, it does not provide a mechanism that is actually responsible for the distribution of the photosynthetic apparatus and as such the hypotheses involved are not strictly testable. The purpose of this study was to build a mechanistic model to describe the distribution of the photosynthetic apparatus inside canopies with the emphasis on processes limiting photosynthetic production at the canopy scale, at time scales of several weeks at the most. To parameterize the model we are using data from a study by Kull & Niinemets (1998) on Populus tremula and Corylus avellana, two species which share the same canopy and have similar photosynthetic properties when evaluated on a leaf nitrogen basis but which show different patterns of leaf nitrogen distribution with respect to PPFD. The model From many experiments in which plants were transferred from one light condition to another, it is known that it takes a few weeks for the photosynthetic apparatus to adjust to the new conditions (Osmond, Björkman & Anderson 1980; Burkey & Wells 1991; Pons & Pearcy 1994). Such an adjustment is always expressed in terms of changes in leaf nitrogen, protein or chlorophyll content; i.e. in the amount of the photosynthetic apparatus in the leaf. To model acclimation of the photosynthetic apparatus to PPFD mechanistically we need to include processes of destruction and (re)generation of the photosynthetic apparatus, averaged over several weeks. The main assumptions listed below are assumptions which form the core of the model. Other, additional assumptions may be replaced without changing the main ideas of the model. MAIN ASSUMPTIONS 1. Dynamic equilibrium between destruction and regeneration of the photosynthetic apparatus is the main mechanism responsible for acclimation of photosynthesis to the local average PPFD at the leaf scale. 2. Although every leaf has its own local environment to which it acclimates, leaves of one plant share common resource pools, particularly nitrogen, and export assimilates into a common sink, or pool, of carbohydrates. These common pools can be assumed to reside in the xylem and phloem but the present model does not explicitly require this. The effect of this assumption is that leaves of the same plant are not independent of each other. 3. We do not include growth processes in the model assuming that these processes are slower than acclimation of the photosynthetic apparatus, implicitly restricting ourselves to mature tree canopies. For woody plants it is reasonable to assume that interactions between the common nitrogen and carbon pools, as well as changes in the pool sizes, occur at longer time scales than changes in leaf photosynthetic apparatus. Therefore, we consider these pools as external driving variables, so that the time scales of acclimation and growth are kept separate. ADDITIONAL ASSUMPTIONS 4. Water plays an important role in photosynthesis, especially when water availability is low. In the present model, however, we assume that water supply is never limiting and concentrate on the effects of the factor that varies most inside canopies: PPFD. 5. We use the biochemical photosynthesis model by Kull & Kruijt (1998) as the leaf photosynthesis unit in our model (see Appendix). This model is based on the model by Farquhar et al. (1980) but was modified with respect to light harvesting. It allows for a heterogeneous PPFD profile inside the leaf, as well as variation in the ratio of light harvesting components to the rest of the photosynthetic apparatus, expressed as the chlorophyll to nitrogen ratio. The model assumes that the driving force in predicting this ratio is the red to far-red (R:FR) ratio in the incident light. It allows a mechanistic description of the photosynthesis light response curve, which is crucial when acclimation to light is studied. The model calculates gross leaf photosynthesis rate (A) as a function of incident PPFD (I 0 ) and the R:FR ratio (ζ) but the leaf nitrogen content (N p ) is also required as an input: A = f(n p,i 0, ζ) eqn 1 6. We use the transport resistance approach introduced by J. H. M. Thornley (e.g. Thornley & Johnson 1990) to model transport processes between a leaf and the common pools. We assume that leaf labile nitrogen and carbohydrates form leaf pools and every leaf has to export carbohydrates into or import nitrogen out of the common pools in the rest of the plant. These exchange processes are assumed to depend on the concentration difference between the leaf and plant common pools and on a conductivity constant representing the net effects of passive and active transport. 7. We assume that mature leaves cannot import carbohydrates from the rest of the plant (Turgeon 1989). Additionally, in calculations of total acclimated canopy photosynthesis, we assume that the canopy lower limit is determined by conditions in which export of carbohydrates out of the leaves becomes zero.

3 26 O. Kull & B. Kruijt 8. To integrate our leaf scale model of photosynthesis up to the whole canopy the dependence of PPFD and R:FR ratio on the leaf area distribution must be defined. For simplicity we are assuming here that an exponential function applies for the relationship between leaf area index and PPFD inside the canopy: I = I 0 e k L L, eqn 2 where L is the cumulative leaf area index and k L is an extinction coefficient. FLOW CHART A schematic flow diagram of the model is shown in Fig. 1. Photosynthesis, A, feeds the labile carbohydrate pool, C, consisting of leaf soluble sugars and starch. Carbohydrates are used to regenerate the photosynthetic apparatus, measured as the amount of nitrogen in it, N p. Synthesis of the photosynthetic apparatus is assumed to be proportional to the sizes of the leaf labile nitrogen pool, N, and the carbohydrate pool, C. During this process of (re)generation some carbon is lost as respiration, R p. This respiration represents leaf maintenance respiration because growth is not included in our model. Part of C is exported to the common carbon pool C c. This export is assumed to be proportional to the concentration difference of C and C c. It is assumed that the export velocity constant k 5 becomes equal to zero if C < C c. In reality there is also some carbon involved in cycling between the photosynthetic apparatus and the pool C, but because this turnover is much slower than turnover of the labile carbohydrate pool C caused by photosynthesis, respiration and export, this carbon flow is ignored for simplicity. Breakdown of the photosynthetic apparatus is assumed to be only dependent on the amount of N p. The labile leaf nitrogen pool, N, is assumed to be in dynamic equilibrium with the common nitrogen pool, N c, because some nitrogen from this labile pool is lost through leaching and some is transported away with the phloem flow. EQUATIONS Fig. 1. Pools and flows in the model. Solid arrows represent flows of nitrogen and carbohydrates, while dashed arrows represent main regulatory interactions between flows of nitrogen and carbohydrates. Table 1. Variables and constants used in the demand function Explanation Unit Standard value STATE VARIABLES C Leaf labile carbohydrates mmol m 2 N p Leaf functional nitrogen mmol m 2 N Leaf labile nitrogen mmol m 2 DRIVING VARIABLES A Photosynthesis rate mmol m 2 s 1 C c Plant common pool of carbohydrates mmol m N c Plant common pool of nitrogen mmol m 2 70 RATE CONSTANTS k 1 m 2 mmol 1 s k 2 s k 3 s k 4 s k 5 s k 6 mmol mmol 1 10 The model can be written as a set of three differential equations. Turnover of photosynthetic nitrogen N p : dn p = k 1 NC k 2 N p. eqn 3 dt Import, loss and use of labile leaf nitrogen N: dn dn p = k 3 (N c N) k 4 N eqn 4 dt dt Production, export and respiration of labile leaf carbon C: dc = A k 5 (C C c ) k 6 k 1 NC. eqn 5 dt PARAMETERIZATION Definitions of variables and constants as well as their units are summarized in Table 1. In the parameterization we used data on P. tremula by Kull & Niinemets (1998). We assume that at steady-state leaves at the top of the canopy receiving full light, with a diurnal (24 h) average rate of photosynthesis of 5 µmol m 2 s 1, have a total leaf nitrogen pool of

4 27 Photosynthesis acclimation in canopy 250 mmol m 2 consisting of N = 50 mmol m 2 and N p = 200 mmol m 2. The total of soluble carbohydrate and starch contents equals 1000 mmol m 2. The standard values for common pools are chosen as 70 mmol m 2 for N c and 500 mmol m 2 for C c to allow free export and import. The rate constant k 2 = s 1 is chosen to allow a 90% decrease in N p within 2 weeks. The rate constant k 6 predicts maintenance respiration of the leaf. Recalculation of measured leaf respiration vs nitrogen content relationships given in the literature (e.g. Field 1983; Hirose & Werger 1987b; Terashima & Evans 1988; Ryan 1991) results in a range for k 6 of 1 10 mmol C mmol 1 N. If we assume steady-state at standard values of the state variables then the ratio of rate constants k 4 /k 3 =(N c N)/N must be The magnitude of these constants is chosen to be of order 10 4 to ensure that the leaf pool N is almost always in dynamic equilibrium with the common pool N c and that adjustment time of leaf N would not affect too much adjustment of N p. The rate constants k 1 and k 5 are calculated from equations 3 and 5, respectively, assuming steady-state at standard values of state variables. In all calculations where photosynthesis is involved the diurnal periodicity of PPFD is considered. The PPFD above the canopy, I 0, is modelled with a half-period sine function with a maximum at noon 1000 µmol m 2 s 1 and a 12 h dark/light period. Also, it was assumed that the R:FR ratio at the top of the canopy, ζ 0, is 1 2 and that this ratio changes within the canopy as: k a k f ζ = ζ 0 (I/I 0 ) k a eqn 6 where k a is the PPFD extinction on chlorophyll and k f is the FR extinction on chlorophyll and I/I 0 is calculated from equation 2. Results ANALYTICAL STEADY-STATE SOLUTION At steady-state, i.e. when the leaves are completely acclimated, the derivatives of the state variables can be assumed zero: dn p dn dc = = = 0 eqn 7 dt dt dt and the relationship between leaf photosynthesis rate and leaf nitrogen content can be evaluated as: ( N c k 1 ) 1 k 5 (1+k 4 /k 3 ) A = N p k 2 k 6 + k 5 C c, eqn 8 when C > C c. Otherwise, if the leaf is not exporting assimilates this relationship reduces to: A = N p k 2 k 6. eqn 9 Thus, the analytical steady-state solution of the model [we refer to this as demand function from now on because it is predicted by plant demand for assimilates and is independent of the photosynthesis ( supply ) model] can be described as a linear relationship with a negative intercept on the photosynthesis axis in conditions when leaves are exporting assimilates. If there is no export, A and N p are proportional (Fig. 2). Equation 8 can also be written as the sum of equation 9 and export: A = N p k 2 k 6 + k 5 (C C c ). eqn 10 Consequently, the demand function can be described as a linear relationship between photosynthesis rate and leaf nitrogen content, where the slope is a function of the plant common nitrogen pool, N c, and the intercept is a function of the plant common carbon pool, C c (equation 8). These common pools also predict a minimum leaf nitrogen N p,min, where export becomes zero (i.e. C = C c ). Combining equations 8 and 9 gives: k 1 /k 2 N p,min = C c N c eqn 11 (1 + k 4 /k 3 ) Fig. 2. The steady-state solution of the model. At leaf nitrogen content less than N p, min, in conditions when leaves are unable to export assimilates the solution is predicted by equation 9, otherwise the solution is predicted by equation 8. The demand function also predicts that, in steadystate conditions, the leaf labile carbon pool and leaf photosynthetic nitrogen content must be proportional: 1 k 2 k 4 C = N p 1+ eqn 12 N c k 1 ( k 3 ) Although the common pool is a highly abstract concept it is possible to calculate ratios of the C and N pools for two species if we know the relationship between average photosynthesis rate and leaf nitrogen content in canopies of two different species at steady-state conditions. If we denote the intercepts on the photosynthesis axis of this relationship as b 1 and b 2 for species 1 and 2, respectively, and if we

5 28 O. Kull & B. Kruijt assume that the rate constants (k 1...k 6 ) are the same for these species, then from equation 8 we can express the ratio of common carbon pools as: C c1 b 1 =, eqn 13 C c2 b 2 where indices 1 and 2 denote different species. Combining equations 13 and 11 gives the ratio of common nitrogen pools: N c1 b 2 N p min1 = eqn 14 N c2 b 1 N p min 2 Fig. 3. Relationship between leaf photosynthetic nitrogen and daily average photosynthesis rate calculated from the leaf photosynthesis model at sinusoidal illumination with 12 h day/night and with midday maxima of PPFD 1500 ( ), 1000 ( ) or 500 ( ) µmol m 2 s 1, respectively. The steady-state demand function calculated with standard parameters (Table 1) is shown by a solid line. SOLVING THE CARBON BALANCE FOR LEAF NITROGEN CONTENT The analytical solution of the model predicts a relationship between leaf nitrogen and photosynthesis rate independently from the photosynthesis model. This relationship is predicted by the demand for assimilates by processes of regeneration and export. The photosynthesis model predicts photosynthesis-nitrogen relationships given the PPFD environment, saturating at high nitrogen content, but at steady-state in a canopy only a single value of leaf nitrogen content is realized. Thus the combination of demand and supply function defines the dependence of photosynthesis and leaf nitrogen on the canopy light environment. This can be shown most easily in a graphical way: Fig. 3 shows the demand function for a given set of common pool parameters, together with the supply function for different values of instantaneous light. If we assume that the light environment is stable over time then the steady-state leaf nitrogen content is predicted by the intersection of a particular supply function and the demand function. This approach is used in dynamic calculations in the entire model. Because the relationship between leaf photosynthesis rate and incident PPFD is instantaneous and very non-linear, the behaviour of a dynamic version of the model depends heavily on the frequency characteristics of the fluctuating PPFD. Because most non-linearity of the model is in the photosynthesis, and daily fluctuations in photosynthesis rate have little influence on the considerably slower regeneration of the photosynthetic apparatus, it is possible to follow the behaviour of the model if we already have the time integrals of leaf photosynthesis. This model can be used to follow transitions in leaf nitrogen, carbohydrate content and photosynthesis rate in response to a step change in PPFD. In Fig. 4 we show such a transition, assuming a sinusoidal diurnal course of PPFD. In this particular case, assuming all parameters listed in Table 1 to be constant, a new steady-state is achieved at about 20 days after transfer to lower PPFD. SENSITIVITY ANALYSIS The sensitivity of state variables N p and C, and leaf photosynthesis rate A to all parameters and driving variables was calculated using 10% parameter increment: Y P j Y S(Y, P j ) = = 10, eqn 15 Y P j Y Fig. 4. Dynamics of leaf photosynthetic nitrogen content (upper curve), leaf labile carbohydrates (middle curve) and photosynthesis rate (shaded bars) at PPFD simulated with a sinusoidal function of 12 h day/night period. The leaf was pre-acclimated up to a steady-state at maximum midday PPFD of 1000 µmol m 2 s 1 and was switched to 500 µmol m 2 s 1 on day 7. All other driving variables including the plant common pools were kept constant. where Y is the steady-state value of the state variable for the standard parameter set and Y is the change in the value of steady-state state variable in response to a P j = 0 1P j increase in the value of parameter P j (Thornley & Johnson 1990). In this sensitivity analysis PPFD was held constant, i.e. there was no diurnal rhythm, and in each case the model was run until steady-state.

6 29 Photosynthesis acclimation in canopy Sensitivity analysis shows that the model is well balanced: all values of S(Y,P j ) are less than unity and there is no single parameter which would influence the result too much (Table 2). The most influential driving variables are C i, I 0 and N c. As it would be expected, the most important rate constant predicting the amount of photosynthetic apparatus is the rate constant of destruction of N p. Table 2. Results from the sensitivity analysis. Values show the relative change in state variable in response to a 10% increase in parameter or driving variable value from the standard value. Within categories parameters are ordered according to their effect on steady-state leaf nitrogen content, N p Parameter N p C A DRIVING VARIABLES C i I N c E-07 ζ C c E-08 O i PHOTOSYNTHESIS MODEL k a n n φ max α k c Γ* n k o n k f n E E-09 MAIN MODEL k E E-06 k E-06 k E-07 k E-07 k E-08 k E-08 COMPARISON WITH DATA We have calculated daily average photosynthesis for leaves in a P. tremula and a C. avellana canopy using actually measured parameters for the photosynthesis model (Kull & Niinemets 1998; see Appendix). Photosynthesis rates were calculated for leaves with measured nitrogen content and light environment (the latter expressed as fractional transmission of PPFD, K sum ). The calculated leaf photosynthesis rates are plotted in Fig. 5. As expected, data points for each species lie on straight lines. Regression analysis of these data shows that, in terms of our model, the main difference between these two species is in the intercept of their demand functions. We can infer from these calculated data that, according to our model, in that particular canopy there were no leaves that were not exporting assimilates, otherwise the data points would lie on a curved line in Fig. 5. This supports the implication of our model that the canopy lower limit is predicted by the leaf nitrogen content at which export becomes zero, i.e. by equation 11. The steady-state solution of the demand function predicts that if two species have similar rate constants k 2 and k 6 then the slopes in equation 9 should also be similar, and a straight line from the origin of the AvsN p plot should cross the data points of the lowest leaves of both species simultaneously (Fig. 5). Although the steadystate relationship of leaf photosynthesis rate and nitrogen content is linear, the relationship between the leaf nitrogen content and the PPFD environment of the leaf is more complicated and the shape of this relationship depends substantially on the intercept of the demand function. Figure 6 shows the relationships of leaf nitrogen and PPFD for P. tremula and C. avellana, derived from the model, with N c and C c values derived from the regression lines in Fig. 5. From regression equations in Fig. 5, we can find the ratio of common carbon pools for P. tremula and C. avellana (equation 13) to be about 7 4 and the ratio of common nitrogen pools (equation 14) to be SCALING UP TO THE CANOPY Fig. 5. Relationships between calculated daily average photosynthesis rate and measured leaf nitrogen content in Corylus avellana ( ) and Populus tremula ( ) grown in the same canopy. Initial data from Kull & Niinemets (1998). Regression equations: A = 0 028N p 0 27 (R 2 = 0 982) for Corylus avellana and A = 0 034N p 1 99 (R 2 = 0 944) for Populus tremula. We have investigated the dependence of whole canopy integrated photosynthesis rate and LAI on the magnitude of the common pools, C c and N c. In integrating the model over the canopy we started at the topmost unshaded leaves and found the values of the steady-state state variables. Then, assuming a relationship between LAI and PPFD environment inside the canopy (Assumption 8), we ran the model for lower leaves down to the point where canopy lower limit conditions were met (Assumption 7). Then we

7 30 O. Kull & B. Kruijt varied the driving variables C c and N c, assuming that by changing the value of the plant common pool of carbohydrates we simulate variation of growth form or shade tolerance of plants forming the canopy, and by changing N c we simulate variations in site fertility. According to our model (Fig. 2), an increase in C c leads to a shift of the demand function towards higher values of N p without changing the slope, whereas an increase in N c leads to a decrease in the slope of the demand function. Increase of both C c and N c leads to an increase of N p at canopy lower limit. With decreasing C c or N c the total canopy LAI increases steadily but total canopy photosynthesis rate, nitrogen and chlorophyll all have dependencies that show a maximum at a certain combination of the common pools (Table 3). Such an optimum appears because, as a result of increasing LAI, nitrogen content and, hence, the amount of photosynthetic apparatus on a leaf area basis decreases beyond a certain value of LAI. Data in this table also show that an upper fully exposed leaf behaves in a different way than the total canopy. In Fig. 7 the total canopy photosynthesis rate for different combinations of common pools of nitrogen and carbon are plotted against total canopy nitrogen. The calculations show that total canopy nitrogen is a good predictor of total canopy photosynthesis rate even if non-photosynthetic nitrogen is not discounted. Discussion Fig. 6. Relationships between daily average PPFD and measured leaf nitrogen content in Corylus avellana ( ) and Populus tremula ( ) grown in the same canopy, initial data from Kull & Niinemets (1998). Solid lines are calculated relationships if the demand functions are derived from the regressions in Fig. 5. The central idea of this study is that acclimation to PPFD occurs because there is permanent turnover of the photosynthetic apparatus. The regeneration rate of this apparatus depends on the amount of available resources, in particular leaf labile nitrogen and carbohydrates, where the latter depends on the leaf PPFD climate through the rate of photosynthesis. Correlation between the amounts of labile carbohydrate and nitrogen in leaves sampled throughout a canopy, as described by Kull & Niinemets (1998) serves as indirect evidence for the proposed mechanism. Our model (equation 12) also predicts such proportionality between N p and C. The other key idea in this study is that leaves of the same plant are not completely independent from each other and share a common source of information. It seems reasonable to assume that this common information is related to the common resources of nutrients and sink strength of Table 3. Canopy and upper leaf parameters, calculated for different combinations of common pools C c and N c, other constants and incident PPFD are the same Canopy total per unit ground area Upper unshaded leaf Leaf Leaf Daily average photosynthetic Leaf total Average leaf Leaf area Daily average photosynthetic Leaf total photosynthesis nitrogen nitrogen nitrogen content index photosynthesis nitrogen nitrogen rate N p N p + N (N p + N)/LAI (LAI) rate N p N p + N µmol m 2 s 1 mmol m 2 mmol m 2 mmol m 2 m 2 m 2 µmol m 2 s 1 mmol m 2 mmol m 2 N c =70 C c = C c = 500 N c =

8 31 Photosynthesis acclimation in canopy carbohydrates. Using Thornley s transport resistance model and common pools of carbohydrates and nitrogen is a simplification justified by lack of good alternative models. In fact, export of assimilates is most likely realized by a mass flow mechanism but still only few attempts with high degree of simplifications have been made to use mass flow models (Kull & Kull 1989; Dewar 1993). As predicted by the model, data show a linear relationship between average photosynthesis rate and leaf nitrogen content in leaves taken from the same canopy. This relationship appears independently from the leaf photosynthesis model as a result of the demand function, which implies that the photosynthetic rate controls the leaf nitrogen. If the pattern of leaf photosynthesis rate in the canopy would change, for instance, as a result of persistent stomatal closure in some part of the canopy then, according to our model, the nitrogen content would be adjusted accordingly. The distribution of leaf photosynthesis rate in the canopy determines the relationship between leaf nitrogen and the PPFD environment at the leaf surface. Thus, a good photosynthesis model is required to understand this relationship. Kull & Niinemets (1998) showed that two co-occurring tree species had similar nitrogen dependencies of photosynthetic parameters but completely different patterns of distribution of photosynthetic apparatus in respect to PPFD inside the canopy. As shown by our analysis, differences between species in nitrogen distribution can be explained with differences in demand function. In light-demanding P. tremula described in our study (Fig. 6), as well as in canopies of several other tree species, the relationship between average PPFD and leaf nitrogen appears to be close to linear and these canopies had also their lower limit at relatively high values of PPFD (DeJong & Doyle 1985; Kull & Niinemets 1993). Meanwhile in several studies, especially with herbaceous canopies, Fig. 7. Relationship between total canopy photosynthesis rate and total (closed symbols) or photosynthetic (open symbols) canopy foliar nitrogen at different combinations of plant common pool sizes., C c = 500 mmol m 2 and N c varies;, N c = 70 mmol m 2 and C c varies. Data from Table 3. this relationship has been described with an exponential relationship (Hirose et al. 1988; Lemaire et al. 1991; Hikosaka, Terashima & Katoh 1994; Hirose & Werger 1994). Usually, herbaceous canopies have their lower limit at substantially lower values of PPFD than trees. From our model it may be hypothesized that herbaceous species have relatively low common pools of carbon and nitrogen and that the curvature of their leaf nitrogen vs PPFD relationship is also substantial. Proportionality between the leaf carbohydrate pool and leaf nitrogen content (equation 12) is predicted because we assume first order kinetics where the leaf carbohydrates control regeneration of N p. Although data from the canopy of P. tremula and C. avellana confirm this assumption (Kull & Niinemets 1998), this may not always be the case. The regeneration reaction may have saturating kinetics instead. For instance, several experiments in elevated CO 2 shown that leaf nitrogen does not increase with increased leaf carbohydrates but instead may even decrease (Luo, Field & Mooney 1994). However, it must be kept in mind that according to equation 12 the same effect can be explained in terms of a decreased ( diluted ) common nitrogen pool, because the proportionality coefficient between the leaf carbohydrate pool and N p depends on the common nitrogen pool. The often documented small intercept in plots of nitrogen vs photosynthetic parameters can be attributed to the leaf labile nitrogen pool as is done in the present approach. According to our model this pool at steady state only depends on the common nitrogen pool N c and is constant on a leaf area basis throughout the canopy. This does not mean that the rest of the leaf nitrogen is involved directly in the photosynthetic apparatus but it does imply that the amounts of all other compounds in the leaf that contain nitrogen are strongly correlated with the amount of photosynthetic apparatus. It has been assumed in this study that water is not limiting. However, to allow wider use of this model water relations should be included because often water limitations cannot be ignored. At a single-leaf scale water is affecting photosynthesis rate through stomatal conductance and C i. At the plant or withincanopy scale, water is most likely to affect export by changing the rate constant k 5 because phloem transport depends on the water potential distribution inside the plant. Pons & Bergkotte (1996) showed in an experiment with Phaseolus vulgaris plants that manipulations with individual leaf vapour pressure differences (VPD) lead to changes in nitrogen and photosynthetic apparatus distributions between leaves. They argue that this could point to a mechanism for acclimation, controlled by transpiration rates involving a messenger from the roots. The experimental plants, however, were small and it is likely that the common pools were different for the different plants. Our model would predict similar results without assuming a messenger, allowing for changes in these

9 32 O. Kull & B. Kruijt 1999 British Ecological Society, Functional Ecology, 13, pools or in the rate constant k 5. However, it is clear that the transport resistance approach used in our model is too simple to model correctly effects of all possible experimental manipulations. In scaling processes from leaf to canopy it is crucial to know what limits the depth of the canopy. According to equation 9 the lower limit of N p does not directly depend on PPFD, although over longer time scales one can expect that the plant common pools depend on total photosynthesis of the plant and thus on incident PPFD. Also, it must be kept in mind that in smaller plants the common pools can change rapidly and thus have substantial influence on the dynamics of acclimation. Our model calculations show that all leaves in the canopies studied are exporting assimilates to the common pools. This situation is not achieved through dropping off lower leaves when they become unable to export. There is no considerable leaf fall in canopies of adult trees during the growing season, even though conditions for photosynthesis are usually deteriorating during the season owing to decreasing PPFD levels at the lowest canopy levels. It is possible that the lower canopy limit appears in a tree canopy as a result of a lack of development of buds near to non-exporting leaves, because the main source of assimilates for buds are neighbouring leaves (Sprugel, Hinckley & Schaap 1991). However, in smaller plants and tree seedlings other mechanisms like leaf abscission owing to senescence may be the dominating process in limiting canopy depth (Michael et al. 1990). If it is correct that the relationship in equation 11 determines the lower limit in the canopy, then an increase in either N c or C c will lead to a higher value of the minimum PPFD that can sustain exporting leaves. This leads to a lower total LAI of the canopy (Table 3). This mechanism allows explanation of two phenomena. First, light demanding species (such as P. tremula in our study) are known to form canopies with less LAI than more shade tolerant species (such as C. avellana in our study). Our model explains this by predicting differences in their common carbon pools. Second, our model predicts that under constant incident light and with increasing N p,min the leaf area index of the canopy decreases and the average canopy leaf nitrogen content increases, a phenomenon described in a transect in Oregon along sites with different productivity (Pierce, Running & Walker 1994). Meanwhile, as shown on the same Oregon data set, annual production correlates well with total canopy nitrogen as predicted by our model (Matson et al. 1994). Integration of photosynthesis over different hypothetical canopies (Table 3) shows that both total canopy photosynthesis rate and total nitrogen have optima at certain values of LAI and total absorbed PPFD. These optima represent the points at which the advantage of a low common carbon pool: exporting capacity even at low leaf photosynthesis rates and hence high leaf area, balances the advantage of a high C c : when the synthesis of photosynthetic apparatus has little competition from export of leaf carbohydrates. However, the independent variation in common pools as shown in Table 3 is of course artificial and to make any inferences about real canopies, the dynamic relationship between the plant carbon and nitrogen pools has to be included into the model explicitly. Oversimplification of known relationships between PPFD and leaf nitrogen content or photosynthetic parameters leads to big leaf models (Kull & Jarvis 1995; Kruijt et al. 1997). According to these models a fully acclimated canopy behaves like upper unshaded leaf in the canopy. The current model, presented here, shows that in response to manipulations with the driving variables, photosynthesis rate and nitrogen content of the upper unshaded leaf do not change in parallel with total canopy photosynthesis rate or nitrogen (Table 3). Such behaviour of the model appears because mechanisms that predict the amount of the photosynthetic apparatus in a single leaf are different from mechanisms predicting total amount of photosynthetic apparatus in a canopy. Scaling the model from leaves to integrated canopy photosynthesis shows that with increasing scale the possible range of the photosynthesis rate as a function of leaf nitrogen decreases and that factors predicting the pattern of this relationship change. For independent leaves, (Fig. 8a) the possible range covers a large area of the A N p surface as predicted by leaf photosynthesis model. The main factors predicting the pattern are PPFD and maximum carboxylation efficiency per unit of leaf nitrogen. The range is limited by an upper boundary only, representing conditions in maximum PPFD. For leaves growing together in a canopy (Fig. 8b), the range of the A N p relationship is also limited by a lower boundary, as a result of the relationship between photosynthesis rate and consumption of assimilates. The main factors predicting the A N p relationship are the demand function and the common carbon and nitrogen pools in the plant. At large scale, for photosynthesis integrated over whole canopies (Fig. 8c), the possible range of the A N p relationship is likely to collapse even more towards a straight line, because a certain amount of total photosynthetic apparatus simply implies its maintenance by a certain level of total productivity. Still, the A N p relationship varies, probably mainly with the ratio of the common pools of nitrogen and carbon. Conclusions This study provides a mechanistic yet still reasonably simple model to explain distribution patterns of foliar nitrogen and photosynthetic properties in a canopy. We have adopted weakly tested hypotheses as well (e.g. the linear dependence of the synthesis of photosynthetic apparatus on leaf carbohydrates), but at least these can (and should) be tested. In the current state, the common

10 33 Photosynthesis acclimation in canopy pools postulated here are still rather theoretical concepts, although they are useful to distinguish between different growth strategies at sub-seasonal time scales. These pools need to be specified further within the framework of a growth and allocation model and need to be expressed in terms of measurable quantities. Although showing that the processes determining average photosynthesis rate are more complex than is often assumed, we do provide the start for a general, mechanistic model predicting photosynthesis and growth of vegetation canopies requiring relatively little independent information and few untestable assumptions. This study makes two practical predictions that relate to large-scale modelling of the biosphere s carbon balance. First, primary production can be quite accurately predicted from leaf nitrogen values and second, canopies cannot be treated as a simple big leaf because the factors predicting the amount of photosynthetic apparatus in a single leaf differ from the factors predicting the total amount of foliage in a canopy. Acknowledgements We are grateful to Paul Jarvis, who initiated and stimulated our collaboration. The work was sposored by Estonian Sciences Foundation and an EC-EERO grant to O.K. and by UK-NERC grants GST/02/597 and GR3/09732 to B.K. Fig. 8. The possible range of nitrogen and photosynthesis rates (shaded area): (a) on single leaf level derived from the leaf photosynthesis model. Curves represent relationships at particular PPFD environment; (b) in leaves from a canopy. Lines present realized relationships at given parameters of the demand function; (c) at a whole canopy scale (hypothetical) when canopy total photosynthesis rate and leaf nitrogen from different canopies are compared. References Burkey, K.O. & Wells, R. (1991) Response of soybean photosynthesis and chloroplast membrane function to canopy development and mutual shading. Plant Physiology 97, Chazdon, R.L. & Field, C.B. (1987) Determinants of photosynthetic capacity in six rainforest Piper species. Oecologia 73, DeJong, T.M. & Doyle, J.F. (1985) Seasonal relationships between leaf nitrogen content (photosynthetic capacity) and leaf canopy light exposure in peach (Prunus persica). Plant, Cell and Environment 8, Dewar, R.C. (1993) A root shoot partitioning model based on carbon nitrogen water interactions and Münch phloem flow. Functional Ecology 7, Ellsworth, D.S. & Reich, P.B. (1993) Canopy structure and vertical patterns of photosynthesis and related leaf traits in a deciduous forest. Oecologia 96, Farquhar, G.D., von Caemmerer, S. & Berry, J.A. (1980) A biochemical model of photosynthetic CO 2 assimilation in leaves of C3 species. Planta 149, Field, C. (1983) Allocating leaf nitrogen for the maximisation of carbon gain: leaf age as a control on the allocation program. Oecologia 56, Givnish, T.J. (1988) Adaptation to sun and shade: a wholeplant perspective. Ecology of Photosynthesis in Sun and Shade (eds J. R. Evans, S. von Caemmerer & W. W. Adams III), pp CSIRO, Australia. Hikosaka, K., Terashima, I. & Katoh, S. (1994) Effects of leaf age, nitrogen nutrition and photon flux density on the distribution of nitrogen among leaves of a vine (Ipomoea tricolor Cav.) grown horizontally to avoid mutual shading of leaves. Oecologia 97, Hilbert, D.W., Larigauderie, A. & Reynolds, J.F. (1991) The influence of carbon dioxide and daily photon-flux density on optimal leaf nitrogen concentration and root:shoot ratio. Annals of Botany 68, Hirose, T. & Werger, M.J.A. (1987a) Maximising daily canopy photosynthesis with respect to the leaf nitrogen allocation pattern in the canopy. Oecologia 72, Hirose, T. & Werger, M.J.A. (1987b) Nitrogen use efficiency in instantaneous and daily photosynthesis of leaves in the canopy of a Solidago altissima stand. Physiologia Plantarum 70, Hirose, T. & Werger, M.J.A. (1994) Photosynthetic capacity and nitrogen partitioning among species in the canopy of a herbaceous plant community. Oecologia 100, Hirose, T., Werger, M.J.A., Pons, T.L. & van Rheenen, J.W.A. (1988) Canopy structure and leaf nitrogen distribution in a stand of Lysimachia vulgaris L. as influenced by stand density. Oecologia 77,

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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 light-saturated 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 available. LIGHT SATURATED PHOTOSYNTHESIS As 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 A1 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 =, C i + Γ* eqn A2 where C i is the intercellular CO 2 concentration and Γ* is the CO 2 compensation point in the absence of