bs_bs_banner

Plant, Cell and Environment (2014) 37, 2077–2085

doi: 10.1111/pce.12291

Original Article

Optimal nitrogen distribution within a leaf canopy under direct and diffuse light Kouki Hikosaka

Graduate School of Life Sciences, Tohoku University, Sendai, Miyagi 980-8578, Japan and CREST, JST, Japan

ABSTRACT Nitrogen distribution within a leaf canopy is an important determinant of canopy carbon gain. Previous theoretical studies have predicted that canopy photosynthesis is maximized when the amount of photosynthetic nitrogen is proportionally allocated to the absorbed light. However, most of such studies used a simple Beer’s law for light extinction to calculate optimal distribution, and it is not known whether this holds true when direct and diffuse light are considered together. Here, using an analytical solution and model simulations, optimal nitrogen distribution is shown to be very different between models using Beer’s law and direct–diffuse light. The presented results demonstrate that optimal nitrogen distribution under direct–diffuse light is steeper than that under diffuse light only. The whole-canopy carbon gain is considerably increased by optimizing nitrogen distribution compared with that in actual canopies in which nitrogen distribution is not optimized. This suggests that optimization of nitrogen distribution can be an effective target trait for improving plant productivity. Key-words: canopy photosynthesis; light distribution; model; nitrogen allocation; nitrogen use; optimization.

INTRODUCTION Nitrogen distribution within a leaf canopy is one of the most important determinants of canopy carbon gain. In most leaf canopies, considerable variation in light availability occurs, and more nitrogen is allocated to leaves receiving higher light intensities (Mooney et al. 1981; DeJong & Doyle 1985; Charles-Edwards et al. 1987; Hikosaka et al. 1994; Wyka et al. 2012). This light-dependent nitrogen allocation is beneficial because the marginal carbon gain per unit nitrogen investment is greater at higher light intensities for a given nitrogen content (Mooney & Gulmon 1979; Hirose & Werger 1987a; Hikosaka & Terashima 1995). A number of simulation studies have reported that nitrogen distribution observed in actual canopies significantly improves canopy photosynthesis compared with uniform nitrogen distribution (for a review, see Hirose 2005). In the last three decades, optimal nitrogen distribution that maximizes canopy carbon gain has been extensively studied. Field (1983) reported that canopy photosynthesis is Correspondence: K. Hikosaka. E-mail: [email protected] © 2014 John Wiley & Sons Ltd

maximized when nitrogen is distributed such that the marginal gain of nitrogen investment is identical among leaves:

∂Ad =λ ∂N

(1)

where Ad is the leaf daily CO2 assimilation rate, N is the leaf nitrogen content and λ is the Lagrange multiplier. Assuming that linear relationships exist among Amax (light-saturated rate of CO2 assimilation), respiration rate and N, Farquhar (1989) indicated that canopy photosynthesis was maximized when Amax was proportional to relative light intensity. Anten et al. (1995) proposed a simple equation for optimal N distribution in which N was proportionally allocated to the gradient in light intensity. Although N distribution in actual canopies is suboptimal (Hirose & Werger 1987b; Niinemets 2012; Buckley et al. 2013), optimal N theory has been used to describe canopy nitrogen distribution in various models of plant functioning (Sellers et al. 1992; Anten 2002; Franklin & Ågren 2002; Hikosaka 2003; Hikosaka & Anten 2012). The physiological and physical constraints explaining discrepancies between theoretical and actual N distribution, have been extensively discussed (Pons et al. 1989; Stockhoff 1994; Hollinger 1996; Schieving & Poorter 1999; Buckley et al. 2002, 2013; Kull 2002; Dewar et al. 2012; Niinemets 2012; Peltoniemi et al. 2012; Tarvainen et al. 2013). Most previous theoretical studies have used simple Beer’s law to describe light distribution in leaf canopies; light intensity exponentially decreases with an increase in leaf area from the top to bottom of the canopy, and the light intensity is assumed to be identical among leaves at the same canopy depth (Monsi & Saeki 1953). However, under field conditions, some leaves are exposed to diffuse light, whereas others in the same depth are exposed to direct sunlight, which has higher intensity than diffuse light; this results in a bimodal light intensity distribution (Goudriaan 1977; Buckley et al. 2002). Because the light response of photosynthesis is not linear, ignoring direct/diffuse light may result in significant errors in estimating canopy gas exchange (de Pury & Farquhar 1997). Furthermore, particularly in lower canopy layers, exposure to direct sunlight may occur stochastically. Because the spatial distribution of direct light spot is affected by many variables, such as solar position and development and movement of upper leaves in the canopy, it is uncertain which leaves receive direct sunlight. Therefore, optimal nitrogen distribution may be different when the availability of direct light to each leaf is 2077

2078

K. Hikosaka

predicted deterministically or stochastically. Several studies have analysed optimal N distribution under direct light. Gutschick & Wiegel (1988) calculated optimal leaf mass per area (analogous to N) under direct and diffuse light, but they did not discuss whether the optimal distribution differs from that derived using Beer’s law. Buckley et al. (2013) analysed optimal photosynthetic resource allocation incorporating various factors including water relations, nitrogen partitioning within leaves and direct–diffuse light distribution. However, their model calculated light environment and optimal nitrogen allocation for each leaf; plants allocated more nitrogen to a leaf that receive higher light, even when the leaf was situated a lower canopy layer. The optimal N was proportional to the absorbed light when other factors were ignored, as in previous models using Beer’s law. de Pury & Farquhar (1997) calculated optimal N distribution in a canopy in which exposure to direct sunlight occurred stochastically. They indicated that optimal N distribution was steeper than the distribution of absorbed light, suggesting that optimal N was not proportional to the absorbed light under direct and diffuse light (also discussed in Buckley et al. 2002). However, it is still unclear whether this holds true in other canopies with different canopy traits such as leaf area index (LAI) and leaf angles. Therefore, the general pattern of optimal N distribution under direct light remains poorly understood. Furthermore, effects of nitrogen distribution on the whole-canopy carbon gain under direct–diffuse light have not been studied. The present study focuses on the effect of direct–diffuse light conditions on optimal N distribution within a leaf canopy. First, an analytical solutions for optimal N distribution under diffuse, direct, and direct–diffuse light conditions were derived using simplified models. Second, optimal N distribution was numerically analysed using more realistic canopy parameters. Third, the extent of improvement in canopy carbon gain by optimizing N distribution was studied.

Analytical solution for optimal nitrogen distribution To derive analytical solution, the light-response curve of photosynthesis is expressed as a rectangular hyperbola:

Amaxφ I c Amax + φ I c

(2)

where A is the CO2 assimilation rate (μmol m−2 s−1), Amax is the maximum rate of A at saturating photosynthetically active radiation (PAR), Ic is the intercepted PAR (μmol m−2 s−1), and ϕ is the initial slope of the curve (mol mol−1). Amax is assumed to be proportional to the leaf photosynthetic nitrogen Np (mmol m−2):

Amax = aN p

I f = I foe − KL F

(4)

where Ifo is the diffuse PAR at the top, KL is the extinction coefficient for diffuse PAR and F is the cumulative LAI from the top of the canopy (m2 m−2). Light scattering by leaves is ignored (i.e. leaves are completely black), and the intercepted diffuse PAR at F is given as

I fc = KL I foe − KL F.

(3)

where a is a measure of photosynthetic nitrogen use efficiency (PNUE; μmol mmol−1 s−1). a is assumed as constant and respiration is ignored in this model.

(5)

Direct PAR on a horizontal plane (Ir) does not change irrespective of canopy depth; thus, the intercepted direct PAR (Irc) is given as

I rc = KL I r.

(6)

KL is assumed to be identical in both direct and diffuse PAR. The fraction of leaves exposed to direct PAR (fsun) decreases with canopy depth:

fsun = e − KL F.

(7)

Here, three scenarios on light condition are considered. In the first model, the canopy receives diffuse PAR only. In this case, A at F is derived as follows:

A=

aN pφ KL I foe − KL F . aN p + φ KL I foe − KL F

(8)

Using Eqn 1, optimal Np is derived as follows:

λ=

dA aφ 2 KL 2 I fo 2 = , dN p (aN pe KL F + φ KL I fo )2

N p = φ KL I foe − KL F

THE MODEL

A=

In the models, diffuse and direct light are taken into account. Diffuse PAR on a horizontal plane (If) decreases with canopy depth (Beer’s law):

a− λ . a λ

(9)

(10)

Eqn 10 indicates that the optimal Np distribution under diffuse PAR is expressed as an exponential function, as has been derived by Anten et al. (1995). In the second model, the canopy receives direct PAR only and assimilation occurs only in leaves receiving direct PAR. Assuming that Np is constant within each canopy layer, the mean value of A at F is given as

A=

aN pφ KL I r e − KL F . aN p + φ KL I r

(11)

Eqn 11 is similar to Eqn 8 except that e −KL F is absent in the denominator in Eqn 11. Optimal Np at F is derived as follows:

λ=

dA aφ 2 KL 2 I r 2 e − KL F = , dN p (aN p + φ KL I r )2

(12)

ae − KL F − λ . a λ

(13)

N p = φ KL I r

© 2014 John Wiley & Sons Ltd, Plant, Cell and Environment, 37, 2077–2085

Optimal N distribution under direct–diffuse light Thus, it is apparent that optimal nitrogen distribution differs depending upon light sources. In the third model, the canopy receives both direct and diffuse PAR. In each canopy layer, some leaves receive diffuse PAR only, whereas others receive both diffuse and direct PAR. Assuming thet Ifo = cIr, where c is a constant, A is derived as follows:

A = (1 − e − K L F ) + e − KL F

aN pφ KL cI r e − KL F aN p + φ KL cI r e − KL F

(14)

aN pφ(KL I r + KL cI r e − KL F ) , aN p + φ(KL I r + KL cI r e − KL F ) aφ 2 KL 2 I r 2 [a2 e 2 KL F N p 2 ( 2c + c 2 + e KL F ) + 2acφ KL I r N pe KL F (1 + c ) (c + e KL F )

+ c 2φ 2 KL 2 I r 2 (c + e KL F ) ⎤⎦ dA = dN p (aNe KL F + cφ KL I r )2 [aNe KL F + φ KL I r (c + e KL F )]2 2

(15)

From Eqn 15, Np is calculated as a function of λ (equation is not described considering its length). These derivations were performed using Mathematica 9 (Wolfram Research, Champaign, IL, USA). These models are an optimal solution for instantaneous assimilation rates. Optimal solutions for daily levels could not be derived.

Simulation models for optimal nitrogen distribution To predict more realistic optimal nitrogen distribution, a multilayer model of canopy photosynthesis was developed based on the model of de Pury & Farquhar (1997), with some modifications. Solar geometry and PAR were modelled as shown in Eqns A1–A6 in Appendix. The canopy comprised 20 layers in which leaves were randomly distributed, and they received direct PAR (Irc), diffuse PAR (Ifc) and scattered direct PAR (Isc). Irc was constant across the layers (Eqn A8), but the fraction of leaves receiving Irc decreased with canopy depth (Eqn A7). Ifc decreased with canopy depth (Eqn A9). Isc was calculated as the difference between light interception by black (no scattering) and actual leaves (Eqn A10). Sunlit leaves received Irc, Ifc, and Isc, whereas shade leaves received Ifc and Isc (Eqns A11 and A12). Light extinction coefficient for direct light was calculated based on leaf and solar angles (Eqns A13–A15) according to Anten (1997) with some modifications. Light extinction coefficient for diffuse light was assumed to be 0.5, 0.7 and 0.9 at leaf angle of 75, 45 and 15°, respectively, based on Monsi & Saeki (1953) and Kamiyama et al. (2010). Leaf angle was assumed to be constant within the canopy for simplicity. CO2 assimilation rates were calculated based on the biochemical model of Farquhar et al. (1980; Eqns A16–A22). For simplicity, leaf temperature and intercellular CO2 partial pressure were assumed to be 21 °C and 25 Pa, respectively. Maximal carboxylation, maximal electron transport and respiration rates were assumed as linear functions of leaf nitrogen content per unit leaf area (N; Eqns A23–A25). Most constants were taken

2079

from data obtained from a wheat canopy (de Pury & Farquhar 1997). Photosynthetic rates of layers were calculated every 30 min from dawn and daily carbon gain was obtained using the trapezoidal rule. Canopy carbon gain was calculated as the sum of daily photosynthesis of layers. Optimal N was numerically obtained. Mean daily carbon gain (Ad) at each canopy layer under various N from 25 to 700 mmol m−2 at every 0.1 mmol m−2 was calculated. Then λ value was calculated for each N.

λ=

dAd Ad ( N + 0.1) − Ad ( N ) ≈ dN 0.1

(16)

The value of N giving a λ value closest to a target value (e.g. 0.4 d−1) was selected for each canopy layer, and then the optimal N distribution with the same λ value was derived. For leaves with high photosynthetic nitrogen use efficiency (PNUE), the target λ value was 0.4, 0.8, 1.2, 1.6 and 2.0 d−1, and for leaves with low PNUE, the target λ value was 0.3, 0.35, 0.4, 0.45 and 0.5 d−1. Optimal N was calculated for canopies with different leaf angles and PNUE, both of these vary considerably between species. Leaf inclination angle tends to be lower (i.e. more horizontal) in forbs and higher in grasses. Results were obtained for leaf angles of 15, 45 and 75°. PNUE is greater in fast-growing species (e.g. herbs and early successional species) than in slow-growing species (e.g. woody species and late successional species). PNUE is a biochemical key of leaf economics spectrum (Hikosaka 2004, 2010; Wright et al. 2004). The ratio of Vcmax to photosynthetic leaf nitrogen content (aV; Eqn A24) was used as an index of PNUE; 1.16 and 0.29 mmol mol−1 s−1 were used as examples for herbs and evergreen trees, respectively. 1.16 was obtained from wheat (de Pury & Farquhar 1997), a fast-growing species, and 0.29 was chosen because PNUE of evergreen trees was 25% of that of herbs in temperate species (Hikosaka & Shigeno 2009).

Effect of nitrogen distribution on canopy carbon gain To assess the effect of N distribution on canopy carbon gain, N distribution was expressed by an exponential function:

N=

K b N T − Kb F e + Nb 1 − e − Kb FT

(17)

where Kb is the coefficient of photosynthetic nitrogen distribution, Nb is the leaf structural nitrogen content (N when Amax = 0) and NT and FT are total nitrogen and LAI in the canopy, respectively (Anten et al. 1995). Daily CO2 assimilation of the canopy at various Kb values was calculated.

RESULTS Analytical solution Optimal distribution of photosynthetic nitrogen (Np) under diffuse light only was described by an exponential function

© 2014 John Wiley & Sons Ltd, Plant, Cell and Environment, 37, 2077–2085

2080

K. Hikosaka With an increase in leaf inclination angle (i.e. more vertical), the optimal N distribution was less steep (Fig. 2b,e). The opposite trend was observed when leaf inclination angle was low (data not shown). With a decrease in PNUE (aV), the N–LAI relationship became steeper (Fig. 2c) and the N–Light relationship exhibited concave curves (Fig. 2f).

Contribution of nitrogen distribution to the whole-canopy carbon gain

Figure 1. Analytical solution for optimal distribution of leaf photosynthetic nitrogen content plotted against cumulative leaf area index (a) and mean relative light interception (b). Dotted, broken and continuous lines are optimal values under diffuse light only, direct light only, and direct–diffuse light, respectively. Values of constants were a = 0.2, ϕ = 0.05, c = 0.33, KL = 0.7, and total photosynthetic nitrogen in the canopy = 200. Ir was 2000 and 1500 for direct light only and direct–diffuse light, respectively (total PAR above the canopy was identical between the three models).

(Eqn 10) as previously reported by Anten et al. (1995), and the optimal Np was proportional to the intercepted light (Fig. 1). Under direct light only, optimal Np distribution was also described by an exponential function (Eqn 13), but the optimal Np became negative values at lower canopy layers. In Fig. 1, Np was assumed to be 0 when the optimal value was negative because negative values of Np are not biologically meaningful. At upper layers, the distribution of Np was much steeper than that under diffuse light only. This difference comes from the absence of e −KL F in the denominator in the direct light model (Eqn 11); since e −KL F decreases with increasing F, A at higher F (lower layers) is lower under direct light if the PAR above the canopy is the same. Therefore, allocating nitrogen to lower layers is relatively disadvantageous under direct light compared with that under diffuse light. Under the condition where both direct and diffuse light were present (direct–diffuse light), optimal Np was always positive, and it was intermediate between that under direct light only and that under diffuse light only. The optimal distribution of Np under direct–diffuse light was steeper than that under diffuse light only. Optimal Np under direct–diffuse light increased more than proportionally with an increase in the intercepted light (Fig. 1b).

Using an exponential function for N distribution, the effect of the slope of N distribution (Kb; Eqn 17) on the whole-canopy carbon gain was assessed (Fig. 3). In this simulation, the leaf inclination angle was 45° (Kf = 0.7), LAI was 4.8 and total canopy nitrogen per ground area was 367.2 mmol m−2 (λ = 0.8 in Fig. 2a).The continuous line in Fig. 3 demonstrates the relationship between canopy carbon gain and Kb under direct–diffuse light condition. The closed circle denotes maximal carbon gain at optimized N distribution (λ = 0.8 in Fig. 2a). The open arrow shows the value of Kb observed in actual canopies; values of Kb in actual canopies are known to be approximately half of those of Kf (Anten et al. 2000; K. Hikosaka et al. unpublished data). The maximized carbon gain was 24% higher than that achieved by actual N distribution. The broken line in Fig. 3 shows the simulation result in canopy carbon gain under diffuse light only (simple Beer’s

Simulation Optimal N distribution was calculated for canopy with different λ values, leaf inclination angles and PNUE under direct–diffuse light. Optimal N increased from lower to upper layers, and the curve was not a simple exponential curve; for example, when λ was 0.4 in Fig. 2a, the slope of optimal N was greatest at middle values of cumulative LAI. Consequently, the relationship between optimal N values and light interception was not linear: sigmoid when λ values were small and concave when λ values were large (Fig. 2d).

Figure 2. Simulation results for optimal distribution of leaf nitrogen content plotted against cumulative leaf area index (a–c) and mean light interception (d–f). Values used in the simulation results shown in Fig. 2a are presented in Table A1. Leaf angle, Kf, and aV are 45°, 0.7 and 1.16 × 10−3 s−1, respectively. For Fig. 2b,e, leaf angle and Kf are 75° and 0.5 and other values are identical to those used in Fig. 2a. For Fig. 2c,f,l aV is 0.29 × 10−3 s−1 and other values are identical to those used in Fig. 2a.

© 2014 John Wiley & Sons Ltd, Plant, Cell and Environment, 37, 2077–2085

Optimal N distribution under direct–diffuse light

Figure 3. Effects of nitrogen distribution on the whole-canopy carbon gain. Continuous and broken lines denote carbon gain under direct–diffuse light and under diffuse light only, respectively, plotted against the nitrogen distribution coefficient (Kb). The dotted line denotes leaf nitrogen content at the top layer. Closed and open circles denote carbon gain of the canopy under direct–diffuse light and under diffuse light only, respectively, where nitrogen distribution is optimized under direct–diffuse light (shown as λ = 0.8 in Fig. 2a). The cross denotes nitrogen content at the top layer in the canopy optimized under direct–diffuse light. Values of constants are the same as those used in Fig. 2a and shown in Table A1. Open arrows denote carbon gain at actual nitrogen distribution, which is assumed to be half of Kf. The closed arrow denotes carbon gain when nitrogen distribution is optimized under diffuse light only.

law), where total PAR above the canopy was identical to the simulation under direct–diffuse light condition. Under diffuse light, canopy carbon gain was maximized when Kb = Kf (closed arrow), as has been previously shown by Anten et al. (1995). Maximized carbon gain was only 6% greater than that achieved by actual nitrogen distribution. The open circle indicates canopy carbon gain under diffuse light when nitrogen distribution is optimized under direct– diffuse light. This carbon gain was 5% lower than the maximized carbon gain.

DISCUSSION The present study demonstrates that optimal nitrogen distribution is different when the canopy receives direct–diffuse light or diffuse light only. Optimal nitrogen distribution under direct light was steeper than that under diffuse light (de Pury & Farquhar 1997). The relationship between the optimal nitrogen content and the intercepted light was linear under diffuse light, whereas it was sigmoid or concave under direct–diffuse light. These differences were caused by the predictability of light availability. The diffuse light model, which uses a simple Beer’s law for light extinction, assumes that light availability is identical among leaves within the same canopy layer. Therefore, plants can allocate an

2081

appropriate amount of nitrogen to leaves, in which the nitrogen content is proportional to light availability. In contrast, under direct–diffuse light condition, some leaves receive both direct and diffuse light, whereas others receive diffuse light only. Therefore, nitrogen investment may be insufficient for leaves receiving direct light, while it is wasteful for those receiving diffuse light (Buckley et al. 2002). Because the position of direct light changes depending on factors such as solar position, and development and movement of upper leaves, plants may not be able to predict which leaves receive more direct light than others. To efficiently utilize nitrogen, it is imperative to allocate more nitrogen to upper layers where light conditions are not only higher but also more predictable. In other words, if the position of direct light is predictable, plants should allocate more nitrogen to the leaves receiving direct light even if the leaves are in lower layers. This may be the case when spatial leaf distribution is strongly heterogeneous (e.g. forest gap). In such a situation, optimal N is proportional to light availability (Buckley et al. 2013). Further, even when the position of direct light is predictable, plants may be unable to acclimate their nitrogen allocation due to limitations in their acclimation ability to mobilize nitrogen if the position changes temporary. One such limitation is the extent by which plant can increase Amax. In Chenopodium album, an annual herb, leaves developed in low light conditions increased Amax by 1.5-fold after transfer to high light, but it was still much lower than Amax of leaves developed in high light (Oguchi et al. 2003). It has been suggested that Amax can increase only when chloroplast volume in the leaf can increase (Oguchi et al. 2003, 2005). However, there may be an upper limitation of Amax, particularly for leaves developed in the shade considering their relatively low thickness. C. album leaves transferred from low to high light conditions could not increase Amax further because there was no space to increase chloroplast volume (Oguchi et al. 2003). Leaves of Fagus crenata, a deciduous tree, developed in low light had no space to increase chloroplast volume and they could not increase Amax when they were transferred to high light conditions (Oguchi et al. 2005).A second limitation is the rate of acclimation. Whereas light acclimation in C. album leaves took only 4 d to increase Amax, it took 2 weeks in Betula ermanii, a deciduous tree (Oguchi et al. 2005). Such slow acclimation rates do not allow for optimal nitrogen allocation under changing light condition. The optimal nitrogen distribution under direct light only or under direct–diffuse light was different depending on total canopy nitrogen, leaf angle and PNUE. When total canopy nitrogen content was low (i.e. high λ values), the N–light relationship was concave, whereas it was a sigmoid curve when total canopy nitrogen content was high. The sigmoid curve may appear when carbon gain of upper leaves is saturated by an increase in leaf nitrogen content. When leaf angle was more vertical (low K-values), optimal nitrogen distribution was less steep.This is partly explained by a more uniform distribution of light interception. However, the dependence of optimal nitrogen content on the intercepted light was not the same between high and low leaf angles. When PNUE was low, the N–light relationship was concave and the saturating

© 2014 John Wiley & Sons Ltd, Plant, Cell and Environment, 37, 2077–2085

2082

K. Hikosaka

dependence of N on the intercepted light at high light disappeared. This was because leaves with lower PNUE need to invest more nitrogen to achieve high Amax. These results suggest that predicting optimal nitrogen distribution under direct–diffuse light is not straightforward because of the interactive effects of various factors; therefore, we may need numerical simulation for respective situation. This contrasts with the optimal nitrogen distribution under diffuse light only, in which optimal nitrogen distribution is expressed as a simple exponential function of Kf and total canopy nitrogen (Eqns 10 and 17). Unfortunately, the predicted optimal nitrogen distribution is not realistic in actual plants. In most canopies, actual nitrogen distribution is less steep not only than optimal distribution under direct–diffuse light but also less steep than optimal distribution under diffuse light only (Hirose & Werger 1987b; Anten et al. 1995, 2000; Buckley et al. 2002, 2013; Niinemets 2012). Previous studies have discussed that this is due to physiological or physical constraints on photosynthesis. In canopies with steep nitrogen distribution, leaf nitrogen content in the canopy top is very high (Fig. 3). High nitrogen content is restricted by structural limitations (Dewar et al. 2012), hydraulic limitations (Peltoniemi et al. 2012; Buckley et al. 2013), mesophyll conductance for CO2 diffusion (Buckley et al. 2013) and/or probability of herbivory (Stockhoff 1994). Effects of these constraints on the optimal nitrogen distribution have been theoretically discussed by Buckley et al. (2013). In the past, nitrogen distribution in plant canopies has received less attention as a targeted trait for improving plant productivity, although nitrogen distribution in actual canopies is known to be suboptimal. This may be probably because the loss in carbon gain by suboptimal nitrogen distribution was shown to be quantitatively small in previous studies using a simple Beer’s law (Hirose & Werger 1987b; Anten et al. 1995; Fig. 3). However, this is not necessarily the case under direct–diffuse light conditions. The present study demonstrated that under direct–diffuse light, the loss in carbon gain because of suboptimal distribution can be greater than 20%. If physiological or physical constraints for high N can be modified, then nitrogen distribution may be a valuable target for improving plant productivity. Artificial manipulation of nitrogen distribution may be possible in herbaceous plants where leaves are successively produced at the top. For example, enhancement of CND41 protein, which may be related to degradation of photosynthetic proteins, has been shown to accelerate senescence of old leaves in tobacco (Kato et al. 2005). There may be a conflict of optimization of nitrogen distribution because optimal distribution is different between sunny (direct–diffuse light) and cloudy (diffuse light only) conditions. However, loss of carbon gain by suboptimal distribution was relatively small under diffuse light (Fig. 3), suggesting that optimization under sunny conditions may be relatively advantageous if plants experience both sunny and cloudy days evenly. In summary, the present study showed that when direct and diffuse light were considered separately, optimal nitrogen

distribution was steeper than that previously reported. The simulation indicated that the whole-plant carbon gain could be considerably improved if nitrogen distribution could be optimized.Actual plants do not optimize their leaf nitrogen distribution probably because of a variety of physiological or physical constraints. However, if these constraints could be overcome, then optimizing nitrogen distribution may be an attractive target for improving plant productivity.

ACKNOWLEDGMENTS The study was supported by KAKENHI (2114009, 25660113, 25440230, 25291095) and CREST, JST, Japan. I thank two anonymous reviewers for comments and Enago (http:// www.enago.jp) for the English language review.

REFERENCES Anten N.P.R. (1997) Modelling canopy photosynthesis using parameters determined from simple non-destructive measurements. Ecological Research 12, 77–88. Anten N.P.R. (2002) Evolutionarily stable leaf area production in plant populations. Journal of Theoretical Biology 217, 15–32. Anten N.P.R., Schieving F. & Werger M.J.A. (1995) Patterns of light and nitrogen distribution in relation to whole canopy carbon gain in C3 and C4 mono- and dicotyledonoous species. Oecologia 101, 504–513. Anten N.P.R., Hikosaka K. & Hirose T. (2000) Nitrogen utilization and the photosynthetic system. In Leaf Development and Canopy Growth (eds B. Marshal & J. Roberts) pp. 171–203. Sheffield Academic, Sheffield. Buckley T.N., Miller J.M. & Farquhar G.D. (2002) The mathematics of linked optimisation for nitrogen and water use in a canopy. Silva Fennica 36, 639–669. Buckley T.N., Cescatti A. & Farquhar G.D. (2013) What does optimization theory actually predict about crown profiles of photosynthetic capacity when models incorporate greater realism? Plant, Cell & Environment 36, 1547– 1563. Charles-Edwards D.A., Stutzel H., Ferraris R. & Beech D.F. (1987) An analysis of spatial variation in the nitrogen content of leaves from different horizons within a canopy. Annals of Botany 60, 421–426. 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 & Environment 8, 701–706. Dewar R.C., Tarvainen L., Parker K., Wallin G. & McMurtrie R.E. (2012) Why does leaf nitrogen decline within tree canopies less rapidly than light? An explanation from optimization subject to a lower bound on leaf mass per area. Tree Physiology 32, 520–534. Farquhar G.D. (1989) Models of integrated photosynthesis of cells and leaves. Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences 323, 357–367. Farquhar G.D., von Caemmerer S. & Berry J.A. (1980) A biochemical model of photosynthetic CO2 assimilation in leaves of C3 species. Planta 149, 78–90. Field C. (1983) Allocating leaf nitrogen for the maximization of carbon gain: leaf age as a control on the allocation program. Oecologia 56, 341–347. Franklin O. & Ågren G.I. (2002) Leaf senescence and resorption as mechanisms of maximizing photosynthetic production during canopy development at N limitation. Functional Ecology 16, 727–733. Goudriaan J. (1977) Crop Micrometeorology: A Simulation Study, Simulation Monographs, Pudoc, Wageningen. Gutschick V.P. & Wiegel F.W. (1988) Optimizing the canopy photosynthetic rate by patterns of investment in specific leaf mass. The American Naturalist 132, 67–86. Hikosaka K. (2003) A model of dynamics of leaves and nitrogen in a canopy: an integration of canopy photosynthesis, leaf life-span, and nitrogen-use efficiency. American Naturalist 162, 149–164. Hikosaka K. (2004) Interspecific difference in the photosynthesis-nitrogen relationship: patterns, physiological causes, and ecological importance. Journal of Plant Research 117, 481–494. Hikosaka K. (2010) Mechanisms underlying interspecific variation in photosynthetic capacity across wild plant species. Plant Biotechnology 27, 223– 229.

© 2014 John Wiley & Sons Ltd, Plant, Cell and Environment, 37, 2077–2085

Optimal N distribution under direct–diffuse light Hikosaka K. & Anten N.P.R. (2012) An evolutionary game of leaf dynamics and its consequences on canopy structure. Functional Ecology 26, 1024–1032. Hikosaka K. & Shigeno A. (2009) The role of Rubisco and cell walls in the interspecific variation in photosynthetic capacity. Oecologia 160, 443–451. Hikosaka K. & Terashima I. (1995) A model of the acclimation of photosynthesis in the leaves of C3 plants to sun and shade with respect to nitrogen use. Plant, Cell & Environment 18, 605–618. 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. Oecologia 97, 451–457. Hirose T. (2005) Development of the Monsi–Saeki theory on canopy structure and function. Annals of Botany 95, 483–494. Hirose T. & Werger M.J.A. (1987a) Nitrogen use efficiency in instantaneous and daily photosynthesis of leaves in the canopy of a Solidago altissima stand. Physiologia Plantarum 70, 215–222. Hirose T. & Werger M.J.A. (1987b) Maximizing daily canopy photosynthesis with respect to the leaf nitrogen allocation pattern in the canopy. Oecologia 72, 520–526. Hollinger D.Y. (1996) Optimality and nitrogen allocation in a tree canopy. Tree Physiology 16, 627–634. Kamiyama C., Oikawa S., Kubo T. & Hikosaka K. (2010) Light interception in species with different functional types coexisting in moorland plant communities. Oecologia 164, 591–599. Kato Y., Yamamoto Y., Murakami S. & Sato F. (2005) Post-translational regulation of CND41 protease activity in senescent tobacco leaves. Planta 222, 643–651. Kull O. (2002) Acclimation of photosynthesis in canopies: models and limitations. Oecologia 133, 267–279. Monsi M. & Saeki T. (1953) Über den Lichtfaktor in den Pflanzengesellschaften und seine Bedeutung für die Stoffproduktion. Japanese Journal of Botany 14, 22–52. Mooney H.A. & Gulmon S.L. (1979) Environmental and evolutionary constraints on the photosynthetic characteristics of higher plants. In Topics in Plant Population Biology (eds O.T. Solbrig, S. Jain, G.B. Johnson & P.H. Raven) pp. 316–337. Columbia University Press, New York. Mooney H.A., Field C., Gulmon S.L. & Bazzaz F.A. (1981) Photosynthetic capacities in relation to leaf position in desert versus old field annuals. Oecologia 50, 109–112. Niinemets U. (2012) Optimization of foliage photosynthetic capacity in tree canopies: towards identifying missing constraints. Tree Physiology 32, 505– 509.

2083

Oguchi R., Hikosaka K. & Hirose T. (2003) Does the photosynthetic lightacclimation need change in leaf anatomy? Plant, Cell & Environment 26, 505–512. Oguchi R., Hikosaka K. & Hirose T. (2005) Leaf anatomy as a constraint for photosynthetic acclimation: differential responses in leaf anatomy to increasing growth irradiance among three deciduous trees. Plant, Cell & Environment 28, 916–927. Peltoniemi M.S., Duursma R.A. & Medlyn B.E. (2012) Co-optimal distribution of leaf nitrogen and hydraulic conductance in plant canopies. Tree Physiology 32, 510–519. Pons T.L., Schieving F., Hirose T. & Werger M.J.A. (1989) Optimization of leaf nitrogen allocation for canopy photosynthesis in Lysimachia vulgaris. In Causes and Consequence of Variation in Growth Rate and Productivity of Higher Plants (eds H. Lambers, M.L. Cambridge, H. Konings & T.L. Pons) pp. 175–186. SPB Academic Publishing, The Hague. de Pury D.G.G. & Farquhar G.D. (1997) Simple scaling of photosynthesis from leaves to canopies without the errors of big-leaf models. Plant, Cell & Environment 20, 537–557. Schieving F. & Poorter H. (1999) Carbon gain in a multispecies canopy: the role of specific leaf area and photosynthetic nitrogen-use efficiency in the tragedy of the commons. New Phytologist 143, 201–211. Sellers P.J., Berry J.A., Collatz G.J., Field C.B. & Hall F.G. (1992) Canopy reflectance, photosynthesis and transpiration. III: a reanalysis using improved leaf models and a new canopy integration scheme. Remote Sensing of Environment 42, 187–216. Stockhoff B.A. (1994) Maximisation of daily canopy photosynthesis: effects of herbivory on optimal nitrogen distribution. Journal of Theoretical Biology 169, 209–220. Tarvainen L., Wallin G., Räntfors M. & Uddling J. (2013) Weak vertical canopy gradients of photosynthetic capacities and stomatal responses in a fertile Norway spruce stand. Oecologia 173, 1179–1189. Wright I.J., Reich P.B., Westoby M., Ackerly D.D., Baruch Z., Bongers F., . . . Villar R. (2004) The worldwide leaf economics spectrum. Nature 428, 821– 827. Wyka T.P., Oleksyn J., Zytkowiak R., Karolewski P., Jagodzinski A.M. & Reich P.B. (2012) Responses of leaf structure and photosynthetic properties to intra-canopy light gradients: a common garden test with four broadleaf deciduous angiosperm and seven evergreen conifer tree species. Oecologia 170, 11–24.

Received 24 November 2013; received in revised form 21 January 2014; accepted for publication 22 January 2014

© 2014 John Wiley & Sons Ltd, Plant, Cell and Environment, 37, 2077–2085

2084

K. Hikosaka

APPENDIX Table A1. List of variables and values in the canopy photosynthesis model used in Fig. 2a. Values are after de Pury & Farquhar (1997) Symbol

Definition

Unit

Value in Fig. 2a

A Ac ai Aj aJ aR aV Ci EaJ EaV EaR F fa fsun h Hd Idiffuse_c Idirect_c Ie If Ifc Ir Irc Isc Jmax Jmax25 Kc Kf Ko Kr K’r M N Nb O Oav P Po Rd Rd25 rg t td Tk to Vcmax Vcmax25 α β δ ΔS ϕj Γ* λs θcj θj ρcb ρcd σ

Assimilation rate RuBP-saturated A Atmospheric transmission coefficient of PAR RuBP-limited A Ratio of Jmax25 to Vcmax25 Ratio of Rd25 to Vcmax25 Ratio of Vcmax25 to photosynthetic nitrogen Intercellular CO2 partial pressure Activation energy of Jmax Activation energy of Vcmax Activation energy of Rd Cumulative leaf area index Forward scattering coefficient of PAR in atmosphere Fraction of sunlit area Hour angle of sun Deactivation energy PAR intercepted by shade leaf PAR intercepted by sunlit leaf Extraterrestrial PAR Diffuse PAR on horizontal plane Diffuse PAR intercepted per leaf area Direct PAR on horizontal plane Direct PAR intercepted per leaf area Scattered direct light intercepted per leaf area Maximal rate of electron transport Jmax at 25 °C Michaelis constant for CO2 Extinction coefficient for diffuse PAR Michaelis constant for O2 Extinction coefficient for direct PAR Extinction coefficient for direct PAR for ‘black’ leaves (no scattering) Optical air mass Leaf nitrogen content Leaf structural nitrogen content O2 partial pressure Average projection of leaves in the direction of direct PAR Air pressure Air pressure at sea level Day respiration rate Rd at 25 °C Gas constant Time of day Day of year Leaf temperature Solar noon Maximal rate of carboxylation Vcmax at 25 °C Leaf inclination angle Solar elevation angle Solar declination angle Entropy term for Jmax Initial slope of light-response curve of electron transport rate CO2 compensation point in the absence of Rd Latitude Curvature of light-response curve of assimilation rate Curvature of light-response curve of electron transport rate Canopy reflection coefficient for direct PAR Canopy reflection coefficient for diffuse PAR Leaf scattering coefficient of PAR

μmol m−2 s−1 μmol m−2 s−1 – μmol m−2 s−1 – – s−1 Pa J mol−1 J mol−1 J mol−1 m2 m−2 – – radians J mol−1 μmol m−2 s−1 μmol m−2 s−1 μmol m−2 s−1 μmol m−2 s−1 μmol m−2 s−1 μmol m−2 s−1 μmol m−2 s−1 μmol m−2 s−1 μmol m−2 s−1 μmol m−2 s−1 Pa – kPa – – – mmol m−2 mmol m−2 kPa – kPa kPa μmol m−2 s−1 μmol m−2 s−1 J mol−1 K−1 h day K h μmol m−2 s−1 μmol m−2 s−1 Radians Radians Radians J mol−1 K−1 mol mol−1 Pa Radians – – – – –

– – 0.72 – 2.1 0.0089 1.16 × 10−3 25 37 000 64 800 66 400 – 0.426 – – 220 000 – – 2413 – – – – – – – 29.16 (at 21 °C) 0.7 20.35 (at 21 °C) – – – – 25 20.5 – 98.7 101.3 – – 8.314 – 298 21 °C 12 – – 45° – −0.227 710 0.425 3.0 (at 21 °C) −35° 0.99 0.7 0.029 0.036 0.15

© 2014 John Wiley & Sons Ltd, Plant, Cell and Environment, 37, 2077–2085

Optimal N distribution under direct–diffuse light

2085

Table A2. Equations in the model. See Table A1 for symbols Solar geometry sin β = sin λs sin δ + cosλs cos δ cos h δ = −23.4πcos[2π(td + 10)/365]/180 h = π(t − t0)/12 Radiation above the canopy I r = ai m I e sin β P m= Po sin β I f = fa (1 − ai m ) I e sin β Light interception by leaves fsun = e − Kr F I rc = (1 − σ ) K r′I r I fc = (1 − ρcd ) K f I f e − Kf F I sc = I r [(1 − ρcb ) K r′ e − K′r F − (1 − σ ) K r e − Kr F ] Idirect_c = Irc + Ifc + Isc Idiffuse_c = Ifc + Isc O K r′ = av sin β Oav = sinβ cosα β > α 2 tan β Oav = ⎡sin β cos α arcsin + sin 2 α − sin 2 β ⎤ α > β ⎦⎥ tan α π ⎣⎢

( )

K r = K r′ 1 − σ

(A1) (A2) (A3) (A4) (A5) (A6) (A7) (A8) (A9) (A10) (A11) (A12) (A13) (A14a) (A14b) (A15)

Gas exchange

Ac + Aj − ( Ac + Aj )2 − 4 Ac Ajθ cj 2θ cj Vc max (Ci − Γ *) Ac = − Rd C i + K c (1 + O Ko ) A=

Aj = J=

J (Ci − Γ *) − Rd ( 4Ci + 8Γ *)

φ j I c + J max − (φ j I c + J max )2 − 4φ j I cθ j J max 2θ j

⎛ E (T − 298) ⎞ Vc max = Vc max 25 exp ⎜ aV k ⎝ rgTk 298 ⎠⎟

J max

⎛ E (T − 298) ⎞ ⎡ ⎛ 298 ΔS − H d ⎞ ⎤ J 25 exp ⎜ aJ k 1 + exp ⎜ ⎟⎠ ⎥ ⎝ rgTk 298 ⎟⎠ ⎢⎣ ⎝ 298rg ⎦ = ⎛ T ΔS − H d ⎞ 1 + exp ⎜ k ⎟⎠ ⎝ rgTk

(A16) (A17) (A18) (A19) (A20)

(A21)

⎛ E (T − 298) ⎞ Rd = Rd 25 exp ⎜ aR k ⎝ rgTk 298 ⎟⎠

(A22)

Vcmax25 = aV(N − Nb) Jmax 25 = aJVc max 25 Rd25 = aRVc max 25

(A23) (A24) (A25)

© 2014 John Wiley & Sons Ltd, Plant, Cell and Environment, 37, 2077–2085