An evolutionary game of leaf dynamics and its consequences for canopy structure

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1 Functional Ecology 1,, 1 13 doi: /j x An evolutionary game of leaf dynamics and its consequences for canopy structure Kouki Hikosaka*,1, and Niels P. R. Anten,3 1 Graduate School of Life Sciences, Tohoku University, Aoba, Sendai, Japan; CREST, JST, Chiyoda, Tokyo, 1-7 Japan; and 3 Ecology Biodiversity, Institute of Environmental Biology, Utrecht University, P.O. Box 8.8, 358TB, Utrecht, The Netherlands Summary 1. Canopy photosynthesis models combined with optimization theory have been an important tool to understand environmental responses and interspecific variations in vegetation structure and functioning, but their predictions are often quantitatively incorrect. Although evolutionary game theory and the dynamic modelling of leaf turnover have been suggested useful to solve this problem, there is no model that combines these features.. Here, we present such a model of leaf area dynamics that incorporates game theory. 3. Leaf area index (LAI; leaf area per unit ground area) was predicted to increase with an increasing degree of interaction between genetically distinct neighbour plants in light interception. This implies that stands of clonal plants that consist of genetically identical daughter ramets have different LAI from other plants. LAI was also sensitive to the assumed vertical pattern of leaf shedding: LAI was predicted to increase with the degree to which leaves were assumed to be shed from higher positions in the canopy. Our model provides more realistic predictions of LAI than previous static optimization, dynamic optimization or static game theoretical models.. We suggest that both leaf dynamics and game theoretical considerations of plant competition are indispensable to scale from individual leaf traits to the structure and functioning of vegetation stands, especially in herbaceous species. Key-words: canopy photosynthesis, evolutionarily stable strategy, game theory, leaf area index, leaf turnover, light competition, model, nitrogen use, optimization Introduction The development of a theoretical framework for physicochemical and physiological functioning of plant vegetation has been a fundamental challenge in biology, ecology, agriculture and meteorology for almost a century (Boysen Jensen 193; Monsi & Saeki 1953; de Wit 195; Hirose 5). Its importance is increasing especially in global sciences because vegetation functioning is not only sensitive to climate change but also feedbacks to global climate (IPCC 7). Current models of canopy photosynthesis are able to predict carbon uptake of vegetation if correct values of canopy structure and leaf physiology are given (e.g. Baldocchi & Harley 1995; Wilson, Baldocchi & Hanson 1; Ito et al. ). However, both canopy structure and leaf physiology greatly vary among stands depending on climate, growth environment and species composition, *Correspondence author. hikosaka@m.tohoku.ac.jp Present address. Center for Crop System Analysis Wageningen University PO Box 3 7 AK Wageningen The Netherlands. and such data are not available for most vegetation. Our ability to predict plant responses to climate change is thus still limited (Dewar et al. 9). Optimality theory has been a powerful tool to predict environmental responses of canopy structure and leaf physiology (Hirose 5; Dewar et al. 9; Anten & During 11). Optimality theory is based on the concept that some performance measure is maximized with respect to one or more plant traits and one or more limiting factors. For example, canopy photosynthesis per unit ground area may be maximized if the canopy has a leaf area index (LAI, amount of leaf area per unit ground area), whereby the lowest leaves receive the light intensity of the compensation point for daily carbon gain (Monsi & Saeki 1953; Saeki 19; Ackerly 1999; Reich et al. 9). This explains why a canopy with vertical leaves, which allow more light penetration into lower canopy layers, has a larger LAI than that with horizontal leaves (Saeki 19). Nitrogen limitation may impose an additional constraint on leaf area growth, as a larger LAI at fixed canopy N will lead to 1 The Authors. Functional Ecology 1 British Ecological Society

2 An evolutionary game of leaf dynamics 15 a dilution of leaf nitrogen content per area. This reduction in leaf nitrogen per area in turn results in lower leaf photosynthetic capacities, since photosynthetic capacity and leaf nitrogen per area are tightly correlated (Field & Mooney 198; Evans 1989; Hikosaka, 1). An optimal LAI can be derived at which whole-stand canopy photosynthesis at a given canopy nitrogen is maximized (Anten et al. 1995b). This optimal LAI increases with increasing canopy nitrogen, which well explains the strong positive correlations that exist between LAI and nitrogen availability (e.g. Prasertsak & Fukai 1997). Recent studies have used this optimization approach to predict canopy traits (e.g. leaf nitrogen content, stomatal conductance or leaf photosynthetic capacities), LAI and vegetation carbon gain under climate change scenarios (e.g. Franklin 7; Ma kela, Valentine & Helmisaari 8; McMurtrie et al. 8). However, predictions by optimality models are not necessarily correct in a quantitative sense (Gersani et al. 1; Anten & During 11). For example, optimal LAI values calculated based on trait values from actual plant canopies were always smaller than the actual ones (Anten ). This discrepancy has been ascribed mainly to two assumptions in the optimality models. First, plant traits are assumed to be optimal when they maximize whole-canopy daily photosynthesis. This implicitly assumes that the performance of a plant is independent of the characteristics of its neighbours (Parker & Maynard-Smith 199). This does not hold true in most vegetation stands where plants compete for light and soil resources. In such cases, evolutionary game theory (EGT), in which individual plant-based maximization is considered relative to the characteristics of neighbours, is more appropriate approach (Givnish 198; Falster & Westoby 3). Hikosaka & Hirose (1997) combined EGT with a canopy photosynthesis model and showed that a leaf angle that maximizes canopy photosynthesis is not necessarily evolutionarily stable especially when the light competition between neighbours is strong. It has similarly been shown that evolutionarily stable LAI (ES-LAI) is greater than the optimal LAI at a given canopy nitrogen content (Schieving & Poorter 1999; Anten & Hirose 1; Anten, 5). Predicted ES-LAI values have been found to be much closer to actual measured values than optimal LAIs (Anten ; Lloyd et al. 1). These results suggest that natural selection may lead to plant communities with non-optimal characteristics in terms of maximized photosynthesis at the community level. The second problem with classic optimization models is that the traits underlying whole-plant photosynthetic nitrogen-use efficiency, that is, nitrogen distribution, LAI and other traits, are treated as being static. However, leaf canopies are dynamic: new leaves are produced using photosynthates, nutrients that are absorbed by roots and resorbed from older leaves are allocated, and old leaves are shed with some fraction of allocated nutrients (Kikuzawa 3; Hikosaka 5; Oikawa, Hikosaka & Hirose 5; Hikosaka, Kawauchi & Kurosawa 1). LAI and canopy nitrogen content thus depend on various factors such as nutrient uptake rate, leaf longevity and nutrient resorption efficiency. Franklin & A gren () indicated that nitrogen resorption efficiency affects optimal LAI: since plants lose nitrogen with dead leaves, reducing LAI is not necessarily advantageous even when the LAI is greater than the LAI that maximizes canopy photosynthesis. They showed that optimal LAI increases with decreasing resorption efficiency. Hikosaka (3) developed a dynamic model of leaf canopy. In the model, leaf area in the canopy increases in time with the production of new leaves, which is proportional to the rate of photosynthesis in the canopy. At each time step, uptake of nitrogen from the soil increases the amount of nitrogen in the canopy. The optimal LAI that maximizes canopy photosynthesis is then calculated. If leaf area is in excess, old leaves are eliminated, and part of nitrogen is lost with dead leaves. Consequently a new canopy having an optimal LAI with a given amount of nitrogen is obtained. Repeating this process simulates the temporal dynamics of leaves in a growing canopy. Recently, several models have been developed incorporating not only leaf dynamics but also processes in non-photosynthetic tissues (Franklin 7; Ma kela, Valentine & Helmisaari 8; Franklin et al. 9). Although the two problems, that is, competition and canopy dynamics, have been overcome through application of the game theory and of the dynamic optimization, respectively, these two approaches have not been combined together; that is, no one has applied EGT to analyse leaf turnover (Hikosaka 5; Anten & During 11). Such an analysis would provide new insights into the way that natural selection might have acted on leaf turnover as a function of the degree of interaction between neighbouring plants. Here we develop for the first time a game theoretical model of leaf dynamics, and thus combine two key features of plant canopies competition and leaf turnover that have not previously been combined in any vegetation model. We modify the optimality model of leaf dynamics of Hikosaka (3) and incorporate EGT into the model. We show that the vertical pattern of leaf fall strongly affects the evolutionarily stable leaf area dynamics. We also compare the real and the modelled ES-LAI of various herbaceous stands using published trait values. The model INTERACTION BETWEEN NEIGHBOURS We assume that plants compete for light with their neighbours. Each plant occupies a certain ground area and develops leaf area within that ground area. There is no overlap of foliage between neighbours. We can thus define LAI at an individual plant level (note that LAI values are the same between individual- and stand-level if the individual-level LAI is identical among individuals). Plants are considered to influence each other s light climate because

3 1 K. Hikosaka & N. P. R. Anten light comes not only from right above but also from various other directions. We thus assume that at any point in the canopy of a target plant, a fraction (g) of the radiation will have passed through canopies of neighbouring plants and a fraction (1 g) through the canopy of the target plant itself (Hikosaka et al. 1). Thus, g indicates the degree of interaction with neighbours (i.e. effect of non-self relative to total shading). The photon flux density on a horizontal surface at a layer j around a leaf of the target (I Tj ) is then described by: I Tj ¼ð1 gþ I expð K T F Tj Þþg I expð K N F NJ Þ eqn1 where the subscripts T and N indicate the target individual and its neighbours, respectively, I is the I at the top of the canopy and F j is the cumulative LAI above layer j over the fraction of ground area occupied by the plants. CANOPY PHOTOSYNTHESIS AND LEAF DYNAMICS Photosynthesis of an individual is calculated based on the canopy photosynthesis model of Anten, Schieving & Werger (1995a). Here we explain the model briefly (see Data S1, Supporting information). Light dependence of the photosynthetic rate is formulated with a non-rectangular hyperbola. Both the light-saturated rate of photosynthesis and dark respiration rate are linearly related to the nitrogen content per unit area. We divided the foliage into 1 horizontal layers and the photosynthetic rate of an individual is obtained as the sum of photosynthesis in each layer. Nitrogen is always reallocated optimally among layers to maximize photosynthesis. Dynamics of leaf area is based on the model of Hikosaka (3), with the addition of a game theoretical sensitivity analysis. Here we describe the model briefly (see Data S1, Supporting information for detail), except for the game theoretical part that is described in detail. We initialize the simulation by setting the LAI and canopy N of an individual plant to given starting values. The plant allocates leaf nitrogen to each layer so that the canopy photosynthesis is maximized (Anten, Schieving & Werger 1995a). The model then runs assuming time steps of 1 days. During this time step, the plant photosynthesizes and allocates a part of the newly obtained assimilates for construction of new leaves. We assumed this part that is allocated to leaves as % of total assimilates, which is regarded as the maximum after subtracting allocation to other organs. New leaves are formed with a given leaf mass per area after subtracting construction costs. The plant simultaneously takes up nitrogen at a given rate that is assumed to be constant during the simulation. At the end of each time step, the LAI will have reached a new value (termed as N-LAI). We then apply a game theoretical sensitivity analysis (see sensitivity analysis below) to determine the extent to which the stand can be invaded by a mutant individual that sheds some of its leaves. At each time step, we thus calculate the ES-LAI. If the value of N-LAI is greater than the ES-LAI, excessive leaf area is eliminated after part of the nitrogen is resorbed. The foliage with ES-LAI photosynthesizes and produces new leaves. Repeating this process provides growth of LAI. GAME THEORETICAL SENSITIVITY ANALYSIS Evolutionarily stable LAI at each time step is obtained as follows. The target individual has the same trait values as those of its neighbours. Both the target and neighbours produce new leaves and then have the same amount of leaf area (N-LAI). (i) We calculate the photosynthesis of the target, which will evidently be the same as that of neighbours (P N ). (ii) We then simulate leaf shedding by slightly reducing the LAI of the target plant (1%). This reduction in LAI thus leads to some loss of N (n d in the model), as not all N can be remobilized from senescing leaves (Aerts & Chapin ), while the retranslocated N is assumed to be optimally reallocated among the remaining leaf layers (as in Anten, Schieving & Werger 1995a), resulting in N contents and associated photosynthetic capacities of those leaves. We then calculate whole-plant photosynthesis in the new situation (P T ). If P N is higher than P T, the N-LAI is regarded as evolutionarily stable. (iii) If not, we reduce LAI of the neighbours to the same level of the target and calculate photosynthesis of the target (P N ). (iv) We further reduce LAI of the target only and obtain target s photosynthesis (P T ). The processes three and four are repeated until we obtain P N > P T. The LAI of an individual that realizes the P N at P N > P T is regarded as ES-LAI. We did not increase LAI because plants produced maximal LAI that allowed by their assimilates. In the next step, both target and neighbours have again the same LAI as a result of the game. Such vegetation stands are considered to be resistant to invasion throughout the growing season. ASSUMPTION OF SPATIAL PATTERN OF LEAF SHEDDING As mentioned earlier, plants shed excessive leaf area. In dense vegetation, light absorption of a given plant depends strongly on the vertical distribution of leaf area relative to that of its neighbours. It is therefore important to consider the vertical pattern of leaf senescence; a leaf dropped from an upper layer in the canopy may have larger positive effect on neighbours light acquisition than dropping a leaf from a low layer. That is, in terms of light competition it is more efficient to drop leaves only from the lowest than to drop them also from higher in the canopy. Here we consider three patterns (Fig. 1). In Case 1, leaves are dropped from all layers equally. This spatial pattern is close to the static EGT model of Anten (). In Case, senescent leaves are dropped strictly from the bottom of the canopy. Case 3 is intermediate between the two: relatively more leaves are dropped from the lower parts of the canopy than from higher up. It is hereby assumed that leaf area

4 An evolutionary game of leaf dynamics 17 Canopy depth Leaf area in a layer Living leaves Senescing leaves Living leaves Senescing leaves Living leaves Case 1 Case Case 3 loss increases linearly from the top towards the bottom of the plant. COMPARISON OF PREDICTED AND REAL CANOPY TRAITS Senescing leaves Fig. 1. The three vertical pattern of leaf shedding used in the simulations (Cases 1 3). We collected data of leaf photosynthesis and canopy traits of 1 stands of 1 species from published articles (Hirose & Werger 1987; Schieving et al. 199; Anten et al. 1995b; Anten, Werger & Medina 1998; Anten ; Borjigidai, Hikosaka & Hirose 9; see Table S1 (Supporting information), including three stands grown at elevated CO, and simulated canopy growth with these data. Four stands are of clonal species (indicated by çlonal in Table S1, Supporting information) and three of them tend to form dense mono-clonal patches. We assumed lmol m s 1 for noon irradiance and calculated the daily pattern of light intensity above the canopy from this value following Hirose & Werger (1987). Simulation started from a small canopy with LAI = 5 and canopy nitrogen = 5 mmol m.we found that LAI in the steady state was independent of the starting conditions. Results Figure shows simulation results of leaf area increment as a function of time using data of Glycine max (Anten, Schieving & Werger 1995a). When the degree of interaction (g) is zero (no interaction with neighbours), LAI exponentially increases at the beginning and the increment rate gradually decreases because of leaf shedding. Finally, LAI reaches a steady state, where leaf production rate is equal to leaf loss rate. These results are almost independent of the assumed vertical pattern of leaf senescence (Cases 1 3) and are quantitatively very similar to those obtained in the dynamic optimization model (Hikosaka 3). When g is larger than zero (i.e. neighbour plants affect each other s light interception), simulation patterns differ strongly between the three cases. In Case 1, LAI greatly increases with increasing g (Fig. a). When g is very high, LAI achieves and then rapidly decreases to zero (data not shown), because canopy photosynthesis becomes negative when LAI is very high (our model is not designed to provide realistic response of canopy traits when carbon gain is negative). In Case, LAI growth is almost independent of g and thus the results are very similar to those of the dynamic optimization model (Fig. b). This is because the alteration in leaf area at bottom layers hardly affects light interception of neighbours. In Case 3, LAI increases with increasing g but to a lesser extent than in Case 1 (Fig. c). Here we compare results of different models: static- vs. dynamic-plant, and simple optimality vs. game theoretical. Figure 3 shows the relationship between LAI and canopy nitrogen for an g of 5 at 3 days (nearly steady state in most situations). As mentioned earlier, results for Case are almost identical to those of the dynamic optimization model (Hikosaka 3) where no light competition among ES-LAI (m m ) (a) Case Interaction = Interaction = Day (b) Case (c) Case Interaction = Fig.. Simulation of growth of evolutionarily stable leaf area (ES-LAI). Noon irradiance and nitrogen uptake rate are lmol m s 1 and 5 mmol m day 1, respectively. Values from a Glycine max canopy (Anten, Schieving & Werger 1995a) are used for leaf and canopy traits. a, b and c shows Cases 1, and 3, respectively. Note that the scale of ES-LAI changes above 8 in (a). There is no difference among lines in Case.

5 18 K. Hikosaka & N. P. R. Anten LAI (m m ) 1 8 Case 1 Case Case 3 8 individuals is assumed. Results of static EGT models (S1, S and S3) are also calculated with an assumption that the nitrogen is not lost by decreasing LAI. The model S1, S and S3 assume the same leaf shedding pattern as in Cases 1, and 3, respectively. S1 is similar to the static EGT model of Anten (), and S is almost identical to the static optimization model (Anten et al. 1995b). LAI shows a linear (Case 1), convex (i.e. saturating with decreasing slope Cases and 3 and S) or concave (i.e. with increasing slope, S1 and S3) relationship with canopy nitrogen. The convex saturating relationship is consistent with previous experimental results, that is, mean nitrogen content per unit leaf area (canopy N per LAI) increases with increasing nitrogen availability (e.g. Anten et al. 1995b). This suggests that the general pattern of the relationship between LAI and nutrient availability is better predicted by dynamic EGT models (Case 3) than by static EGT models (S1 and S3). When compared at the same canopy nitrogen, LAI is lowest in the static optimization model (S). LAI in dynamic models is largest for Case 1, followed by Case 3, and Case. LAI in static EGT models (S1 and S3) is higher than that in the static optimization model especially at lower canopy nitrogen. LAI in Case 1 is higher than that in S1 across all canopy nitrogen values. LAI in Case 3 S Canopy nitrogen (mmol m ) Fig. 3. Leaf area index as a function of the canopy nitrogen per unit ground area. g is 5 in every case. Open symbols denote calculated results at 3 days under nitrogen uptake rates of 1 mmol m day 1, and triangle, square and diamond denote Cases 1, and 3, respectively (two data points of Case 1 are outside the frame). Continuous lines are the regression using linear (Case 1) or quadratic (Cases and 3) functions. Dotted lines are the regression for static evolutionary game theory models where no nitrogen loss at leaf shedding is assumed (symbols are not shown). S1, S and S3 assume the same leaf shedding pattern as Cases 1, and 3, respectively. Closed circle denotes data obtained in a real stand of Glycine max (Anten, Schieving & Werger 1995a). S3 S1 is higher than that in S3 at canopy nitrogen values lower than 5 mmol m while the opposite holds at the higher canopy nitrogen values. The actual LAI values obtained from real stands are closer to the predicted values based on Case 3 than on those based on the others. Leaf area index values under various nitrogen uptake rates were calculated using leaf traits obtained from 1 herbaceous stands. We obtained a regression line between LAI and canopy nitrogen at the steady state for each species (see Fig. 3 for G. max) and calculated LAI at the canopy nitrogen content observed in the real stand. Figure shows the predicted LAI values calculated based on the Cases 1 3, as a function of the 1 measured LAI values. In all three cases, predicted LAI was strongly correlated with real LAI (r > 5) but the relationship was quantitatively different among leaf shedding patterns. When Case 1 was used, the predicted LAI was much greater than the real LAI (Fig. a). Case predicted LAIs that were slightly smaller than real values (Fig. b). The regression of predicted on real LAI was very similar to the 1:1 relationship in Case 3 (Fig. c). However, in the case of the three clonal grass species, which formed dense mono-clonal patches, predicted LAI values were closer to real ones in Case than in Cases 1 and 3 (open symbols in Fig. ). In the simulation, an ESS is calculated every 1 days. This time step may correspond to plastochron length, which varies from to 1 days in herbaceous plants dominating in open habitat (Hofstra, Hesketh & Myhre 1977; Oikawa, Hikosaka & Hirose 5). We applied various additional time steps, however, to test whether the simulation results are robust (Fig. S1, Supporting information). In Cases 1 and, LAI slightly increases with increasing Predicted LAI (m m ) (a) Case 1 r = (b) Real LAI (m m ) Case r = 5 (c) Case 3 r = Fig.. Predicted and real leaf area index using data obtained from 1 stands of 1 species (see Table S1, Supporting information for species list). a, b and c shows Cases 1, and 3, respectively. Three clonal species (H. amplexiculis, Leersia hexandra, Paspalum fasciculatum) are given as open symbols. g is 5 in every calculation. Solid and broken lines are the regression for all data points and the 1 : 1 relationship, respectively.

6 An evolutionary game of leaf dynamics 19 time step length, but the relationship between LAI and canopy nitrogen is not affected. In Case 3, the increase in time step slightly decreases LAI at a given canopy nitrogen, but the difference was smaller than 1%. These results indicate that our findings are robust and do not depend on the chosen time step. Discussion The model presented in this study is the first to combine canopy photosynthesis, leaf dynamics and EGT together. Our results clearly show that the predicted LAI is influenced strongly by the assumptions regarding the leaf area dynamics and degree of light competition among neighbouring plants. Both competition and leaf turnover are dominant processes in vegetation stands, and we show that their inclusion in canopy models is needed to make realistic predictions of LAI. The LAI predicted by the static optimization model have been shown to be consistently lower than real LAIs (Anten et al. 1995b, ; Anten ; Hirose et al. 1997; S in Fig. 3). Franklin & A gren () suggested that incorporating dynamics of leaf and nitrogen improves the prediction of LAI, but their model did not consider the temporal dynamics of N uptake and leaf turnover. We incorporated leaf dynamics using multiple time steps into the optimization model and, compared to the static optimization model, obtained a better match with observed LAIs (Case vs. S in Fig. 3). Even so, these predictions were still lower than the actual LAI in most cases (Fig. b). On the basis of the view that optimal LAIs may be evolutionarily unstable as they can be invaded by mutants producing larger leaf areas, Anten () proposed that static EGT model should provide better predictions of LAI than simple optimization models. However, we show that the response of LAI to nitrogen availability is unrealistic in the static EGT model; LAI increases more than proportionately with canopy nitrogen (S1 and S3 in Fig. 3). On the other hand, our Case 3 model successfully predicts realistic responses of LAI to nitrogen availability (Fig. 3) and quantitatively valid values of LAI (Fig. ). We thus indicate that both leaf dynamics and competition are important factors for determining LAI in real plants. Predicted LAI values were higher when plant competition was taken into account as in EGT models than when it was disregarded as in the simple optimization model (Figs,3 and ). Leaf shedding may have a positive effect on photosynthesis because it results in concentrating nitrogen in the remaining leaves thus enhancing their photosynthetic capacity, but also has a negative effect as it reduces area for light capture. There exists an optimum where these two effects are balanced. However, when plants compete for light, a reduction in leaf area in one plant not only reduces its own light acquisition but also enhances light availability to neighbours. A delay of leaf shedding may thus be advantageous, and by consequence, the ES-LAI (i.e. a population with this LAI cannot be invaded by a mutant with other leaf dynamics) is higher than the optimal LAI (Anten, 5). Our results show that the vertical pattern of leaf shedding strongly affects ES-LAI. Previous static EGT models assumed that leaf area is similarly altered in every vertical layer (Schieving & Poorter 1999; Anten & Hirose 1; Anten ; Case 1 in Fig. 1). Anten () showed that the static EGT model provides more realistic values of LAI than those of optimal models (S1 in Fig. 3). In the present study, however, the Case 1 model, which used the same shedding pattern as Anten (), provides unrealistically high values of LAI (Figs 3 and ). As the inclusion of leaf dynamics and that of competition may both lead to an increase in predicted LAI, a combination of these aspects results in very high LAI values. On the other hand, the Case model, in which leaves are shed only from the bottom, provides lower LAI values than that of the Case 1 model. Its predicted LAI values are almost identical to those by dynamic optimization model (Hikosaka 3). The Case 3 model, in which leaves are shed from all layers but more from lower than from higher layers, predicts ES-LAI values that are intermediate between those of Cases 1 and. Moreover, the predictions assuming Case 3 converge most closely to the real measured values of LAI (Figs 3 and ). The considerable differences between the predictions from Cases 1 to 3 probably reflect differences in the assumed degree of leaf area loss in the upper layers. Because light availability is greater at upper layers, small change in upper layers has a large influence on light availability of neighbours and thus ES-LAI should be high (Case 1). If the leaf area reduction occurs only at lower layers, benefit of the delaying senescence is limited and ES-LAI should be close to the optimal LAI (Cases and 3). Considerable differences in the predicted LAI among leaf shedding patterns imply that ES-LAI may differ between plants with different growth forms. For example, erect herbaceous species develop leaves mainly from meristems located towards the top of the plant and shed them mainly from the bottom. In some grass species that maintain their meristem near the ground surface, on the other hand, shedding of a long leaf often results in loss of leaf area from several canopy layers. In our data set, Carex acutiformis develop their leaves from the ground (Hirose, Werger & van Rheenen 1989). There was no obvious difference between C. acutiformis and other species in the LAI nitrogen relationship (data not shown), which is not consistent with the hypothesis. However, our data set may not be sufficient to test this hypothesis because of the limited number of species for each growth form. In addition, in erect plants, leaves attached to lateral branches often remain even when leaves attached to main stem are shed (K. Hikosaka, personal observation); Case 3 may thus be applicable to erect plants. Further study on the spatial pattern of leaf senescence in combination with our modelling approach may be necessary for a better understanding of its ecological significance in leaf dynamics. Our results show that the predicted LAI is sensitive to the degree of interaction with neighbours, g: the predicted LAI

7 13 K. Hikosaka & N. P. R. Anten increased with increasing g (Fig. ). As g may be greater when plant density is higher, our result is consistent with the fact that plants increase their leaf area by increasing specific leaf area when plant density is high (Nishimura et al. 1). Parameter g may also be influenced by other factors such as vertical length of foliage cluster, leaf size, petiole length and so on. For example, g is probably low in trees that tend to have relatively broad crowns, but relatively high if the plant has vertically long crown (e.g. erect herbaceous plants). Some climbing plants may have particularly high g values. g has not been estimated in real plant stands except for two stands of an annual, Xanthium canadense, which had relatively high values (7 and 85 for low- and high-density stands, respectively; Hikosaka et al. 1). However, X. canadense may have exceptionally high g values even for herbaceous plants. When it was grown at a density where the distance between plants was 15 cm, mean petiole length of fully expanded leaves was 1 cm, that is, leaves were placed in spaces occupied by neighbours (Hikosaka et al. 1). Such a horizontal overlap of foliage cluster is not observed in stands of other herbaceous species such as Chenopodium album (K. Hikosaka, personal observation), which may have lower values of g. Evaluation of the degree of interaction in various plant stands would be necessary. Stands of clonal plants, that is, plants that propagate vegetatively whereby mother ramets produce genetically identical daughter ramets along horizontal spacers (e.g. stolons and rhizomes), provide an interesting case for game theoretical analyses of plant interactions. This is because the degree of non-self/self-interaction depends on the clonal architecture, and neighbour-dependent responses such as analysed here may have evolved differently among species depending on their clonal structure (Semchenko et al. 7). For example, in stands of plants exhibiting the socalled phalanx growth form, which involves the production of short spacers and associated clustering of genetically identical ramets, the degree of self-shading may predominate, and thus g would be very low. Such plants would be expected to exhibit more optimal leaf strategies resulting maximum stand-level performance (Hikosaka & Hirose 1997; Anten & During 11). In our data set, we had four stands of clonal species (Leersia hexandra, Hymenachne amplexicaulis, Paspalum fasciculatum and Solidago altissima). The first three tend to form large mono-genotypic patches with very high density (>1 plants m ; N.P.R. Anten, personal observation). Interestingly, the real LAIs of the stands of these three species were considerably lower than the values that the EGT model predicted under the assumption that g = 5 (Fig. ). Lower g values, thus assuming more self-shading, yielded more accurate predictions (data not shown). Their real LAI is closer to the predicted LAI in Case than that in Case 3, suggesting that they had a more optimal LAI. This result is consistent with our expectation that clonal plants may have optimal strategies rather than evolutionarily stable ones. In the present model, we assume that at every time step, the plants realize ES-LAI. This implicitly assumes that plants that do not realize this trait value would be eliminated from the stand. We also assumed that in each time step, plants produce maximal leaf area at the top of the canopy, which is allowed by their assimilates; otherwise, plants may be overshaded by neighbours that produced greater leaf area. These assumptions are based on the fact that competition for light tends to be asymmetric. That is, if, at any point during its vegetative growth, a plant fails to develop sufficient leaves at the top of the canopy, it will be shaded by the neighbours, resulting in a reduced growth rate, and the growth difference is magnified over time (Nagashima, Terashima & Katoh 1995; Weiner 199; Nagashima & Hikosaka 11). Furthermore, such subordinate plants have higher mortality and smaller seed production than dominant plants (Matsumoto et al. 8). It should be noted that many shade tolerant species can survive and reproduce in sub-canopy and understorey layers. Our model is therefore most applicable to canopy species. Conclusion In this study, canopy photosynthesis, leaf area dynamics and EGT are for the first time combined together. As such, two dominant processes in vegetation stands competition and leaf turnover are quantitatively integrated into a model calculation. We focused on nitrogen and light limitation but the approach can be extended to include water limitation (see McMurtrie et al. 8). Our model provides better predictions of LAI than previous static EGT or dynamic-plant optimization models. Specifically it shows that ES-LAI and associated stable canopy photosynthesis is sensitive to several traits such as leaf shedding patterns and the degree of interaction with neighbours in vegetation stands, although further studies are necessary because values of these two traits are uncertain for most stands. We believe that our integrated approach provides a more mechanistic basis to analyse how plant competition and its associated selection on leaf dynamics and leaf area growth scale to the structure and functioning of vegetation stands. In so doing, we believe that it may also allow a more mechanistic scaling of plant acclimation to environmental change to vegetation structure and functioning, which is becoming an increasingly important issue in climate change studies (Corlett 11). Acknowledgements We thank Hendrik Poorter for valuable comments to the early draft. The study was partly supported by KAKENHI (No. 771 and 1119) and Global COE program (J3). References Ackerly, D.D. (1999) Self-shading, carbon gain and leaf dynamics: a test of alternative optimality models. Oecologia, 119, Aerts, R. & Chapin, F.S. III () The mineral nutrition of wild plants revisited: a re-evaluation of processes and patterns. Advances in Ecological Research, 3, 1 7.

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9 13 K. Hikosaka & N. P. R. Anten 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, 13, Schieving, F., Pons, T.L., Werger, M.J.A. & Hirose, T. (199) Vertical distribution of nitrogen in photosynthetic activity at different plant densities in Carex acutiformis. Plant and Soil, 1, Semchenko, M., John, E.A. & Hutchings, M. J. (7) Effects of physical connection and genetic identity of neighbouring ramets on root-placement patterns in two clonal species. New Phytologist, 17, 5. Weiner, J. (199) Asymmetric competition in plant populations. Trends in Ecolgy and Evolution, 5, 3 3. Wilson, K.B., Baldocchi, D.D. & Hanson, P.J. (1) Leaf age affects the seasonal pattern of photosynthetic capacity and net ecosystem exchange of carbon in a deciduous forest. Plant, Cell and Environment,, de Wit, C.T. (195) Photosynthesis of Leaf Canopies. Pudoc, Wageningen. Received 17 April 1; accepted 5 July 1 Handling Editor: Ken Thompson Supporting Information Additional Supporting Information may be found in the online version of this article: Data S1 Detailed explanation of the model. Fig. S1. Effect of time step of the calculation on the leaf area index (LAI) as a function of canopy nitrogen per ground area. Table S1. List of species used in simulation. As a service to our authors and readers, this journal provides supporting information supplied by the authors. Such materials may be re-organized for online delivery, but are not copy-edited or typeset. Technical support issues arising from supporting information (other than missing files) should be addressed to the authors.