Optimal nitrogen allocation controls tree responses to elevated CO2


  • Oskar Franklin

    1. IIASA, Institute for Applied Systems Analysis, 2361 Laxenburg, Austria;
    2. School of Biological, Earth and Environmental Sciences, University of New South Wales, Sydney, NSW 2052, Australia
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Author for correspondence: Oskar Franklin Tel: +432236807251 Fax: +432236807599 E-mail: franklin@iiasa.ac.at


  • • Despite the abundance of experimental data, understanding of forest responses to elevated CO2 is limited. Here I show that a key to previously unexplained production and leaf area responses lies in the interplay between whole-plant nitrogen (N) allocation and leaf photosynthesis.
  • • A simple tree growth model, controlled by net growth maximization through optimization of leaf area index (LAI) and plant N, is used to analyse CO2 responses in both young, expanding and closed, steady-state canopies. The responses are sensitive to only two independent parameters, the photosynthetic capacity per leaf N (a) and the fine-root N : leaf N ratio.
  • • The model explains observed CO2 responses of photosynthesis, production and LAI in four forest free air CO2 enrichment (FACE) experiments. Insensitivity of LAI except at low LAI, increase in light-use efficiency, and photosynthetic down-regulation (as a result of reduced leaf N per area) at elevated CO2 are all explained through the combined effects on a and leaf quantum efficiency.
  • • The model bridges the gap between the understanding of leaf-level and plant-level responses and provides a transparent framework for interpreting and linking structural (LAI) and functional (net primary production (NPP) : gross primary production (GPP) ratio, light-use efficiency, photosynthetic down-regulation) responses to elevated CO2.


Modelling of forest responses to elevated CO2 and environmental factors is a cornerstone of climate change research. In many models, light-use efficiency (ɛGPP) in combination with estimates of light absorption, often obtained from remote sensing methods, is used to estimate gross primary production (GPP). A maximum potential ɛGPP is reduced in response to environmental constraints and combined with a net primary production (NPP) : GPP ratio or a respiration function to obtain NPP. However, the assumptions and values used for these factors vary substantially. For the same forest type, maximum ɛGPP varies threefold between models (Xiao et al., 2005), while others argue that ɛGPP is conservative (Goetz & Prince, 1999). The common assumption that the NPP : GPP ratio is invariable (Waring et al., 1998; Medlyn & Dewar, 1999) has also been challenged (Goetz & Prince, 1999). In summary, a general consensus on the appropriate assumptions for forest NPP modelling is lacking, which also carries over to the modelling of elevated CO2 effects.

Experimental evidence of the effects of elevated CO2 from free air CO2 enrichment (FACE) and other investigations are accumulating. When all studies are compared, the range of observed responses in productivity and biomass is large. This large range is mostly the result of differences in the age of the studied stands; that is, if it is a young forest still increasing resource acquisition or if it has reached steady state in terms of fine roots and LAI (Korner, 2006). For closed-canopy forests, NPP responses are conservative across species and sites (on average 23% higher at 550 than at 376 ppm CO2) (Norby et al., 2005). Nutrient additions strongly enhance the growth response to elevated CO2 (Oren et al., 2001; Reich et al., 2006a). Light-use efficiency (ɛNPP) is increased while leaf area index (LAI) is usually little affected (Norby et al., 2003), although at low LAI the CO2 effect on LAI can be as large or larger than the effect on ɛNPP (Norby et al., 2005). For the allocation to wood relative to fast turnover tissues (leaves and fine roots), both positive (Hamilton et al., 2002; DeLucia et al., 2005) and negative effects (Norby et al., 2004) have been observed. Explanations for the above responses have been suggested mostly in qualitative terms. Nutrient limitation constrains the potential growth response, particularly for woody biomass increment (Korner, 2006), LAI is conservative because the gain in absorbed PAR per additional unit of LAI is small at higher LAI. To my knowledge, an explanation for the conservative NPP responses among closed-canopy forests (Norby et al., 2005) is lacking. However, the question addressed here is as follows: can these different CO2 responses be integrated and explained in a common framework?

In contrast to the variable responses of whole-plant properties to CO2, the primary functional responses of leaves appear to be limited to increased photosynthesis and reduced stomatal conductance (Gifford, 2004). Observed down-regulation of photosynthetic capacity at elevated CO2 can be attributed to reduced leaf nitrogen (N) (Ellsworth et al., 2004), while photosynthetic capacity per leaf N per area (a) and quantum efficiency (initial slope of leaf photosynthesis vs PAR, φ) are consistently increased by elevated CO2. This consistency suggest changes in a and φ as primary effects for up-scaling of elevated CO2 responses. To scale up these leaf responses to the whole-plant level, they must be put into a framework that includes the effects of other limiting resources, such as nutrients and water. For water, however, the main response is stomatal regulation, which in this framework is included indirectly through a.

Nutrients, particularly N, commonly limit plant growth and its response to elevated CO2 (Reich et al., 2006a). The fact that N is very often a limiting and depletable resource for plant growth suggests that the plants should strive to optimize their use of N. Furthermore, for exponentially growing plants, growth rate is linearly related to plant N concentration and N supply (Ingestad, 1979), which is a strong indication of the close relation between plant N and plant growth. Because of self-shading, the linearity does not hold as the plants get larger, but this is no reason to question the link between N and plant functioning. On the contrary, because of its key role in the metabolic machinery, not only photosynthesis but also respiration scales with N (Vose & Ryan, 2002; Reich et al., 2006b). Based on this dual role of plant N, it has been hypothesized that plant canopy N content is determined by optimizing NPP through a tradeoff between N-induced photosynthesis and whole-plant respiration (Dewar, 1996).

Here I extend Dewar's (1996) theory of optimal canopy N by including effects of shifts in foliage : root : sapwood ratios, to capture effects of changes in fine-root allocation in response to nutrient availability as well as the effect of sapwood accumulation. In this framework, leaf-level effects of CO2 (on a and φ) are scaled up to the whole-tree level. The hypothesis is that this optimization at the whole-plant level can elucidate less well understood forest responses to elevated CO2, such as the variation in NPP response among sites, the small responses in LAI (and absorbed PAR) relative to ɛ in most but not all cases, and the effects on wood : litter production ratio. The model should also provide insights into why and under what circumstances the NPP : GPP ratio is conserved in response to CO2 and nutrient availability. Observations from four forest FACE experiments are used to evaluate the hypothesized model.

Theory and model description

Evolutionary principles state that optimization of fitness, determined by reproductive success, ultimately controls plant behaviour. But since fitness is difficult to measure and model, for tree modelling some measure of production is usually used as a substitute, for example NPP (Dewar, 1996) or canopy carbon export (Dewar et al., 1998). However, here I assume that net biomass increment + reproductive production is more closely linked to fitness than either NPP or canopy carbon export. Looking at any instant in time, it seems logical that a plant maximizes its NPP, which is allocated according to the current demands of different organs. But in optimizing instantaneous NPP we are not accounting for the development over time, that is, that the amount and allocation of current NPP will affect NPP and survival the next year. Over its lifetime, growth and survival of a tree are determined by competitiveness and ability to acquire resources, for example, avoiding being overtopped by neighbouring trees, which is directly related to size (and often height). As size is equal to integrated biomass increment over time, size and hence fitness are likely to be maximized if biomass increment (net growth) is maximized at each moment in time. Furthermore, maximizing biomass increment at each instant in time can be seen as an approximate way of maximizing NPP over the lifetime, as NPP (per plant) generally increases with size. In addition to biomass increment, by definition, reproductive production should contribute to fitness. Therefore, net growth + reproductive production, that is, NPP less annual turnover (and any other carbon expenses) of leaves and fine roots, is the chosen target for optimization and is hereafter denoted as G. Turnover of woody structures, such as branches, are not deducted from G because of their long life span relative to leaves and fine roots. To obtain a framework for optimization of G, G must be formulated in terms of its components: canopy photosynthesis (gross primary production, GPP), respiration (R) and litter turnover (T).

Upscaling from leaf to canopy photosynthesis

Leaf photosynthesis is described by the nonrectangular hyperbola model, which predicts leaf responses much more accurately than the rectangular hyperbola model (Thornley, 2002). In this model, light-saturated photosynthesis (Amax) is a linear function of N content per unit area (NA) and minimum NA per leaf area (Nmin), Amax = a(NNmin). The slope of the photosynthetic capacity vs leaf N (a) is central to the optimal plant behaviour and is related to the allocation of N to structural and photosynthetic uses in the leaf and to stomatal conductance (Hikosaka, 2004). a is increased by elevated CO2 and reduced by water deficit (through stomatal regulation).

Using Beer's law of light extinction and optimal distribution of canopy N (Nc), as described in Franklin & Agren (2002), the total daily canopy photosynthesis (GPP, see Eqn 1a) can be derived as a function of Nc and absorbed PAR (Ia) through integration of leaf photosynthesis over the canopy (Supplementary Material, Eqns S1, S2). More complex canopy models, for example, differentiating sun and shade leaves, would probably be more accurate in absolute terms (dePury & Farquhar, 1997; Thornley, 2002). However, for the purpose of this paper, that is, to elucidate relative differences between CO2 treatments, the increased complexity would mainly serve to obscure the results.

image(  Eqn 1a)

(h, day length; φ, quantum efficiency; θ, a curvature parameter of leaf light response (parameter values and units are given in supplementary material Table S1)). Ia is related to radiation above the canopy (I0), LAI (L) and the light extinction coefficient (k) according to:

Ia = I0(1 − ekL) (Eqn 1b)

LAI (L) is determined by maximizing GPP (Eqn 1a) for a fixed Nc. Increasing LAI at small LAI increases GPP through increased light absorption. As LAI gets larger, light absorption saturates while the proportion of N that is nonphotosynthetic increases linearly with LAI (through the term Nmin L in Eqn 1a), reducing GPP. Thus, for a fixed Nc, GPP has a maximum with respect to LAI (Fig. 1). This optimal LAI, for simplicity hereafter denoted just LAI or L, is approximately linearly related to Nc (Fig. 2), which means that mean canopy leaf N per area (NA = Nc/LAI) is conservative during canopy development and among mature stands with differing Nc. However, NA increases with photosynthetic capacity per N (a) and decreases with quantum efficiency (φ) (Fig. 1). These shifts in NA happen because, for a fixed Nc, φ increases the initial slope of GPP vs LAI, while a increases GPP only at higher LAI (Eqn 1, Fig. 1). A combined increase in a and φ, where the increase in φ is one-third of the increase in a, as expected at elevated CO2 (Cannell & Thornley, 1998), decreases NA slightly for all Nc (Fig. 2). As GPP and LAI have been derived as functions of Nc, it is necessary to evaluate optimal Nc before they are fully defined.

Figure 1.

Gross primary production (GPP) as a function of leaf area index (LAI) and NA (= canopy nitrogen/LAI) for a fixed canopy nitrogen (Nc). Solid line with optimum a, baseline values of photosynthetic capacity per leaf N (a) and leaf quantum efficiency φ, Dashed line with optimum b, 50% increase in a. Dotted line with optimum c, 17% increase in optimum φ. Dashed-dotted line with optimum d, combined 50 and 17% increase in a and φ, respectively (representative of an elevated CO2 effect). Dotted vertical lines denote the optimal LAI and NA values. Note that φ controls the initial slope of GPP while a controls GPP at higher LAI (Eqn 1a), causing the different shifts in the optimum. Nc = 7.8 g m−2. Parameter values for Oak Ridge (Supplementary Material, Table S1).

Figure 2.

Leaf area index (LAI), fraction light absorbed (FPAR) and light-use efficiency (ɛGPP) at variable canopy nitrogen (Nc). ɛGPP is more conservative than FPAR and LAI at changing Nc. ɛGPP is significantly increased by elevated CO2, while there is only a small increase in FPAR and LAI at a fixed Nc. Solid and dashed lines are for ambient and elevated CO2, respectively. The dotted vertical lines indicate optimal canopy N (inline image) for the ambient (leftmost line) and elevated CO2 treatments.

Respiration and turnover

Respiration is modelled using the maintenance + growth respiration approach. Growth respiration (Rg) is a fraction of net assimilation, Rg = (1 – y)(GPP – Rm), where y is the biosynthetic conversion efficiency, which is conservative; y = 0.7 for whole-plant, woody species (Choudhury, 2001). Maintenance respiration (Rm) is proportional to N content across all living tissues, that is, canopy, sapwood and roots (Vose & Ryan, 2002), which can be explained through respiratory costs of protein turnover (Dewar et al., 1998). A factor qr > 1 accounts for the fact that fine roots have a higher respiration per N than other tissues (Ryan et al., 1996):

Rm = r(1 + qrfr + fs)Nc = rwNc( Eqn 2a)

(r, basic respiration rate per unit nitrogen; fs, fr, ratios of N in sapwood and fine roots to N in canopy; rw, whole-plant respiration per canopy nitrogen). Subscripts c, r and s, represent canopy, fine roots, and sapwood, respectively. The ratios fs, fr are restricted by the need for root and stem tissue to maintain the canopy (pipe theory; Shinozaki et al., 1964), but changes in response to environmental and ontogenetic factors, such as soil nutrient availability (changes fr) and tree height (changes fs).

Turnover (T) is expressed as a function of Nc, mean residence times of tissues (t), and N : C ratios (n) of canopy and roots:

image(Eqn 2b)

(lw, whole-plant litter production (turnover) per Nc).

To simplify the following expressions, an aggregated variable (w) of respiration and turnover per Nc is defined to represent total carbon costs per canopy nitrogen:

w = yrw + lw( Eqn 2c)

fr and fs are the main controls of w and are ultimately increased by root allocation in response to reduced soil N availability and increased mass of living wood, respectively. Compared to fr and fs, changes in the N : C ratios (n) and turnover times (t) have a smaller impact since they only enter the turnover function (Eqn 2b) and not the respiration function (Eqn 2a). Furthermore, they tend to be inversely correlated, for example, increased leaf N : C ratio (nc) is correlated with shorter life span (tc) (Wright et al., 2004). Nevertheless, no such relation is imposed here and effects of changes in nc at elevated CO2 were evaluated.

It should be noted that, although Nc and nc both occur in the expression for turnover, because leaf mass per area is not fixed, they are mathematically independent. Thus the derivation of optimal Nc (see following section) would not be invalidated by a changing nc.

Production and efficiency of expanding and steady-state canopies

For expanding canopies, the development of GPP, Rm and T as functions of canopy N (Nc) can be derived directly from Eqns 1a and 2a,b. Here LAI is optimized for each Nc, as described above. NPP and G are then calculated according to Eqn 3a. As the canopy expands, Nc eventually reaches an optimal value where G is maximized and where no further expansion occurs (Fig. 3), unless there is a change in parameters. Optimal Nc is thus determined by the optimal tradeoff between the N-based carbon gain (GPP) and carbon losses (Rm + Rg + T). The state reached after full canopy expansion is hereafter referred to as steady state, which also includes any subsequent shifts in canopy optimal size resulting from changes in parameters, such as increasing sapwood (fs) with height. Because all the terms of G are functions of Nc, the steady-state Nc (Eqn 3b) is readily derived by maximizing G (Eqn 3a) with respect to Nc (Supplementary Material). This optimal state of the system represents acclimation over timescales not shorter than the response time of the slowest relevant response mechanism. For example, in response to a change in CO2 concentration, it may take a growing season for the root : foliage ratio and Nc to reach a new equilibrium; therefore, modelled optimal growth rate represents a growing season average and not shorter-term fluctuations.

Figure 3.

Canopy expansion and optimal steady states. (a) For expanding canopies gross primary production (GPP), T (litter production) and Rm (maintenance respiration) are increasing with canopy nitrogen (Nc) up to inline image that maximizes net growth (G), where yGPP and T + yRm are parallel (cf. Eqn 3a). (b) The paths of net primary production (NPP) and G of expanding canopies (solid lines) and steady-state canopies (dashed lines). For steady-state canopies, the curves of NPP and G are given by varying the slope of T +yRm. This slope changes with age or soil fertility as a result of shifts in stem wood N: canopy N ratio (fs) or root N: canopy N ratio (fr). These changes in N partitioning move NPP* and G* along the dashed lines; for example, increasing stem wood (fs) with age causes a decrease.

By inserting inline image in the expressions for GPP and Rm, the properties GPP*, NPP*, and G* of the steady-state canopy are obtained (Eqns 3b–f, where * denotes the optimized steady-state canopy). NPP and G, but not GPP, follow different paths in relation to Nc during canopy expansion and at steady state (Fig. 3).

G = NPP − T = y(GPP − Rm) − T = yGPP − wNc(Eqn 3a)
image(Eqn 3b)

(ɛsat=a(inline imageNminL)/Ia, light-saturated photosynthetic light-use efficiency, that is, if all leaves operate at Amax).

GPP* = hIaɛGPP( Eqn 3c)


image(Eqn 3d)

The light-use efficiency of GPP (ɛGPP) has an upper theoretical limit of φ (2.73 µg C J−1, Wong et al., 1979).

G* and NPP* are given by

image( Eqn 3e)
image(Eqn 3f)

G, slope of the light-use efficiency of G).

GPP*, NPP*, G* and inline image are all approximately linear functions of absorbed PAR where the light-use efficiencies (the slopes) are controlled by the leaf quantum efficiency (φ) and the ratio ahy/w. The factors in this ratio thus strongly regulate the system; the numerator reflects responses in photosynthetic capacity (a) and day length (h) and the denominator, total carbon costs per canopy N (w), responds to the relative allocation to nonphotosynthetic parts, that is, roots (fr) and sapwood (fs). While GPP*, NPP*, G* all monotonically increase with the ratio ahy/w, the effect on inline image is more complex. inline image is increased by the ratio ahy/w but at the same time it decreases with a (denominator in the first factor in Eqn 3b), which makes the inline image response to a small. An important consequence of this is that inline image is much less sensitive to changes in photosynthetic capacity (a) than to changes in root and sapwood allocation (through w). The response to a is also variable, that is, positive at small inline image and negative at larger inline image. As inline image occurs where the slopes of GPP and yRm +T vs Nc are parallel (cf. Fig. 4), the response of inline image to a is determined by the change in slope of GPP vs Nc in response to a [= (∂/∂a) (∂GPP/∂Nc)]. This change of slope is positive at small inline image and negative at larger inline image.

Figure 4.

Optimal canopy state and effects of elevated CO2 and root nitrogen : leaf nitrogen ratio (fr). Net growth (G* = yGPP –Ncw, arrows; cf. Eqn 3a) and optimal canopy nitrogen (inline image; dotted vertical lines) resulting from photosynthesis at ambient vs elevated CO2 (GPPa and GPPe, respectively) and from different w1, w2 (= slopes of yRm + T, respiration and litter production) because of shifts in fr (cf. Fig. 3). The position of inline image is shown for control conditions (a); elevated CO2 only (b); elevated CO2+ increased w (c); ambient CO2+ increased w (d). Shifting conditions from a to b, compared with shifting from d to c, illustrates the effect of elevated CO2 at high vs low inline image.Shifting from a to c compared with from a to b represents the difference between a CO2 response restricted by increased root allocation and an unrestricted response. Applied leaf CO2 effect; 50% increase in a and 16.7% increase in φ.

Effects of elevated CO2 enter the system through a combined increase in a and φ (Cannell & Thornley, 1998). These parameters directly affect GPP and, as shown in Eqn 1a, elevated CO2 raises both the initial slope (through a) and the maximum (through φ) of GPP as a function of Nc. The increase in φ has a positive effect on inline image, while, as discussed above, the effect of a on inline image is negative unless inline image is very small. The combined increases in φ and a cause a small positive net effect of elevated CO2 on inline image, although the effect increases at decreasing inline image (Fig. 4). However, if at the same time carbon costs per Nc (w) increases, for example because of increased fine-root allocation, the total effect may be reduced inline image at elevated CO2 (Fig. 4).

The carbon use efficiency = NPP/GPP ratio can be expressed and, for steady-state canopies, approximated by:

image(Eqn 3g)

where the function Q is insensitive to variation of its parameters (Q ≈ 1.3 for all realistic parameter values; Supplementary Material, Eqn S7). The NPP/GPP* ratio has an upper limit of y (≈ 0.7) and is rather insensitive to changes in relative root and stem allocation (fr and fs) and associated changes in inline image. This invariance is not surprising since both GPP and Rm are increasing functions of Nc (Eqns 1a, 2a). The NPP/GPP* ratio is increased by elevated CO2 through the effect on a (Eqn 3g) and decreases during canopy expansion (Fig. 5). The effect of canopy expansion is the result of the saturating response of GPP combined with the linear increase in Rm (Fig. 3).

Figure 5.

Net primary production (NPP) : gross primary production (GPP) ratio vs canopy nitrogen (Nc). NPP : GPP ratios for an expanding canopy (upper lines) and for a steady-state canopy (lower lines) at ambient CO2 (solid lines) and elevated CO2 (dashed lines). Arrows indicate possible directions of canopy development. NPP : GPP decreases with Nc for an expanding canopy, while for steady-state canopies NPP : GPP is positively related to inline image.

Optimal LAI of the expanding canopy (L) and the steady-state canopy (L*) are identical for a fixed Nc (Fig. 1). However, for the steady-state canopy an analytical expression for L*, including the effect of optimal Nc, can be obtained by inserting Ia (Eqn 1b) in G* (Eqn 3e) and maximizing with respect to L, which gives:

image(Eqn 3h)

The PAR absorption of the optimized canopy (Ia) is then obtained through its direct link to L (Eqn 1b) as

image(Eqn 3i)

PAR absorption saturates earlier with increasing canopy size than light-use efficiency because of its exponential nature (Fig. 2).

As shown above, LAI vs Nc (NA) increases slightly with CO2 for a fixed Nc. Here Eqn 3h shows that also when including the effect of CO2 on Nc, for steady-state canopies, L* (at constant w) is slightly increased by elevated CO2 through the increased light-use efficiency (ɛG). However, the L* response to CO2 is always smaller than the response of ɛG, since L* is a logarithmic function of ɛG.

Modelling the CO2 effects in FACE experiments

To evaluate the hypothesized model, published observations from four forest FACE sites (whole stand elevated CO2 experiments) representing closed-canopy stands (meaning canopies horizontally filling the growing space) were used. The sites are: Oak Ridge (sweet gum, steady-state canopies), Duke forest (Loblolly pines, steady-state canopies), POPFACE (poplars, expanding canopies) and Aspen FACE (mixed aspen dominated, expanding canopies). The observations used here all represent elevated and ambient CO2 treatments where no other treatments were applied. Further information about the sites and relevant references are given in Table 1.

Table 1.  Site data and primary CO2 effects (Δa, Δφ, Δfr) applied for modelling of the forest free air CO2 enrichment (FACE) sites*
Site nameLocationMean temp (°C)SpeciesPlanting yearCanopy stateanbΔa (%)cΔφ (= Δa/3) Δfr (%)d
POPFACEItaly: 42°22′-N, 11°48′-E 14.1Three poplar species1999Expanding353117.7 49.82,3
Aspen FACEUSA: 45°36′-N, 89°42′-W  4.9Aspen, birch1997Expanding8214 7  4.15
Duke forestUSA: 35°59′-N, 79°6′-W 15.5Loblolly pine1983Steady state138612.7 52.27,8
Oak RidgeUSA: 35°54′-N, 84°20′-W14.2Sweetgum1988Steady state158619.3105.39

Parameters for the control plots of the FACE stands were collected from publications, except for a, fr and r, which were determined by fitting of observed data (GPP, G, NPP, LAI) (supplementary material, Tables S1 and S2), using length of growing season to derive annual numbers from the daily values given by the equations. The modelling of the elevated CO2 stands was then done with the same parameter values as for the control stands, except for the leaf photosynthetic capacity per N (a) and the root N : canopy N ratio (fr), which were multiplied by the observed relative changes (in percentage) in these parameters caused by the elevated CO2 treatment for each site (Table 1). In addition, an a-dependent increase in quantum efficiency (φ) was applied, equal to one-third of the increase in a (Cannell & Thornley, 1998; Long et al., 2004). By fitting the parameters a and fr for control stands and then applying observed relative changes to model the changes caused by elevated CO2, the influence of potential errors in the measured absolute values in these highly spatially and temporally variable parameters is removed. In this way focus is kept on the changes caused by elevated CO2 while minimizing potential effects of problems in baseline predictions or observations.

The observed CO2-induced increase in aa) was obtained by fitting observed leaf AmaxNA data for ambient and elevated CO2 treatments to separate slopes and a common Nmin, since estimated Nmin was not significantly different between treatments. The effects on frfr) were calculated from observed data on differences between elevated and ambient CO2 treatments in amounts and nitrogen concentrations of fine roots and leaves. For Duke forest, Δfr was partly estimated by extrapolation in time because of missing data for the main part of the investigated period. For the poplar sites (POPFACE and Aspen FACE), despite slight differences among the species within each site, one value of Δfr per site was used because Δa was available for one species per site only.

Small changes in physiological parameters resulting from CO2 treatment were also observed for leaf and fine-root N : C ratios and turnover rates. These effects only marginally affected the results (slightly improving the fit in Fig. 7) and were excluded from the further modelling in order to keep focus on the more important factors. The reasons for the small effects of changes in N : C ratios in this framework are that photosynthesis (within a species) is much more strongly linked to NA, which is used in this model, than to N : C ratio (Meir et al., 2002), while for respiration, the effects of N : C ratio are indirectly included through changes in total N.

Figure 7.

Modelled vs observed properties in free air CO2 enrichment (FACE) sites. Elevated/ambient CO2 (E/A) values for net primary production (NPP; open symbols), gross primary production (GPP; black symbols) and leaf area index (LAI; grey symbols) for the FACE sites, POPFACE (circles), Aspen FACE (triangles), Oak ridge (diamonds) and Duke forest (squares). r2 = 0.83 for all modelled vs observed data. Modelling of CO2 effects done as in Fig. 6. Data sources are in Supplementary Material, Table S2. Note that for Duke forest LAI, apparently other data exist than those shown here, since in another study E/A > 1 for LAI (Norby et al., 2005). This indicates a potential explanation for the discrepancy between model and observation, where E/A < 1, used here for LAI in Duke forest.

Because the poplar stands were in a phase of expanding canopy, the preoptimal production equations as functions of canopy N were used, while for Oak Ridge and Duke forest the optimized equations were used since these stands had reached steady-state canopies.

Results and Discussion

Neglecting seasonal and daily variations in environmental variables, the presented model is clearly focused on mechanistic understanding rather than predictive ability. Nevertheless, the predicted CO2 responses (the relative differences between elevated CO2 and control treatments) are in reasonable agreement with observations (Figs 6–8). Furthermore, given the inherent variation and uncertainty in estimates of forest production, the value of further improved matching between model and observations is questionable.

Figure 6.

Development of poplar stands (Aspen FACE) in relation to their canopy nitrogen (Nc). Modelled (lines) and observed (points) G (net growth; lower lines, circles) and NPP (net primary production; upper lines, triangles) of developing poplar stands (Aspen FACE) in ambient CO2 (solid lines, open symbols) and elevated CO2 (dashed lines, closed symbols). In modelling the ambient CO2 treatment, the model has been fitted to measured data by adjusting fr (root nitrogen : leaf nitrogen ratio) and a (of photosynthetic capacity per leaf N). For modelling the elevated CO2 treatments, observed changes in fr and a at elevated CO2 have been applied without refitting any parameters. r2 = 0.68, 0.81 for modelled vs measured CO2 effects on NPP and G, respectively.

Figure 8.

Observed vs modelled and potential light-use efficiency of gross primary production (ɛGPP). ɛGPP modelled for steady-state (lines) and expanding canopies (triangles), and ɛGPP observed (circles) at ambient CO2 (open symbols, solid line) and elevated CO2 (closed symbols, dashed line) vs the ratio ahy/w. The steady-state canopies (Duke forest and Oak ridge; the four leftmost points) are already at their steady-state ɛGPP (cf. Eqn 3d). The expanding canopies (POPFACE) ɛGPP are expected to increase vertically towards the lines representing steady-state canopies. Modelling of expanding canopies at ambient and elevated CO2 is done as in Fig. 6, using one set of parameters and CO2 effects for each site. r2 = 0.90 for the modelled vs measured CO2 effect. The ratio ahy/w controls photosynthetic capacity vs respiration + litter production per canopy N.

Variation in NPP responses

Looking at the NPP responses to CO2, they are large for the POPFACE compared with the other sites, which is also true for the LAI responses (Fig. 7). These large responses are the result of the well known effect of accelerated development in young stands, where not only biomass but also production increases faster over time at elevated than at ambient CO2 (Fig. 6). Disregarding the effects of accelerated development, the CO2 responses of NPP are similar among sites, as has been pointed out by Norby et al. (2005). In light of this theory, the similarity of NPP responses is a product of dissimilar photosynthetic (Δa, Δφ) and allocation (Δfr) effects, adding up to similar total effects. The stronger the photosynthetic response, the stronger the increase in fr (Table 1), causing down-regulation of production because of increased root respiration and turnover. This balance of effects is probably the result of the fact that enhanced photosynthesis, caused by increased Δa, increases nutrient demand, which is followed by augmented root allocation. Consequently, increased nutrient availability (fertilization) should substantially increase the CO2 response of wood and leaf production, especially at infertile sites, as has been observed (Oren et al., 2001). The leaf-level mechanisms behind the differences in Δa among the sites (Table 1) are not within the scope of this paper but a possible explanation has to do with temperature differences, which strongly affect the response of a (Long et al., 2004). Indeed, temperature effects could explain the small Δa in Aspen FACE, which has a significantly lower mean temperature than the other sites (Table 1).

Light-use efficiency, LAI and light absorption

An interesting aspect of the CO2 effect, especially in relation to remote sensing-based modelling approaches, is the response in light-use efficiency relative to light absorption (APAR). Here APAR responses are mediated solely through changes in LAI, although APAR also depends on light extinction k because, to my knowledge, significant CO2 effects on k have not been observed in the modelled sites. Large CO2 effects on LAI are only seen in the poplar sites and can mainly be attributed to an accelerated development effect (as discussed earlier). The small observed CO2 effects on LAI of the steady-state canopies of Duke forest and Oak Ridge and in other experiments have previously mainly been interpreted as a consequence of saturation of APAR. Here I suggest a new interpretation of the general insensitivity of LAI to CO2 as well as of the observed increased sensitivity at low LAI (Norby et al., 2005).

Through leaf photosynthetic capacity per N (a) and quantum efficiency (φ), elevated CO2 increases both the initial slope and the maximum of GPP as a function of canopy N (Nc) (Eqn 1a). As illustrated in Fig. 4, unless Nc is very low, this lifts the GPP vs Nc curve without much change in its slope and therefore only marginally increases inline image. Together with the simultaneous small effect of elevated CO2 on optimal LAI for a given Nc (Figs 1, 2), the small effect on inline image accounts for the small effects of CO2 on LAI. Furthermore, the photosynthetic effects of CO2 are often followed by an increase in fine-root allocation that increases carbon costs per Nc(w). This allocation effect further reduces the LAI response and can even lead to decreased LAI through down-regulation of inline image (Fig. 4), as, at the same time, the LAI : Nc ratio remains largely unchanged (Fig. 2).

Furthermore, the larger increase in LAI caused by elevated CO2 at smaller than at larger LAI can be attributed to the shape of the GPP–Nc curves. Despite the generally low sensitivity of the shape of the GPP–Nc curves to CO2, the larger CO2 effect on a (increasing initial slope) than on φ (increasing maximum GPP; increase in φ is equal to one-third of the increase in a) does cause the curves for ambient and elevated CO2 to become less parallel at low Nc. For a fixed w this leads to a larger effect of elevated CO2 on inline image at low than at high inline image (Fig. 4). This effect on inline image then carries over to LAI, as discussed above.

As predicted by the model and as expected from leaf responses, light-use efficiency of GPP (ɛGPP) is significantly increased by elevated CO2 (Figs 2, 8). However, contrary to assumptions in some studies (Goetz & Prince, 1999), ɛGPP is here predicted to increase with Nc and LAI, both during canopy development and if caused by changes in w at steady-state conditions (Fig. 2). In agreement with this, observed and predicted ɛGPP for a site with expanding canopies (POPFACE) are lower than the theoretical prediction for steady-state conditions, while for the steady-state FACE sites they are on average slightly higher than the theoretical steady-state prediction (Fig. 8). In further agreement with the model predictions, a positive correlation between Nc and light-use efficiency during canopy expansion and in response to fertilization has been observed for loblolly pine stands (Martin & Jokela, 2004).

Leaf responses

In agreement with the observations, the model predicts that canopy average leaf N per area NA (= Nc/LAI) is slightly reduced by elevated CO2, −8.1 and −9.7% for observed and modelled data, respectively. In line with the results by Ellsworth et al. (2004), the reduction in NA causes a down-regulation of leaf photosynthetic capacity (Amax) without changing the basic relations among leaf photosynthesis, leaf N and CO2 concentration. Previous explanations for the down-regulation have focused on leaf internal mechanisms or N dilution in response to source and sink changes (Ellsworth et al., 2004). However, here a fundamentally new interpretation is suggested for the ultimate reason behind the more proximate effects of leaf-level changes. The reduction in NA and associated photosynthetic down-regulation follow from whole-plant optimization of LAI and canopy N rather than as a secondary consequence of primary leaf internal effects.

In the presented framework, mass-based leaf N concentration or N : C ratio does not directly influence photosynthesis (which is controlled by NA) and plays a small role in controlling the CO2 and N responses discussed in this paper (with the possible exception of litter : wood production ratio as discussed below). It should be noted that the within-species acclimation responses discussed here should not be confused with the sometimes strong leaf N : C ratio–photosynthesis correlations observed among species. Furthermore, because no relation is imposed between leaf mass per area and NA, effects on N : C ratio cannot be predicted here. Thus, it is implicitly assumed that mechanisms not included in the present framework control leaf N : C ratio. Theses mechanisms can be revealed by adding a nutrient uptake model to the present framework, to predict N : C ratio responses from optimized mass balance, as will be shown in future work.

NPP : GPP ratio

The model predicts NPP : GPP ratio to increase by elevated CO2, to decrease during canopy expansion, but to increase with inline image for steady-state canopies (Fig. 5). Because of the small number of observations available here (n = 5) combined with the small effects, the measured and modelled CO2 effects here (11 and 4%, respectively) are not significant.

The theory lends support to the common assumption that the NPP : GPP ratio can be conservative under different conditions. Under a range of soil fertility (change in root : canopy N ratio, fr) or age (increase in sap wood : canopy N ratio, fs), there are only small differences in NPP : GPP (Eqn 3g) although, in agreement with observations (Mäkelä & Valentine, 2001), a slight decrease at increasing fs is predicted. The mechanistic background for the commonly observed invariance in NPP : GPP ratio has previously been elucidated in relation to temperature and short-term fluctuations in photosynthesis (Dewar et al., 1998, 1999). The presented theory expands the theoretical support for these findings to include effects of longer-term shifts in leaf : root : stem ratios (fr, fs).

Litter vs wood production

An important question for the sustainability of potential CO2-induced carbon accumulation is the allocation of production to fast turnover litter (foliage and fine-root production, T) vs allocation to wood (wood : litter ratio). The wood : litter ratio can be approximated by


(lw, litter production per canopy N (Nc) ). NPP/Nc is increased by elevated CO2 but otherwise conservative in relation to inline image for steady-state canopies (Fig. 3). Thus, the wood : litter ratio is increased by elevated CO2 (through NPP/Nc) and decreases with the litter production per Nc (through lw), where lw is sensitive to fr (the root N : foliage N ratio), as discussed in the theory section. Since fr is controlled by soil N availability, this explains why the wood allocation response to elevated CO2 is sensitive to N availability. However, the FACE plots analysed here either are not steady-state canopies (POPFACE, Aspen FACE), where NPP/Nc is decreasing with Nc (Fig. 3), or show a substantial increase in fr (Duke forest, Oak ridge), counteracting the elevated CO2 effect on wood : litter ratio. Thus, as expected, the CO2 effects on wood : litter ratio in the sites presented here are small, on average 10 and 1% for modelled and measured responses, respectively. Because the wood : litter ratio is largely controlled by lw (Eqn 2b), the generally negligible influences of N : C ratios and life spans of leaf and roots (see section on ‘Modelling the CO2 effects in FACE experiments’) may be more important for this particular response. Indeed, including measured effects on N : C ratios and life spans lowers the modelled CO2 effect on wood : litter ratio to, on average, 2% (SD = 4.0%), not significantly different from the 1% (SD = 4.3%) measured response. CO2-induced lowering of N : C ratios reduces the wood : litter ratio mainly through increased litter carbon losses per Nc at elevated CO2 (cf. Eqn 2b), as at the same time inline image is largely unaffected.

Rationale and limitations of the approach

In ecophysiological optimality models, there is usually very little discussion of the choice of target for optimization, although it is fundamental. The rationale for the chosen optimization criterion of NPP minus root and leaf litter production (G) has been explained above. Supporting the principle, experiments on stands of spruce and beech have shown that competitiveness is determined by the standing foliage mass and the annual branch volume increment rather than annual investments in foliage (Reiter et al., 2005). Providing support for the inclusion of reproductive production in G, reproductive enhancement by elevated CO2 has been observed (Ladeau & Clark, 2006). However, to evaluate the effect of optimizing G vs NPP in this framework, a version of the model based on optimization of NPP was analysed. In general this modification did not significantly alter the results, except that higher N contents were predicted and that NPP as a function of Nc (canopy N productivity) assumed a more curved upwards shape than the almost straight (for steady-state canopies) or slightly curved down (for expanding canopies) relation predicted by the original model (Fig. 3). The canopy N productivity curve of the original G maximizing model corresponds better to observations (Smith et al., 2002).

Scaling up CO2 responses from observed leaf responses, not describing the effects within the leaves, makes the suggested model incomplete from some practical perspectives. However, the approach taken serves to focus the analysis on the consequences of the leaf effects in a whole-plant perspective, rather than probing into the leaf internal CO2 responses, which are already well understood (Gifford, 2004). A natural extension of the presented framework is the addition of a soil nutrient uptake model. This addition would make it possible to analyze effects of changes in soil nutrient availability on forests production explicitly, rather than the currently used implicit effects through root allocation. However, the restriction of the system boundaries to explicitly include only plant properties (and not soil) in the analysis presented here serves to minimize the amount of uncertainty, in terms of both model assumptions and measurements, and to maximize the significance of the current conclusions.


The framework presented offers a transparent whole-tree optimality perspective on forest responses to CO2 and nitrogen. It is used to show how primary leaf photosynthesis and fine-root allocation responses scale up to control whole-system behaviour, explaining the range of NPP responses observed in forest FACE experiments. It shows how production (GPP and NPP) and structure (LAI and canopy N) are linked in response to N availability (through the fine-root : leaf N ratio). It suggests a novel interpretation of the small and variable CO2 responses on LAI, based on the change in slope of the GPP–canopy N relation shifting the optimal canopy N only slightly. It predicts that there is a consistent increase, although small, in optimal LAI vs canopy N at elevated CO2, that is, a reduction in NA, thus suggesting a new ultimate explanation for the CO2-induced leaf photosynthetic down-regulation, as leaf photosynthesis is largely controlled by NA.


Four anonymous reviewers, Ross McMurtrie, David Pepper and Francesco Tubiello provided comments and suggestions for the manuscript. Anniki Mäkelä, Roderick Dewar and Göran I Ågren have provided comments on an earlier version of the manuscript. Support for the work was provided by IIASA, Austria, and the US Department of Energy Office of Science, Biological and Environmental Research Program.