Allocation of gross primary production in forest ecosystems: allometric constraints and environmental responses


  • Guangshui Chen,

    Corresponding author
    1. Key Laboratory for Subtropical Mountain Ecology (Ministry of Science and Technology and Fujian Province Funded), School of Geographical Sciences, Fujian Normal University, Fuzhou, China
    2. Institute of Biological & Environmental Sciences, School of Biological Sciences, University of Aberdeen, Aberdeen, UK
    • Author for correspondence:

      Guangshui Chen

      Tel: +44 7787323981


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  • Yusheng Yang,

    1. Key Laboratory for Subtropical Mountain Ecology (Ministry of Science and Technology and Fujian Province Funded), School of Geographical Sciences, Fujian Normal University, Fuzhou, China
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  • David Robinson

    1. Institute of Biological & Environmental Sciences, School of Biological Sciences, University of Aberdeen, Aberdeen, UK
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  • Understanding the allocation of gross primary production (GPP) and its response to climate is essential for improving terrestrial carbon (C) modelling.
  • Here, we synthesize data on component GPP fluxes from a worldwide forest database to determine the allocation patterns of GPP across global gradients in climate and nitrogen deposition (Ndep).
  • Our results reveal that allocation of GPP is governed in an integrated way by allometric constraints and by three trade-offs among GPP components: wood production (NPPwood) vs fine-root production (NPPfroot), NPPwood vs foliage production (NPPfoliage), and autotrophic respiration (Ra) vs all biomass production components. Component fluxes were explained more by allometry, while partitioning to components was related more closely to the trade-offs. Elevated temperature and Ndep benefit long-term woody biomass C sequestration by stimulating allometric partitioning to wood. Ndep can also enhance forest C use efficiency by its effects on the Ra vs biomass production trade-off. Greater precipitation affects C allocation by driving the NPPwood vs NPPfoliage trade-off toward the latter component.
  • These results advance our understanding about the global constraints on GPP allocation in forest ecosystems and its climatic responses, and are therefore valuable for simulations and projections of ecosystem C sequestration.


The allocation of gross primary production (GPP) is an important issue in carbon (C) cycling and global climate modelling. How the assimilated C is allocated to biomass production vs respiration, and to labile vs recalcitrant tissues, determines the residence time of C in ecosystems, which has a strong effect on biomass and soil C stocks, and hence has a profound impact on regional and global C storage and flux (Dufresne et al., 2002; Ise et al., 2010). For example, a recent model analysis showed that different C partitioning schemes can result in large discrepancies in estimates of global equilibrium woody biomass from 48 to 226 Pg C (Ise et al., 2010). Also, changes in GPP allocation in response to climate (e.g. warming, changing patterns of precipitation and increasing anthropogenic nitrogen (N) deposition) will feed back on climate by influencing the strength of the terrestrial C sink and thus the net accumulation of CO2 in the atmosphere (Dufresne et al., 2002; Hyvönen et al., 2007). Surprisingly, however, the allocation of GPP to various C pools and fluxes is one of the less well-understood ecosystem processes and typically is described in far less detail in C cycle models than either photosynthesis or GPP itself (Malhi, 2012). This limits the capacity to model terrestrial C cycling and accurately predict its responses to and feedbacks on climate (Franklin et al., 2012).

The terminology on C allocation in the literature is inconsistent and sometimes confusing, and hence we followed Litton et al. (2007) by referring to allocation from three aspects: that is biomass, the dry mass present; flux, the C flow to a given component; and partitioning, the fraction of GPP used by a given component. However, we focus here only on component fluxes and partitioning.

Most of our understanding of C allocation in plants is at the individual level and is based on seedling studies and manipulative experiments. Different allocation patterns might be obtained at the stand level, in mature trees and across environmental gradients, but relatively little information is available to test that possibility. Allocation naturally implies trade-offs among components, so to understand the allocation process it is necessary to determine the form and function of those trade-offs. As the number of components increases, more trade-offs are possible. Only when all the important components are measured can we detect which trade-offs do occur. However, only a few studies have measured all major components of an ecosystem's C budget to allow estimation of allocation and its trade-offs. Previous allocation studies focused mainly on biomass (Tilman, 1988; Cairns et al., 1997), less frequently on NPP (Wolf et al., 2010; Malhi et al., 2011), and autotrophic respiration is usually excluded. However, as Litton et al. (2007) indicated, biomass is a poor predictor of both C flux and partitioning. So far, only one study has addressed the allocation pattern of GPP across broad environmental gradients, albeit based on a limited number of sites (Litton et al., 2007), and this indicated a global pattern of GPP allocation, for example, partitioning to stems increases and to roots decreases with GPP, and partitioning to foliage and autotrophic respiration is conservative. Yet, the underlying constraints on these global GPP allocation patterns remain unclear. Critically, variations across sites were quite large for partitioning of GPP to its components, for example, total belowground C allocation (TBCA) ranged from 21% to 75% of GPP (Litton et al., 2007). This implies that the observed patterns represent only central tendencies and might not necessarily be sufficiently accurate for estimating allocation of GPP at a specific site. Site-to-site variations could reveal much-needed information on biotic and abiotic factors regulating site-specific GPP allocation.

Allocation of assimilated C among plant structures can be described from several perspectives, including empirical modelling, allometric scaling, functional balance, entropy- and evolution-based theories (Franklin et al., 2012), although there is clearly overlap among them. For example, any evolution-based allocation model will be constrained ultimately by allometric limitations imposed by biophysics. Of the approaches reviewed by Franklin et al. (2012), only those based on allometric scaling and functional balance principles have yet been widely adopted (McConnaughay & Coleman, 1999; Reich, 2002; McCarthy & Enquist, 2007). For simplicity, we confine our attention here to these, while recognizing the potential for other theoretical paradigms to provide useful perspectives. The functional balance theory suggests that plants adjust their biomass among various organs in response to environmental changes to capture the most growth-limiting resource (Bloom et al., 1985; Chapin et al., 1987). Allometric scaling theory predicts that plants generally have been selected to allocate biomass to various organs in a size-dependent manner constrained by fundamental biophysical limitations on internal transport and structural integrity (Enquist & Niklas, 2002; Niklas & Enquist, 2002; Enquist & Bentley, 2012). Because plants allocate biomass not only in response to changes in size, but also react to environmental factors such as resource availability (Pretzsch, 2010), both mechanisms can operate simultaneously (McCarthy & Enquist, 2007). Indeed, it could be argued that allometric scaling defines fundamental constraints on variation in allocation patterns at evolutionary scales, whereas functional balance allows an individual to adjust allocation in response to its immediate environment, but only within the envelope of possibilities defined by allometry. Attributing GPP allocation patterns to one or other of these constraints is, however, difficult, but essential to fully understand the relative importance of these mechanisms and the processes that drive them (McConnaughay & Coleman, 1999; McCarthy & Enquist, 2007).

During the latest decade, data on near-complete annual C budgets in forest ecosystems have become increasingly available with the establishment of regional flux networks. In the present study, we used a recently compiled global database on component GPP collected at FLUXNET sites (Luyssaert et al., 2007), to characterize allocation patterns of GPP in forest ecosystems and their dependence on environmental factors. Specifically, we aimed to address these questions:

  • How strongly do allometric constraints govern the component C fluxes and partitioning of GPP?
  • What are the forms and functions of trade-offs among GPP components after the effects of allometric constraints are accounted for?
  • How do these trade-offs respond to environmental changes across the broad scale gradients of climate and resource availability?

Materials and Methods


The global forest database (Luyssaert et al., 2007) is available online at Of the total 558 forests, 111 provided estimates of GPP and at least one of its components (Supporting Information Table S1) and this is the dataset used for examining the allometric scaling relationships between GPP and its components. Of the 111 forests in Table S1, 81 simultaneously provided an estimate of tree biomass production (NPPbio), that is, the sum of stem, branch, foliage, coarse root and fine root production (termed TNPP1 in Luyssaert et al., 2007), and an estimate of autotrophic respiration (Ra), and this is the dataset used in a principal component analysis (PCA) to identify the associations among GPP components.

We rearranged NPPbio into three components, that is, production of foliage (NPPfoliage), wood (NPPwood, the sum of all woody parts including stem, branch and coarse root), and fine root (NPPfroot). NPPwood was further divided into two components: NPPstem, the sum of stem and branch production; and NPPcroot, coarse root production. Note that NPPbio does not represent the total NPP, as production of reproductive organs, understorey biomass, root exudates and mycorrhizas, and biomass loss to herbivores, burning or other forms of destruction are not included (Luyssaert et al., 2007).

The GPP of these 111 forests was estimated via eddy covariance (= 54), component integration of NPP and Ra (= 54), or modelling (= 24). Twelve forests provided GPP estimates simultaneously using two or three of these methods (Table S2). One hundred and four out of the 111 forests have estimates of Ra (Table S1). Ra was estimated by scaling up chamber measurements of foliage, stem and root respiration (= 56), modelling (= 1) or C balance methods (= 5; Table S3). One site had no information of the estimation method used. It should be noted that the estimates of GPP or Ra from modelling were included in the original Luyssaert database only when a mechanistic process model was used and when the model was calibrated by site-specific measurements (Luyssaert et al., 2007).

Ra can also be estimated indirectly as the difference between GPP and NPP (because, by definition, GPP = NPP + Ra) or the difference between ecosystem respiration (Reco) and heterotrophic respiration (Rh) (because Reco = Rh + Ra), where the necessary variables have been measured. Field-based NPP measurements rarely account for components other than NPPbio (or TNPP1 in Luyssaert et al. (2007)), so values based on the difference between GPP and TNPP1 can overestimate Ra. We substituted corrected (gap-filled) NPP values for TNPP1 in the present analysis; details of gap-filling procedures are given in Vicca et al. (2012). Finally, we also included Ra estimates by these two indirect methods in the dataset (= 62 for the GPP–NPP method; = 36 for the RecoRh method). Thirty-six sites had Ra estimates based on at least two of the above methods (Table S3).

Of the 111 forests, 101 have estimates of NPPfoliage, 98 have estimates of NPPstem, and 86 have estimates of NPPcroot (Table S1). NPPfoliage was usually determined by collecting leaf/needle fall plus any biomass increment, and NPPstem and NPPcroot were determined mostly using species- and region-specific allometric equations (Luyssaert et al., 2007).

Perhaps the most difficult production component to quantify reliably in any ecosystem (Robinson, 2004), NPPfroot was estimated by various techniques of different quality. Here, when NPPfroot estimates were provided simultaneously by two or more techniques, only data obtained by techniques of the highest quality (as defined subjectively by Wolf et al., 2010) was included. Of the 111 forests, 88 have estimates of NPPfroot (Table S1). The methods used vary from ‘highest quality’ techniques using mini-rhizotrons or root windows (= 14 sites) and ‘modest quality’ techniques with root in-growth cores or mesh bags (= 7 sites), fine-root biomass with an assumed turnover rate (= 49 sites), or a mass balance method (= 1 site), to ‘lower quality’ techniques using sequential cores (= 11 sites), harvesting (= 1 site), or by applying a statistical relationship derived by Raich & Nadelhoffer (1989) between soil-surface CO2 flux and litterfall (= 1 site; Table S4). Three sites used literature data, and one had no information of the estimation method used (Table S4).

In addition to C-flux data, stand characteristics, such as stand biomass, stem density, age, mean tree height (H), and mean diameter at breast height (D), climatic factors (mean annual air temperature, MAT; and mean annual precipitation, MAP), and total N deposition (Ndep), are also documented in the database. We also extracted monthly sunlight (percentage of daylength with full sunlight) and relative humidity (RH; percentage) from a global climate database (New et al., 2002) using latitude and longitude for each site.

Data analysis

When multiple years of data were available, data were averaged over all years. Except for NPPfroot, for which only one estimate from the best quality technique was selected as indicated above, estimates of both GPP and its components were averaged over all estimation methods when multiple methods of data were available.

We focused our analysis mainly at the stand level. However, because Wolf et al. (2010) suggested that allocation of NPP at the average tree level can be largely explained by tree NPP itself, we compared the allometric scaling relationship of each component against GPP both at the stand and average tree levels to assess different roles of allometric constraints in controlling C allocation. Average tree GPP and its components were computed by dividing total stand values by the stem density at each site. GPP and its components both at the stand and average tree levels were all log10-transformed and the outliers of each variable were discarded in the following analysis. An outlier was defined as any datum > 1.5 interquartile ranges below the first quartile or above the third quartile.

The reduced major axis (RMA; type II) regression (SMATR v2.0; Warton et al., 2006) was conducted to determine the allometric scaling relationship between GPP (y) and its components (x) both at the stand and average tree levels using the form log(y) = log(α) + β log(x) + ε, where α is a constant, β the scaling exponent and ε the estimation error.

A PCA based on a correlation matrix of log10-transformed stand-level GPP components was carried out to evaluate how these components were associated with each other. All the four PC axes were included in the analysis. Pearson correlations were performed to assess the relatedness of the PC axes to partitioning of GPP to each component. To determine factors affecting the associations amongst GPP components, log10-transformed stand characteristics were related to the PC axes by Pearson correlations, and log10-transformed environmental factors (MAP, MAT, sunlight, RH, Ndep) were regressed against the PC axes by multiple stepwise regressions. To avoid bias due to varying number of sites per study, site-specific data from studies with multiple sites were down-weighted by the inverse of the corresponding number of sites (Ptacnik et al., 2008). The statistical significance level was set at = 0.05.


Allometric constraints on allocation of GPP

At the stand level, all the GPP components except for NPPfroot scaled allometrically with GPP when log-transformed, with the slopes significantly larger than 1 (Fig. 1; Table S5). NPPbio and Ra scaled similarly with GPP, indicating that these components vary in a fixed proportion with GPP. The scaling slopes for NPPstem and NPPwood were significantly higher than for NPPfroot (Fig. 1; Table S5).

Figure 1.

Reduced major axis regressions between log10 gross primary production (GPP) and log10 of its component fluxes (in g C m−2 yr−1): (a) foliage production (NPPfoliage); (b) stem production (NPPstem); (c) wood production (NPPwood); (d) fine root production (NPPfroot); (e) total biomass production (NPPbio); and (f) autotrophic respiration (Ra).

At the average tree level, only Ra scaled allometrically with GPP (Table S5). By contrast, the other GPP components were all isometric with GPP and the scaling exponents indistinguishable from 1, indicating that partitioning to these components does not change with GPP. Note that the slope of the Ra vs GPP regression was significantly higher than that of the NPPbio vs GPP regression, indicating a larger autotrophic respiratory cost relative to biomass production as GPP increases.

The regressions of each component against GPP at the average tree level showed that most (55–94%) of the variation could be explained by the magnitude of GPP itself (Table S5). By contrast, the explanatory power decreased at the stand level to 7–70% (Fig. 1; Table S5). Most prominently, the percentage variation in NPPfroot explained by GPP was only 7% at the stand level, compared with 55% at the average tree level (Fig. 1; Table S5).

The PCA analysis showed that the first axis explained 55% of the variance in GPP components (Table 1). However, only 7% of variation in NPPfroot was explained by this axis. Except for NPPfroot, all GPP components were highly correlated and contributed to most of the first axis variance (Table 1). The first PC is therefore essentially an axis of allometric increase of each component with GPP, representing the overriding allometric constraint on GPP and its components.

Table 1. Loadings for, and percentage variation explained by, the four axes extracted by a principal components analysis on log10-transformed component fluxes of gross primary production (GPP)
Component fluxPC1PC2PC3PC4
  1. NPPfoliage, foliage production; NPPwood, wood production; NPPfroot, fine root production; Ra, autotrophic respiration. The constraints on, or trade-offs among GPP components implied by each PC axis are also indicated.

R a 0.7820.017−0.6210.056
% of Variance55.024.613.66.8
Constraint or trade-offAllometric constraintFine root-woody biomass production trade-offRespiration-biomass production trade-offPhotosynthetic vs nonphotosynthetic biomass production trade-off

There were large inter-site variations in partitioning of GPP, with partitioning to Ra having the lowest CV (Table 2). Across this broad GPP gradient, a decreasing trend in partitioning to NPPfroot and an increasing trend in partitioning to NPPstem (and to lesser extent, NPPwood) was found, while partitioning to Ra, NPPbio and NPPfoliage was relatively conservative (Fig. 2). However, GPP itself could explain no > 30% of the variation in its partitioning (Fig. 2). Similarly, no > 30% of the variation was captured by the first PC axis, PC1 (= 0.51, i.e. r2 = 0.26; Table 3). Note that PC1 captured hardly any variation in partitioning to Ra.

Table 2. Means and variations in the relative partitioning of gross primary production (GPP) to its various components
  n MeanMinMaxLower CIUpper CISDCV (%)
  1. NPPfoliage, foliage production; NPPstem, stem production; NPPwood, wood production; NPPfroot, fine root production; NPPbio, total biomass production; Ra, autotrophic respiration.

Table 3. Pearson correlations (r) between PC axes and log10-transformed partitioning of gross primary production (GPP) to its various components
  1. NPPfoliage, foliage production; NPPstem, stem production; NPPwood, wood production; NPPfroot, fine root production; NPPbio, total biomass production; Ra, autotrophic respiration.

  2. Statistically significant (< 0.05) correlation coefficients are in bold. = 76 in each case.

 r 0.472 0.347 0.390 0.5100.1690.005
 P < 0.0010.0020.001< 0.0010.1440.967
 r −0.1160.3570.392 0.786 0.019−0.044
 P 0.3190.002< 0.001< 0.0010.8700.708
 r 0.537 0.644 0.647 0.248 0.863 0.873
 P < 0.001< 0.001< 0.0010.031< 0.001< 0.001
 r 0.618 0.430 0.459 0.0220.2000.066
 P < 0.001< 0.001< 0.0010.8500.0840.570
Figure 2.

Ordinary least-squares linear regressions between log10 of gross primary production (GPP) and log10 of its partitioning to: (a) foliage production (NPPfoliage); (b) stem production (NPPstem); (c) wood production (NPPwood); (d) fine root production (NPPfroot); (e) total biomass production (NPPbio); and (f) autotrophic respiration (Ra).

Collectively, these results indicate that although the allometric constraint is a relatively good predictor of component fluxes of GPP, especially at the average tree level (Fig. 1; Table S5), it is a poor predictor of partitioning of GPP (Table 3), so emphasizing the importance of mechanisms other than allometry in controlling GPP partitioning.

Trade-offs among GPP components

Because trade-offs among components can be caused by either allometric constraints or plastic responses to the environment, we define those caused by factors other than allometry as ‘true trade-offs’; otherwise they are ‘apparent trade-offs’.

The correlation analysis indicated apparent trade-offs between NPPfroot/GPP and NPPwood/GPP, and between Ra/GPP and NPPfoliage/GPP and NPPwood/GPP (Table 4).

Table 4. Correlation matrix among the proportions of gross primary production (GPP) components
  1. NPPfoliage, foliage production; NPPwood, wood production; NPPfroot, fine root production; Ra, autotrophic respiration.

  2. Statistically significant at: *, = 0.05; **, = 0.01.


Once PC1 was accounted for, the other three PC axes reflected the true trade-offs among GPP components (Table 1). The second PC axis, PC2, whose contribution was 24.6%, had a strong positive correlation with NPPfroot and a weak negative correlation with NPPwood (Table 1). PC2 represents mainly an increasing allocation to fine roots, at the expense of woody biomass production. The methods by which NPPfroot was estimated had no significant effect on the PC2 scores (one-way ANOVA, = 0.411), indicating that this trade-off is unlikely to be a methodological artifact.

The third PC axis, PC3, which explained 13.6% of the variance, was strongly and negatively correlated with Ra and positively correlated with all of the NPP components (Table 1). PC3 summarizes a true trade-off between respiratory cost and biomass production.

The fourth PC axis, PC4, which contributed 6.8%, had a positive correlation with NPPwood and a negative correlation with NPPfoliage (Table 1). It reflects a true trade-off between production of photosynthetic and nonphotosynthetic biomass.

The partitioning to NPPfroot and Ra was captured mostly by PC2 and PC3, with (respectively) 62% and 76% of the variation explained (Table 3). However, the partitioning to other components cannot be explained solely by any trade-off axis. The variation in partitioning to NPPwood was explained more by axes 2–4 than by PC1, while the variation in partitioning to NPPfoliage was captured more by PC3 and PC4 than by PC1 (Table 3).

To summarize, PC1 reflects the variation in GPP associated with allometric constraints, PC2 represents the fine root–woody biomass production trade-off, PC3 the respiration–biomass production trade-off, and PC4, the trade-off between photosynthetic vs nonphotosynthetic biomass production.

Factors affecting trade-offs among GPP components

Most of the tree size- or GPP-related stand characteristics were uncorrelated with the trade-off PC axes (Table 5), verifying the independence of these trade-offs from the allometric constraint. However, PC2 was correlated significantly with stem density, PC3 showed significant correlation with stem density and stand age, and PC4 was related significantly to tree height (H ).

Table 5. Pearson correlations between scores of PC1, PC2, PC3 and PC4 and the log10-transformed stand characteristics
ComponentsLAI M above M total m above m total D H DensityStand age
  1. LAI, leaf area index (m2 m−2); Mabove, stand aboveground biomass (g C m−2); Mtotal, total stand biomass (g C m−2); mabove, average tree aboveground biomass (kg C per stem); mtotal, average tree biomass (kg C per stem); D, diameter at breast height (cm); H, tree height (m).

  2. The coefficients of statistically significant (< 0.05) correlations are in bold.

n 735955484755646274
r 0.537 0.433 0.425 0.466 0.458 0.360 0.365 −0.105−0.106
P < 0.0010.0010.0010.0010.0010.0070.0030.4170.371
r −0.075−0.112−0.129−0.026−0.034−0.0170.1290.3030.063
P 0.5260.4000.3490.8620.8220.8990.3080.0170.594
r 0.006−0.065−0.128−0.128−0.162−0.153−0.078 0.436 0.431
P 0.9620.6230.3510.3850.2780.2660.540< 0.001< 0.001
r −0.017−0.128−0.064−0.0290.0050.0330.2670.002−0.123
P 0.8840.3350.6440.8460.9750.8110.0330.9850.297

The multiple stepwise regressions revealed that PC1 was positively affected by both MAT and Ndep (Table 6). None of the environmental factors was significantly related to PC2. PC3 was positively affected by Ndep, while PC4 was influenced negatively by MAP (Table 6).

Table 6. Multiple stepwise regression analysis between the axis scores of PC1, PC2, PC3 and PC4 and the climatic variables
YModelDirection of responsePredictor P
r 2 P
  1. MAT, mean annual air temperature (°C); MAP, mean annual precipitation (mm); Ndep, annual nitrogen deposition (g N m−2 yr−1).

  2. –, no data.

PC10.626< 0.001PositiveMAT< 0.001


Allometric constraints on GPP allocation

We found differences in the strength with which GPP allocation varied with allometric constraints at the levels of the stand and average tree. GPP component fluxes at the average tree level are explained mostly by the average tree GPP itself. This supports the conclusion by Wolf et al. (2010) who reported that component NPP of the average tree was explained largely by the average tree NPP itself (r2 = 67–91%). However, the explanatory power of allometric constraints on GPP decreased at the stand level, which may reflect the change in spatial scale. Because stem density varies inversely with average tree GPP (Wolf et al., 2010), the variation in GPP is inevitably wider among average trees compared with that at the stand level. Therefore, a larger percentage of variation in GPP may appear to be related to allometric constraints at the average tree level.

The allometric scaling relationship also differed between these two levels. Most notably, on a log-transformed basis, the scaling slopes of NPPfoliage, NPPstem, NPPwood and NPPbio against GPP for the average trees were not significantly different from 1, but were significantly above 1 at the stand level (Table S5). This difference could be explained if competition for light increases with stand productivity. That would be likely to select individuals partitioning more C to aboveground production, specifically stem growth.

At both the stand and average tree levels, all components scaled with GPP with slopes larger than or not different from 1 when variables were log-transformed (Table S5). This is not surprising since we were unable to include all the GPP components in the scaling analysis. Even so, our analysis predicts that those unmeasured components (root exudates, mycorrhizas and understorey vegetation) would collectively scale with GPP with a slope < 1 to ensure the isometric relationship between combined components and GPP. Estimating the ‘missing’ components of GPP with sufficient accuracy to test this prediction would obviously be a formidable undertaking.

Little (c. 30% at most) of the variation in the partitioning of GPP could be explained solely by allometric constraints. This is understandable because allometric partitioning of plant growth is generally unresponsive to environmental factors, reflecting instead an over-arching constraint within which environmentally induced allocation responses can be expressed (Enquist & Niklas, 2002). Of the GPP components we considered, NPPfroot is relatively independent of allometric constraints. This has implications for modelling NPPfroot, predictions of which must invoke factors other than size-related stand characteristics. Finér et al. (2011) found that size-related parameters such as basal area, stem density and stand age were either statistically unrelated to NPPfroot, or explained only small fractions (c. 6%) of its overall variation.

Although different partitioning schemes of GPP have been used in different analyses, that is, GPP was partitioned into four components in this study compared with five or six in Litton et al. (2007), some global allocation patterns reported in Litton et al. (2007) were also evident in our study. However, we showed additionally that these global patterns are largely allometrically constrained. For example, partitioning to NPPstem increased with increasing GPP, and to NPPfroot (TBCA in Litton et al., 2007) decreased, because the scaling slope of NPPstem was the largest and that of NPPfroot smallest among the GPP components (Fig. 1; Table S5). Partitioning to Ra, NPPbio and NPPfoliage was relatively conservative (Fig. 2), as their scaling slopes were intermediate among those of all the components included in the analysis (Fig. 1e,f; Table S5). Besides these global patterns, we found substantial inter-site variations in partitioning of GPP. For example, although partitioning to Ra was relatively conservative (with the lowest CV), it varied from 0.30 to 0.81 (Table 2), comparable with the 0.42–0.71 range reported by Litton et al. (2007). This indicates that the broad-scale pattern may not provide accurate estimates of the GPP partitioning at a specific location.

Trade-offs among GPP components

The apparent NPPwood−NPPfroot trade-off manifested in our analysis (Table 4) was reported previously (Wolf et al., 2010; Malhi et al., 2011). Dybzinski et al. (2011) proposed such trade-off in old growth mixed-age stands to arise from the co-limitation of productivity by resources captured aboveground (light) and below (nutrients and water). Increased availability of soil-derived resources means that relatively less C is needed for the production of fine roots and relatively more C can be used to capture light. In most forests, greater light interception is achieved by height (wood) growth due to the strong and asymmetric competition for light. However, Wolf et al. (2010) indicated that this apparent trade-off is constrained mainly allometrically. This allometrically constrained trade-off was also supported in the current study, because the scaling slope of NPPwood with GPP was highest and that of NPPfroot lowest among the GPP components we examined (Fig. 1; Table S5). However, a true NPPwood−NPPfroot trade-off was also detected here, as reflected by PC2 (Table 1). Thus, our study is the first to show that this NPPwood−NPPfroot trade-off is not only an apparent one caused by allometry, but also a true trade-off that is a phenotypically plastic response of vegetation to environmental factors.

The PC2 axis showed no significant correlation with any stand characteristics examined, but was related negatively to stem density. This may be because plants grown at high densities invest more C to stems to achieve greater height in order to maximize light gain (Poorter et al., 2012). PC2 had no significant relationship with Ndep or MAP (Table 6), which may to some extent represent soil N and water availability. This seems to contradict the functional balance theory in which a decrease in NPPfroot and an increase in NPPwood would be expected with increasing nutrient and water availability. However, inconsistent effects of manipulated nutrient and water availability on NPPfroot are reported in the literature and a consensus is yet to emerge (Joslin et al., 2000; Nadelhoffer, 2000; Liu & Greaver, 2010). It seems that the relationship between NPPfroot and soil resource availability is not monotonic and that the functional balance theory is too simple to account for observed relationships. Interestingly, evolution-based allocation theories, for example, optimal response models, do predict a nonmonotonic humped relationship between NPPfroot and nutrient availability (Dewar et al., 2009). Because the PC2 axis captured most of the variation in NPPfroot, accurately modelling and predicting NPPfroot in terms of GPP will necessitate further understanding of the mechanisms controlling this trade-off.

The PC4 represents the trade-off between photosynthetic vs nonphotosynthetic biomass production (Table 1), or the functional trade-off between light interception and height growth that has been reported in numerous studies (Kohyama, 1987; King, 1990). This trade-off reflects an active adjustment of plants to light availability especially in a closed-canopy forest where light is usually a growth-limiting resource. Among the stand characteristics we tested, tree height had a negative correlation with the PC4 axis (Table 5) which we postulate reflects the trade-off between production of photosynthetic and nonphotosynthetic biomass. Shorter trees invest relatively more C in height growth to avoid shading and taller trees invest relatively more C in foliage growth to increase light interception and shade smaller individuals. However, the PC4 axis was not directly correlated with sunlight itself (Table 6), perhaps because for forest trees light availability is determined predominantly by competition among individuals (McCarthy & Enquist, 2007). Light availability locally for a stand may also be related to MAP. This is because, other things being equal, a higher MAP is more likely to result in the formation of more cloud and fog and, therefore, to reduce the direct radiation flux onto the canopy. Thus, the negative correlation of the PC4 axis with MAP (Table 6) could indicate that the increased investment of C in light interception would probably have been associated with conditions of more water and less light.

The PC3 axis represents the trade-off between autotrophic respiration and biomass production, which is related directly to an ecosystem's C use efficiency (CUE; DeLucia et al., 2007). CUE is usually defined as NPP/GPP, although Vicca et al. (2012) have argued that this ratio should be defined more precisely as the biomass production efficiency, because the production and loss of volatile organic C compounds, root exudates and exports to root symbionts are hardly ever estimated or included in total NPP budgets. Even so, CUE is usually assumed as a first approximation to be constant (Waring et al., 1998; Chambers et al., 2004; Litton et al., 2007). As previously indicated, partitioning of GPP to Ra (or NPPbio) is indeed relatively conservative at a broad scale as a result of allometrically constrained allocation (Fig. 2e,f; Table S5). However, site-specific Ra/GPP and NPPbio/GPP ratios varied substantially within a range (Table 2) comparable with that for CUE (0.2–0.8) reported by DeLucia et al. (2007). Thus, it seems that the apparently conservative nature of CUE is a product of the coarse resolution with which its components are usually estimated.

The PC3 axis correlated positively with stem density and negatively with stand age. These correlations are not size-dependent because such effects are encapsulated by PC1. Increasing stem density enhances light competition and causes increased C investment in the stem fraction (Poorter et al., 2012). As stems have low specific respiration rates and a high CUE relative to other organs (Litton et al., 2007), the overall stand CUE of densely packed trees will therefore increase.

The negative correlation of the PC3 axis with stand age is similar to the findings in studies that show CUE declining as forests age (Makela & Valentine, 2001; Goulden et al., 2011; Yang et al., 2011). This effect might be because of demographic differences between young and older forest stands. Younger stands, or stands recovering from disturbance, would tend to have larger populations of younger individuals that allocate more C to active growth, in contrast to older stands dominated by mature or near-mature individuals that invest more C in maintaining existing biomass (Malhi, 2012).

The relationship between the PC3 axis and Ndep (Table 6) indicates enhanced CUE with increasing ecosystem N loads. There is evidence that N fertilization increases CUE for some tree species such as Pinus radiata and Eucalyptus saligna (DeLucia et al., 2007). The increase of CUE with N availability could simply be a result of altered allocation, that is, less C allocation to fine roots (with high C turnover and respiration) and more to wood (with low C turnover), as predicted by evolution-based optimal response models (Franklin, 2007).

Some studies have suggested possible influences of temperature on CUE (Atkin et al., 2005; Zhang et al., 2009; Piao et al., 2010). However, MAT had no effect on the trade-off between respiration and biomass production reflected by the PC3 axis. Although temperature does affect the PC1 axis (namely GPP itself; Table 6), this should not result in a large effect on CUE since the scaling slopes of NPPbio and Ra are similar. Other studies have also indicated that partitioning of GPP to Ra is relatively unresponsive to experimentally manipulated air temperatures (Tjoelker et al., 1999; Atkin et al., 2007).

Implications for C modelling and projection

Fully understanding the mechanisms driving C allocation processes is critical if terrestrial ecosystem models are to accurately predict changes in C sequestration and its responses to climate. Here, we have shown that allometric constraints and phenotypic responses to environmental factors are not mutually exclusive, but can be integrated into a scheme for understanding how GPP is partitioned (Fig. 3). These mechanisms are clearly important to understanding C allocation but have yet to be incorporated into vegetation C models. For example, most of the current vegetation models use only a single mechanism to address C allocation, by a single allometric relation (e.g. in the ED and SEIBDGVM models; Metcalfe et al., 2011) or account for only a single trade-off according to soil water or nutrient limitations (e.g. O-CN, LPJ, LPJGUESS, aDGVM, sDGVM, CLM-CN and ORCHIDEE).

Figure 3.

A scheme for partitioning of gross primary production (GPP) in forest ecosystems, which is governed by allometric constraints and trade-offs as responses to environment factors. Thick solid arrow, net photosynthesis; thin solid arrows: allometric partitioning of GPP to each component; the double broken thin arrows, trade-offs among GPP components. The ‘+’, ‘−’ or ‘0’ in brackets following a parameter indicates a positive, negative or no effect of that parameter. MAT, mean annual air temperature; MAP, mean annual precipitation; Ndep, nitrogen deposition; GPP, gross primary production; NPPbio, total biomass production; Ra, plant autotrophic respiration; NPPfoliage, foliage production; NPPwood, sum of stem, branch and coarse root production; NPPfroot, fine root production.

The responses of multiple trade-offs to environmental variables must be made explicit to predict how resource availability or environmental change influences C allocation in forests. The widely used functional balance approaches are suitable to derive simple (e.g. monotonic) allocation relationships, but may be incapable of describing more complex allocation patterns (Franklin et al., 2012), such as the NPPfroot vs NPPwood trade-off in response to soil N availability as indicated above. We argue that a ‘bottom-up’ approach, such as the functional balance theory, would struggle to accommodate the multiple trade-offs that we have identified, especially in relation to variable environments and taxonomic diversity. Instead, a ‘top-down’ approach, that is, one controlled by an evolutionarily based governing principle (e.g. growth or entropy maximization), could provide more reliable frameworks for modeling C allocation (Franklin et al., 2012).

Among the NPPbio components, foliage and fine roots both trade off independently with wood production. The commonly assumed (Tilman, 1988), but frequently doubted (Shipley & Peters, 1991; Grime & Mackey, 2002), functional trade-off between above- and belowground components does not occur directly as a trade-off between fine roots and foliage. Instead, it arises from two separate trade-offs between foliage or fine roots and their supporting woody organs. Based on a trade-off between biomass partitioning to roots and shoot, Smith & Huston (1989) suggested a trade-off between drought- and shade-tolerance in plants. However, the lack of a trade-off between NPPfoliage and NPPfroot in our analysis may imply that the drought- and shade-tolerances of forest trees are generally independent of each other (Markesteijn & Poorter, 2009).

Our analyses lead to specific predictions of the impacts of climate change on forest C sequestration. GPP is predicted to increase with increasing temperature and N deposition (Fig. 3), which of course is in accordance with many previous reports of greater GPP in response to such drivers (Garbulsky et al., 2010; Quinn Thomas et al., 2010; Wu et al., 2011). Increasing temperature is expected to affect partitioning of the elevated GPP through allometry (Fig. 3), with greater partitioning to the long-lived woody components. N deposition is predicted to influence GPP partitioning both through allometry and via the Ra–NPPbio trade-off (Fig. 3). These two C allocation processes will together increase C partitioning to NPPwood, so potentially benefiting C sequestration in recalcitrant woody tissues. However, long-term C sequestration in the wood component is also determined by the residence time of wood (Galbraith et al., 2013). Although a general increase in rainfall may be predicted by most global climate models, there are inconsistent projections in precipitation patterns at regional and local scales (IPCC, 2007). Thus, the influence on global C allocation by future redistributions of MAP is unclear.

Because the components of GPP interact with each other, partitioning studies based on incomplete information about component C fluxes may produce partial or even misleading information. But most C partitioning studies are inevitably based on incomplete information about the components of GPP or NPP. In particular, Ra is rarely included as a direct measurement. Probably for that reason, the Ra–NPPbio trade-off (Fig. 3) has never previously been proposed. It should be stressed that our study is also based on incomplete C budgets, because unknown fractions of GPP such as root exudates and exports to mycorrhizal symbionts are always unaccounted for in any dataset. Reliably quantifying all C budget components in any ecosystem remains as elusive a prospect as ever. As indicated in the 'Datasets' section, a variety of methods have been used to estimate GPP and its components, especially Ra and NPPfroot. Testing the potential effects of different estimation methods on component estimates is impeded by having insufficient replication of data obtained by certain methods. Currently, the relative accuracy of most of these methods is unknown. Averaging over methods can reduce the uncertainties, but this is a compromise to allow some analyses to be made even if the data on which they are based are incomplete. Despite these limitations, our analysis identifies fundamental constraints on, and trade-offs among, components of GPP that determine the fate of C in forest ecosystems across the globe and which allow predictions to be made about their interactions and responses to climatic factors.


We thank all site investigators, their funding agencies, the various regional flux networks (Afriflux, AmeriFlux, AsiaFlux, CarboAfrica, CarboEurope-IP, ChinaFlux, Fluxnet-Canada, KoFlux, LBA, NECC, OzFlux, TCOS-Siberia, USCCC), and the Fluxnet project, whose support is essential for obtaining the measurements without which the type of integrated analyses conducted in this study would not be possible. The research was funded by the National Natural Science Foundation of China (Nos. 31130013 and 31000321), the Program for Changjiang Scholars and Innovative Research Team in University (PCSIRT) (No. IRT0960), and the Science Foundation of the Fujian Province, China (No. 2010J06009). We also thank three reviewers for their valuable comments on an earlier version of this paper.