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.
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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.