Pattern and control of biomass allocation across global forest ecosystems

Abstract The underground part of a tree is an important carbon sink in forest ecosystems. Understanding biomass allocation between the below‐ and aboveground parts (root:shoot ratios) is necessary for estimation of the underground biomass and carbon pool. Nevertheless, large‐scale biomass allocation patterns and their control mechanisms are not well identified. In this study, a large database of global forests at the community level was compiled to investigate the root:shoot ratios and their responses to environmental factors. The results indicated that both the aboveground biomass (AGB) and belowground biomass (BGB) of the forests in China (medians 73.0 Mg/ha and 17.0 Mg/ha, respectively) were lower than those worldwide (medians 120.3 Mg/ha and 27.7 Mg/ha, respectively). The root:shoot ratios of the forests in China (median = 0.23), however, were not significantly different from other forests worldwide (median = 0.24). In general, the allocation of biomass between the belowground and aboveground parts was determined mainly by the inherent allometry of the plant but also by environmental factors. In this study, most correlations between root:shoot ratios and environmental factors (development parameter, climate, altitude, and soil) were weak but significant (p < .01). The allometric model agreed with the trends observed in this study and effectively estimated BGB based on AGB across the entire database.

hypotheses have been corroborated by experimental data (Niklas, 2006;Yang, Fang, Ji, & Han, 2009). Biomass partitioning is described using the allometric model BGB = aAGB b , where a is a normalizing scaling constant, and b is an allometric scaling exponent (Huxley & Tessier, 1936;. BGB scales nearly isometrically with respect to AGB for both woody and nonwoody plants . This model has been validated across ecologically diverse species worldwide using plants with a wide range of total body mass at the individual plant level. (Niklas, 2005(Niklas, , 2006. Similarly, many allometric BGB-AGB models have also been proposed for the major forest types in China (Cheng & Niklas, 2007;Hui et al., 2014;Luo, Wang, Zhang, Booth, & Lu, 2012). These were based on community-level data sets. Some studies indicated that the scaling exponents between AGB and BGB varied by forest origin, phylogeny, leaf habit, forest type, stand age, and climate (Hui et al., 2014;Luo et al., 2012) on different scales. Others reported that using different regression methods might result in scaling exponent differences (Li, Han, & Wu, 2005). Although allometric models may be useful for predicting BGB at specific sites and in particular species (Brown, 2002;Li, Kurz, Apps, & Beukema, 2003;Mokany et al., 2006), more evidence is required to demonstrate a universal scaling relationship. Once this parameter is fully validated, allometric relationships can be applied to predict BGB across wide temporal and spatial scales.
Plants adjust their biomass allocation between the belowground and aboveground parts (root:shoot ratios) in ways characteristic of each species (Monk, 1966). Temperature, precipitation, solar radiation, soil texture, and resource availability (such as soil moisture and nitrogen) significantly affect biomass allocation (Mokany et al., 2006;Reich, 2002). In general, environmental stressors force plants to invest their resources in organ growth (Cairns et al., 1997;Cambui et al., 2011;Poorter & Nagel, 2000). Previous studies have investigated variations in the root:shoot ratios associated with species characteristics, stand development, stand density, resources, soil texture, and climate at the regional or global level (Cairns et al., 1997;Cambui et al., 2011;Mokany et al., 2006;Poorter & Nagel, 2000;Reich, 2002;, but they reported different findings. More evidence is needed to determine whether the root:shoot ratios responds on a large scale to biotic and abiotic factors.
Several studies have investigated the forests of China and cited significant findings (Hui et al., 2014;Luo, Wang, Zhang, Ren, & Poorter, 2013;Luo et al., 2012;Wang, Fang, & Zhu, 2008;, but these results may not be consistent with those of the forests elsewhere. The mechanisms by which plants partition photosynthate under environmental stress are incompletely understood. In the short term, the responses of the root:shoot ratios to biotic and abiotic factors are predictable for individual species (Chapin, 1980;Hawkins, Kiiskila, & Henry, 1999;Mooney et al., 1988;Vogel et al., 2008). Nevertheless, it is difficult to forecast large-scale biomass allocation patterns in response to biotic and abiotic stressors, and on a global scale, the results are inconsistent. In the effort to identify large-scale biomass allocation patterns across forest ecosystems, data were gathered from the literature worldwide for root:shoot ratios, BGB, and AGB or for standing leaf, stem, flower and fruit dry weights, respectively. Geographical factors, vegetation parameters, and environmental variables were also determined to evaluate biomass allocation in response to biotic and abiotic factors. Data were specifically collected for the forests of China. The following questions were addressed in this study: (1) on a global scale, how do trees partition their biomass between organs and between aboveground and belowground parts? (2) how does the allometric theory hold up at the individual plant and community levels?
(3) how do biotic and abiotic variables affect the root:shoot ratios? and (4) on a worldwide basis, how well does the allometric theory predict BGB (root biomass)?

| Data collections
All correlations between the root:shoot ratios and biotic and abiotic factors were analyzed using the data sets of Luo et al. (2012) and Mokany et al. (2006). Luo et al. (2012)  The estimated MAP was significantly correlated with the measured MAP (R 2 = .92, p < .01). The estimated MAT was also significantly correlated with measured MAT (R 2 = .90, p < .01). Soil texture data for the forests of China were obtained from texture maps (Institute of Soil Science, Chinese Academy of Sciences, 1986) and were based on the location (longitude and latitude) of the data site. For the Mokany et al. (2006) data set, missing MAT and MAP were estimated using a Local Climate Estimator (LocClim, FAO, 2002). This tool estimates basic climate variables from the latitude, longitude, and altitude. The accuracies of the estimated MAT and MAP were validated by comparing them with the literature measurements (Mokany et al., 2006).
The generality of the allometric partitioning theory was tested using two community-level data sets (i.e., Luo et al. (2012) and Mokany et al. (2006)) and one data set at the individual plant level(Enquist and Niklas (2002)). The latter data set included both woody and nonwoody plants. For woody plants, 346 biomass records were selected from Edwards (1983). Data for nonwoody plants in Enquist and Niklas (2002) were collected from primary literature published between 1987 and 2002. All standing biomass units were converted into kilogram of dry weight per plant. Enquist and Niklas (2002) cited 257 woody and nonwoody species, and more than one thousand dry mass measurements spanning ten orders of magnitude of AGB and BGB. Only biomass data (leaf, stem, and root biomass in kg dry matter/plant) were presented in the Enquist and Niklas (2002) data set.
Therefore, it was only used to analyze allometric relationships in plant organ biomass.

| Statistical analyses
Linear regression analysis was used to evaluate the relationship between the root:shoot ratios and biotic and abiotic factors. Ordinary least squares (OLS) were used to establish regression formulas to forecast BGB based on AGB measurements. The reliability of the BGB predicted from AGB measurements was determined by calculating the % prediction errors Pred.Error = Obs.BGB − Pred.BGB ∕Pred.BGB × 100 (Smith, 1980).  Niklas, 2005). Assuming that the roots are the only underground organs, M R = M B , then, The regression curve describing the allometric relationship had the form logM 1 = logβ+αlogM 2 , where M 1 and M 2 are the plant organ biomasses, logβ is the y-intercept of the regression curve (the allometric constant in RMA analyses), and α is the slope of the regression curve (the allometric scaling exponent in RMA analyses). Reduced major axis (RMA) regression was applied to establish allometric models for logtransformed data for BGB and AGB Niklas, 2005). The significance of the differences between slopes (allometric scaling exponent) of the RMA regression formulas was evaluated using the univariate analysis of variance function in SPSS V. 17.0.  (Figure 1).

| Factors influencing forest biomass and root:shoot ratios
Both AGB and BGB increased significantly (p < .01) with stand height, mean DBH, and stand age. On the other hand, both AGB and BGB were negatively correlated with stand density (p < .01). The root:shoot ratios decreased significantly (p < .01) with increasing stand height and mean DBH, and increased slightly with stand density (Figure 2).
There was no significant relationship between root:shoot ratios and stand age. The root:shoot ratios in clay and loam soils were significantly lower than those in sandy and sandy loam soils (Figure 3f). Clay loam soil,

| Allometric models
The scaling exponent of the allometric model for M B and M A ranged from 0.75 to 1.00 for woody plants Niklas, 2005). These predictions (α Pred. in Table 3) aligned with the trends in the entire database (Table 3). In general, data presented at the individual plant level (kg dry matter/plant)-fit best with the allometric model ( Figure 4; Table 3).

| Factors influencing forest biomass and root:shoot ratios
The response of root:shoot to various biotic and abiotic factors was examined. The variables included stand height, stand density, mean DBH, stand age, precipitation, temperature, ET, SH, altitude, and soil type. Previous reports have indicated that root:shoot ratios are either positively or negatively correlated with annual precipitation at the local or regional scale (Kang et al., 2013;Li et al., 2012;Wang et al., 2008) but decreased with increasing precipitation on the global scale (Mokany et al., 2006). Temperature also influenced the root:shoot ratios differently with region and vegetation type (Luo et al., 2013;Read & Morgan, 1996). Soil texture, nutrient availability, vegetation type, and plant structure also influenced the root:shoot ratios across ecosystems and regions (Mokany et al., 2006). Data sets based on specific regions and precise classifications may account for general tendencies in root:shoot ratio variations and explain the regional differences in the responses of the root:shoot ratios to the same factor.
A key contribution of this study is the investigation of the response of root:shoot to biotic and abiotic factors using a large worldwide database. The root:shoot ratios were negatively correlated with MAP and MAT and positively correlated with SH ( Figure 3). A comprehensive ET/PET index may best describe the response of the root:shoot ratios to climate. The root:shoot ratios also increased slightly with altitude.
This finding is consistent with previous studies (Leuschner, Moser, Bertsch, Roderstein, & Hertel, 2007;Luo et al., 2005). Changes in climate with altitude may cause variations in the root:shoot ratios.
In general, the root:shoot ratios increased with forest soil coarseness (from clay to sand). The root:shoot ratios were significantly higher in sand and sandy loam soils than those in clay and loam soils. The relatively lower water content and nutrient availability of coarse soil may explain the large root:shoot ratios. It is easier to sample root biomass from sandy than finer soils, and this property may also account for the higher root:shoot ratios in coarser soils (Mokany et al., 2006). with stand height, mean DBH, and stand age, these factors were only weakly (but significantly) correlated with the root:shoot ratios ( Figure 2). Therefore, the root:shoot ratios may be genetically stable despite multiple environmental stressors.
Young plantation stands (<10 years) were included in all analyses although they are affected by traditional practices such as selected harvest and thinning which may influence the root:shoot ratios (King et al., 2007;Sheng and Fan, 2005;Luo et al., 2012). The lack of field observations for these forests, however, prohibited further analysis in this study. Fortunately, there were very few young plantations included in the analysis, and so the effects of selected harvest and thinning on the root:shoot ratios can be safely ignored here.
Plants tend to adapt to environment variations by adjusting their root:shoot ratios (Friedlingstein, Joel, Field, & Fung, 1999;McConnaughay & Coleman, 1999). The analyses of this study indicated that biomass allocation between the belowground and aboveground parts is determined mainly by the inherent allometric relationships in the plant but also environmental factors. Most of the correlations between the root:shoot ratios and environmental parameters were significant (p < .01) but weak. Biomass allocation has been changing for thousands of years, whereas documented measurements of biomass, climate, and soil properties span only several decades. Most of the earlier studies on environment allocation correlations were based on data from sporadic experiments. One or two factors were studied, whereas the others were fixed or suppressed (Agren & Franklin, 2003;Gholz et al., 1991;Kellomaki & Wang, 1996;Li et al., 2012;Matsui, Fukuda, Inoue, & Matsushita, 2003;Read & Morgan, 1996). Nevertheless, biomass allocation is the result of complex environmental factors that short-term studies cannot represent. For this reason, despite decades of research, no strong or general correlations were found between biomass allocation and environment factors at the global scale.

| Allometric models
The regression slopes across the entire database at the individual plant level were predicted by models (α Pred. ;Niklas, 2005; Enquist and Niklas (2002) data set, the related regression curve coefficients improved (Table 3).
It is apparent that the allometric theory is completely empirical. The slopes and regression curve constants vary with region and vegetation type. Various data sets yield different slope and constants (Cheng & Niklas, 2007;Luo et al., 2012;Mokany et al., 2006;Yang et al., 2009).  Figure 5a). The percentage error of the BGB predicted by AGB using OLS regression formula decreased as AGB increased (Figure 5b). That is, the reliability of the OLS regression formula increased with AGB (or plant size) across global forest communities. The precise estimation of allocation patterns is essential for predicting global carbon budget and climate change, and for ecosystem modeling. Although many carbon allocation schemes were constructed in the last few decades, none of them accurately described the long-term allocation dynamics in various environments. The allometric theory empirically evaluates global root biomass but its scaling components vary with environmental conditions. It also indicates that it will be possible to trace biomass allocation and determine when it reaches homeostasis.

| CONCLUSION
Using a large database of global forest ecosystems, the root:shoot ratios and their responses to environmental factors were investigated in this study. Both aboveground and belowground biomass in the forests of China were lower than those of global forests. Nevertheless, the root:shoot ratios were not significantly different from each other. They were determined primarily from the inherent allometric relationships of plants, but they were significantly affected by developmental parameters, climate variables, altitude, and soil (p < .01).
The root:shoot ratios responded to changes in mean annual temperature, mean annual precipitation, and the potential water deficit index. They were negatively correlated with mean annual precipitation, mean annual temperature, and potential water deficit. Soil texture, developmental parameters, and climatic conditions influenced the magnitudes of the root:shoot ratios. The allometric theory aligned with the trends observed in this study and correctly estimated BGB based on AGB for the entire database.
F I G U R E 4 Allometric plots of logtransformed data for (a) leaf and stem biomass(Sig. p = 0), (b) root and stem biomass (Sig. p = 0), (c) root and leaf biomass (Sig. p = 0), and (d) below-and aboveground biomass (Sig. p = 0). Solid lines represent OLS regression curves for the Niklas (2005) and Niklas and Enquist (2002) and community-level data sets. All correlations are significant at p < .01. Sig. p indicates the significance of difference in the slopes of the linear regression between two data sets. Sig. p > .05 means no significant difference in regression slopes; Sig. p < .05 means significant difference in regression slopes F I G U R E 5 Accuracy of OLS regression formulas in predicting BGB based on AGB. (a) correlation analysis between measured and predicted BGB, and (b) variation in percentage prediction error with AGB