Issue 
Ann. For. Sci.
Volume 67, Number 4, June 2010



Article Number  410  
Number of page(s)  10  
DOI  https://doi.org/10.1051/forest/2009131  
Published online  02 April 2010 
Original article
Heartwood and sapwood allometry of seven Chinese temperate tree species
Allométrie du bois de cœur et de l’aubier pour sept espèces d’arbres tempérées chinoises
College of Forestry, Northeast Forestry University,
26 Hexing Road
Harbin, 150040, China
^{*} Corresponding author:
wangckcf@nefu.edu.cn
Received:
20
May
2009
Accepted:
9
October
2009
• Allometry of sapwood/heartwood is essential for understanding tree growth, water transport and carbon allocation, timber production and use, but such an allometry is lacking for Chinese temperate tree species.
• We studied the allometry and development of heartwood and sapwood for seven Chinese temperate tree species: Korean pine (Pinus koraiensis Sieb. et Zucc), Dahurian larch (Larix gmelinii Rupr.), Japanese elm (Ulmus davidiana Planch var. japonica (Rehd.) Nakai), Manchurian ash (Fraxinus mandshurica Rupr.), Manchurian walnut (Juglans mandshurica Maxim.), Amur corktree (Phellodendron amurense Rupr.), and Mongolian oak (Quercus mongolica Fisch.).
• All heartwood parameters investigated, including heartwood radius (HR), heartwood formation rate (HFR), heartwood ring number (HRN), heartwood initiation age (HIA), and heartwood volume ratio (HVR), were positively correlated with tree cambial age (CA). The HR, sapwood width (SW), sapwood area (SA), heartwood and sapwood volumes were significantly related to stem diameter at breast height (DBH) or xylem diameter. There was a polynomial relationship between the sapwood ring longevity (SRL) and sapwood ring number (SRN). However, most of the allometric relationships were speciesdependent. The hardwood formation patterns were different between coniferous and broadleaved tree species. A power function was suitable to scale SA from DBH, but the exponent varied from 1.32 for the larch to 2.19 for the corktree.
• Our allometry provided a practical means to assess wood development and related physiology for the temperate tree species.
Résumé
• L’allométrie de l’aubier/bois de cœur est essentielle pour comprendre la croissance de l’arbre, le transport de l’eau et l’allocation, la production et l’usage du bois, mais cette allométrie est manquante pour les espèces d’arbres chinoises de milieu tempéré.
• Nous avons étudié l’allométrie et le développement du bois de coeur et de l’aubier pour sept espèces d’arbres tempérées chinoises : le pin de Corée (Pinus koraiensis Sieb. et Zucc), le mélèze de Dahurie (Larix gmelinii Rupr.), l’orme du Japon (Ulmus davidiana Planch var. japonica (Rehd.) Nakai), le frêne de Mandchourie (Fraxinus mandshurica Rupr.), le noyer de Mandchourie (Juglans mandshurica Maxim.), le phellodendron de l’Amur (Phellodendron amurense Rupr.), et le chêne de Mongolie (Quercus mongolica Fisch.).
• Les paramètres du bois de coeur étudiés sont le rayon (HR), le taux de formation (HFR), l’âge d’initiation (HIA) et le ratio du volume (HVR) : ils sont corrélés positivement à l’âge cambial (CA). Le rayon du bois de cœur (HR), la largeur d’aubier (SW), la surface d’aubier (SA), les volumes de bois de cœur et d’aubier sont significativement liés au diamètre à hauteur de poitrine (DBH). Il y a une relation polynomiale entre la durée de vie des cernes d’aubier (SRL) et le nombre de cernes (SRN). Cependant la plus part des relations allométriques dépendent des espèces. Le patron de formation du bois de cœur diffère entre résineux et feuillus. Une fonction puissance est adaptée pour calibrer les variations de SA à partir de DBH mais l’exposant varie de 1,32 pour le mélèze à 2,19 pour le phellodendron de l’Amur.
• Pour les essences d’arbres tempérées, notre allométrie fournit un moyen pratique pour estimer le développement du bois en tenant compte de la physiologie qui y est associée.
Key words: allometric equation / heartwood formation / sapwood area / wood development
Mots clés : équations d’allométrie / formation du bois de cœur / surface d’aubier / développement du bois
© INRA, EDP Sciences, 2010
1. INTRODUCTION
The xylem of most mature trees is composed of heartwood in the inner part and sapwood at the periphery, which are histologically similar but physiologically different (Pinto et al., 2004). Developing allometry of sapwood/heartwood and exploring wood development are essential for understanding tree growth, water transport and carbon allocation, timber production and use (Mäkelä, 2002; Ogle and Pacala, 2009; Pinto et al., 2004), because (1) sapwood contains water conducting pipes (i.e., tracheids and vessels); (2) sapwood stores most carbohydrates for tree survival and growth (Hoch et al., 2003); (3) the living parenchyma cells in sapwood and sapwood growth contribute to most respiration cost of the whole tree (Pruyn et al., 2003); and (4) heartwood contains abundant extractives that improve heartwood natural durability and enhance the crown support (Taylor et al., 2002), although it is physiologically inactive in terms of water conduction and energy reserve materials.
Once heartwood formation begins, heartwood is added every year, and consequently the tracheids or vessels disuse simultaneously. However, there are no conclusive results on sapwood longevity and heartwood formation rate (HFR) yet. For instance, Yang and Hazenberg (1991a) reported a constant HFR (0.6 ring per year) for Populus tremuloides until 90 years old, while Knapic and Pereira (2005) found that the heartwood of Pinus pinaster increased 0.5 ring per year before 50 years old and 0.8 ring per year afterwards. The mean sapwood ring longevity varied with tree species, e.g., ∼ 45 y for Picea abies (Longuetaud et al., 2006), ∼ 67 y for Pinus sylvestris (Mäkelä, 2002). Up to now there are no data on sapwood transformation for Chinese temperate tree species.
Transpiration and stem respiration are tightly correlated to sapwood area (SA) for individual trees and stands (e.g., Damesin et al., 2002; Meinzer et al., 2001). A power function model for scaling SA from stem diameter has been widely accepted, but the universal exponent of 7/3 of the power function proposed by Enquist (2002) has been challenged. For example, Meinzer et al. (2005) investigated 25 temperate and tropical species, and reported that the exponents varied from 1.42 to 1.90 depending upon species groups. Clearly, more measurements on sapwood allometry for diverse tree species are needed for validating the theoretical model (Enquist, 2002).
In this study, we investigated the heartwood and sapwood development for seven temperate tree species in northeastern China. These species were Korean pine (Pinus koraiensis Sieb. et Zucc), Dahurian larch (Larix gmelinii Rupr.), Japanese elm (Ulmus davidiana Planch var. japonica (Rehd.) Nakai), Manchurian ash (Fraxinus mandshurica Rupr.), Manchurian walnut (Juglans mandshurica Maxim.), Amur corktree (Phellodendron amurense Rupr.), and Mongolian oak (Quercus mongolica Fisch.). Our objectives were to (1) develop allometric models of heartwood and sapwood parameters (e.g., heartwood radius, sapwood width, sapwood area, sapwood volume) for the seven tree species; and (2) examine development of sapwood (e.g., sapwood longevity, sapwood ring number) and heartwood (e.g., heartwood formation rate, heartwood initiation age) for the species. We hypothesize that (1) there are allometric relationships of sapwood/heartwood parameters on tree age or stem diameter, but the relationships are speciesdependent; (2) the characteristics of wood development differ significantly between coniferous and broadleaved tree species.
2. MATERIALS AND METHODS
2.1. Study area description
The research site is located at the Maoershan Forest Ecosystem Research Station in Heilongjiang Province (127°30′–34′ E, 45°20′–25′ N). The site has an average altitude of 400 m above sea level and an average slope of 10°–15°. The parent material is granite bedrock and the soil is Haplumbrepts or Eutroboralfs. The climate is continental monsoon climate with mean annual values: 700 mm precipitation, 884 mm evaporation , and 2.8 °C air temperature (Wang, 2006).
The primary forest was dominated by Korean pine mixed with such deciduous species as Betula spp., Populus spp., Quercus spp., Ulmus spp., etc. Since the turn of the 20th century, the forest was repeatedly harvested by largescale industrial logging. The current forests are mainly composed of secondary forest types (mainly Mongolian oak, mixed deciduous forest, hardwood forests) and plantations (mainly Korean pine and Dahurian larch plantations). In this study, we sampled trees from stands with 50 − 60 years old age, 1800 − 3100 trees ha^{−1} density, 12 − 22 cm mean diameter at breast height (DBH), and 27 − 40 m^{2} ha^{−1} basal area. Refer to Wang (2006) for details.
2.2. Field sampling
We sampled seven tree species, including Korean pine, Dahurian larch, Japanese elm, Manchurian ash, Manchurian walnut, Amur corktree, and Mongolian oak. For each species, two dominant, three codominant, three intermediate, and two suppressed healthy trees were destructively sampled in August 2004 (the elm trees were sampled in August 2005). Tree height (H, m) and DBH (cm) were measured after the tree was fallen. Stems were cut into 1 m sections. At the end of each stem section, a 5 cm thick disc was cut and taken to the laboratory for heartwood and sapwood measurements. The characteristics of the sampled trees were summarized in Table I.
Characteristics of the sampled trees for the seven tree species. DBH stands for stem diameter at breast height. The sample size for heartwood radius (HR), sapwood width (SW), heartwood ring number (HRN), and sapwood ring number (SRN) is provided. The age is the tree age at breast height.
2.3. Heartwood and sapwood determination
Each of the discs was planed and polished until the annual rings were clearly determined, and then scanned with a professional scanner equipped for a tree ring analyzer (Windendro2003, Regent Instruments Co., Canada). The heartwood radius (HR, cm), sapwood width (SW, cm), xylem radius (XR, the sum of HR and SW), annual ring numbers of heartwood (HRN) and sapwood (SRN), and cambial age (CA, the sum of HRN and SRN) were measured from 4 radial directions of each disc (north, south, east and west) with the Windendro2003, and averaged. The discs whose rings or heartwood could not be determined were excluded.
2.4. Data analysis
2.4.1. Calculation of heartwood and sapwood parameters
Sapwood area (SA, cm^{2}): assuming wood section and heartwood region were circular, we calculated SA as: (1)
Heartwood volume (HV, cm^{3}) and sapwood volume (SV, cm^{3}): the HV and xylem volume (XV, cm^{3}) for each stem segment were calculated as a truncated cone by the Simpson formula (Pinto et al., 2004): (2)where h was the stem segment length (cm). The A_{1} and A_{2} were the area of the two segment ends (cm^{2}). The tree top was only comprised of sapwood, of which the volume was calculated as a cone. The treelevel HV and XV were calculated by summing all stem segment volumes for the individual tree. The SV was computed as the difference between XV and HV. The Heartwood volume ratio (HVR) was defined as the ratio of HV to XV.
Heartwood formation rate (HFR, rings y^{−1}), heartwood initiation age (HIA, y) and heartwood initiation xylem radius (HIXR, cm): the slope of the function of HRN against CA represented the HFR (the rings transformed from sapwood to heartwood per year). The HIA was estimated by extrapolating the regressive curve of HRN against CA to zero HRN (Pinto et al., 2004). Similarly, the slope of the function of HR against XR represented the radial heartwood formation rate, and the extrapolation was HIXR.
Sapwood ring number (SRN) and sapwood ring longevity (SRL, y): the agedependent dynamic model of SRN was given by Mäkelä (2002): (3)where SRN(k) was the SRN at cambial age k. SRN(k) could also be written as equation (4) (Longuetaud et al., 2006). This formula permitted estimation of SRL by nonlinear regression (4)
To examine relationships between tree growth and wood development, we calculated three growth parameters: mean first decade ring width (MFRW, cm), mean last decade ring width (MLRW, cm), and mean sapwood ring width (MSRW, cm).
2.4.2. Statistical analysis
The Pearson’s correlation analysis was used to correlate sapwood and heartwood parameters across the seven tree species. A simple linear regression equation was fitted for HRN against CA, and HR against XR. The relationship of SRL against SRN across all species was fitted with a polynomial function.
The allometry of sapwood crosssectional area at breast height (i.e., sapwood basal area, SBA) against DBH was often described as a power function in the literature (Pruyn et al., 2003). To linearize the function, a loglog equation was fitted for all species as: (5)To correct for the systematic bias introduced by logarithmic transformation (Sprugel, 1983), a correction factor (CF) was computed for all equations. The regressions of SV, HV and XV against DBH or SBA were also fitted with the same equation form as equation (5). All the statistical analyses were performed with the SPSS 13.0.
3. RESULTS
3.1. Heartwood allometry
All heartwood parameters investigated (i.e. HR, HFR, HIA, and HVR) were positively correlated with the cambial age (CA) (Tab. II). The heartwood radius (HR) and heartwood volume ratio (HVR) were also significantly correlated with DBH, while heartwood formation rate (HFR) and heartwood initiation age (HIA) were not. The HFR was positively correlated to HR.
Correlation coefficients between heartwood and sapwood parameters across the seven tree species. The parameters examined includes cambial age (CA, y), stem diameter at breast height (DBH, cm), heartwood radius (HR, cm), sapwood width (SW, cm), heartwood formation rate (HFR, rings y^{−1}), heartwood initiation age (HIA, y), heartwood volume ratio (HVR), sapwood ring number (SRN), sapwood ring longevity (SRL, y), mean first decadal ring width (MFRW, cm), mean last decadal ring width (MLRW, cm), and mean sapwood ring width (MSRW, cm). The HR, SW, SRN, and ring widths are all at breast height.
Pooling the data across all tree species, the heartwood ring number (HRN) was linearly related to CA (HRN = 0.967CA − 6.82, n = 569, R^{2} = 0.97, P < 0.001), while HR was closely related to xylem radius (XR) (HR = 0.902XR − 0.632, n = 894, R^{2} = 0.97, P < 0.001). However, tree species significantly (P < 0.05) affected both intercepts and slopes of the equations. The speciesspecific linear models of HRN against CA explained > 91% variations in HRN (Tab. III), while those of HR against XR did > 97% variations in HR (Tab. IV). The mean heartwood formation rate (HFR) varied from 0.68 ring y^{−1} for the pine to 1.04 ring y^{−1} for the corktree. The HIA ranged from 4.2 y for the elm to 8.5 y for the ash. The HIXR varied from 0.2 cm for the corktree to 2.1 cm for the larch. The HFR and HIA of the conifers tended to be less than those of the angiosperms, whereas the HIXR showed a contrary pattern (Tabs. III and IV).
Allometric equations of heartwood ring number (HRN) against cambial age (CA, y) for the six tree species. The heartwood initiation age (HIA, y) is extrapolated from the equations. N and R^{2} are sample size and determination coefficient. The equations are all significant (P < 0.001).
Allometric equations of heartwood radius (HR, cm) against xylem radius (XR, cm) for the seven tree species. The heartwood initiation xylem radius (HIXR, cm) is extrapolated from the equations. N and R^{2} are sample size and determination coefficient. The equations are all significant (P < 0.001).
3.2. Sapwood allometry
The sapwood area (SA) was positively correlated with DBH and HR (Tab. II). Combined the data from different heights within a specific tree species, the sapwood width (SW) was positively correlated to stem diameter. The correlation coefficients ranked in an order of oak (0.79) > pine (0.75) > ash (0.69) > corktree (0.69) > walnut (0.43) > elm (0.43) > larch (0.40) (all P < 0.001).
Both sapwood ring number (SRN) and sapwood ring longevity (SRL) were negatively correlated to HFR and HVR (Tab. II). The SW was positively correlated to DBH and HR, but was not significantly affected by CA.
The SRL was ranked as: pine (13.0 ± 0.4 y, mean ± SE) > ash (9.8 ± 0.2 y) > larch (8.9 ± 0.2 y) > walnut (7.3 ± 0.1 y) > elm (5.2 ± 0.1 y) > corktree (4.4 ± 0.2 y). The SRL of the pine was nearly three times as great as that of the corktree. Pooling the data across the six species, we found a highly significant (P < 0.001) polynomial relationship between the SRL and SRN (Fig. 1).
Figure
1 Relationship between sapwood ring longevity (SRL) and sapwood ring number at breast height (SRN) across the six tree species. 
Combining the seven species, sapwood basal area (SBA) was significantly correlated to DBH on a logarithmic scale (log_{10}SBA = − 0.733 + 1.852log_{10}DBH, N = 63, R^{2} = 0.79, P < 0.001). However, tree species significantly affected the intercepts (P < 0.001) but not the slope (P = 0.181). The R^{2} of the speciesspecific equations varied from 0.71 to 0.96 (Tab. V).
Allometric equations of sapwood basal area (SBA, cm^{2}) against stem diameter at breast height (DBH, cm) for the seven tree species. The equations are of the form log_{10}SBA = a(log_{10}DBH) + b. The sample size (N), coefficients (a and b), determination coefficient (R^{2}), standard error of the regression (SEE), P values, and the logarithmic correction factor (CF) are given.
3.3. Heartwood and sapwood volumes
The heartwood volume ratio (HVR) was positively correlated to CA, DBH, HR and HFR, but negatively to SW (Tab. II). The xylem volumetric components were all significantly correlated with DBH on a logarithmic scale when the data for all species were combined (Figs. 2a–2c), among which the sapwood volume (SV) equation was the poorest (R^{2} = 0.81). The regression of log_{10}SV against log_{10}SBA substantially improved the fit (R^{2} = 0.97, Fig. 2d). However, all the relationships above were significantly affected by tree species (all P < 0.001).
Figure
2 Xylem volume (XV, cm^{3}) (a), heartwood volume (HV, cm^{3}) (b) and sapwood volume (SV, cm^{3}) (c) relating to stem diameter at breast height (DBH, cm), and SV relating to sapwood basal area (SBA, cm^{2}) (d) on a 10based logarithmic scale across the seven tree species. 
The speciesspecific equations provided better fittings than the generalized models for some species (Tab. VI). Overall, the regressions of SV against DBH had the largest variations among the xylem volumetric components (R^{2}: 0.70–0.98), while the larch had the poorest fitting (R^{2}: 0.70–0.90) among the seven species. Using SBA as the independent variable, instead of DBH, improved the speciesspecific allometric regressions of SV (R^{2} increased by 0.04–0.21).
Allometric equations relating xylem volume (XV, cm^{3}), heartwood volume (HV, cm^{3}), or sapwood volume (SV, cm^{3}) to stem diameter at breast height (DBH, cm) or sapwood basal area (SBA, cm^{2}) for the seven tree species. All slope coefficients are significant (P < 0.05). The sample sizes are 9, 6, 10, 10, 9, 10, and 6 for the pine, larch, elm, ash, walnut, corktree, and oak, respectively. The coefficients (a and b), determination coefficient (R^{2}), standard error of the regression (SEE), P values, and the logarithmic correction factor (CF) are given.
To exclude the effect of DBH on xylem volume (XV), heartwood volume (HV) and sapwood volume (SV) of the seven species, we standardized the DBH to 20 cm (Fig. 3). The greatest XV, HV and SV all occurred in the larch, whereas the least occurred in the corktree, the pine, and the corktree, respectively. The interspecific variability in SV was the greatest among the wood volumetric components.
Figure 3 Comparison of the xylem volume (XV), heartwood volume (HV) and sapwood volume (SV) among the seven tree species when standardizing the DBH to 20 cm. 
4. DISCUSSION
4.1. Heartwood allometry
The generalized allometric models between heartwood ring number (HRN) and tree age or between heartwood radius (HR) and stem diameter for the Chinese temperate tree species provide an important means to estimate the heartwood formation rate or sapwood mortality. However, the corresponding speciesspecific models did improve the fitting (Tabs. III and IV). This result was in accordance with previous studies on Acacia melanoxylon (Knapic et al., 2006), Populus tremuloides (Yang and Hazenberg, 1991a), and Eucalyptus globules (Miranda et al., 2006). Synthesizing the model forms of HRN against cambial age (CA) in the literature (Fig. 4), we found that the five angiosperms had an excellent linear fit of HRN against CA (R^{2} > 0.98) (Tab. III; Yang and Hazenberg, 1991a), whereas the seven conifers had divergent fits. In addition to the Korean pine and Dahurian larch in this study, the Norway spruce also had a linear relationship between HRN and CA (Longuetaud et al. 2006). The rest four coniferous species had a polynomial function (Fig. 4). We tried a quadratic equation of HRN against CA for the Korean pine and Dahurian larch, and slightly improved the fitting (the R^{2} increased by 0.01 compared to the linear model for both species). Longuetaud et al. (2006) also showed a better fitting of an agedependent HRN curvilinear model for the Norway spruce, although the authors did not provide comparative statistics for the linear and curvilinear models. However, we found that the curvilinear model failed to extrapolate the heartwood initiation age (HIA) for the Korean pine, Dahurian larch and Norway spruce (i.e. negative HIA), perhaps because of their relatively young age ( < 45 y). These results suggested that angiosperms and gymnosperms may have different heartwood formation patterns, which are related to the mean first decadal ring width (MFRW) (Tab. II). The heartwood rings of the angiosperms increased with a constant rate as trees age (e.g. Hazenberg and Yang, 1991; Tab. III), whereas those of some conifers increased slower (Tab. III) but progressively (e.g. Björklund, 1999; Fig. 4).
Figure 4 Comparison of allometric model forms of heartwood ring number (HRN) against cambial age (CA) for diverse tree species. The models for Picea mariana, Picea abies, Pinus sylvestris, Pinus pinaster 1, Pinus pinaster 2, Larix decidua, Populus tremuloides are from Hazenberg and Yang (1991b), Longuetaud et al. (2006); Björklund (1999); Pinto et al. (2004); Knapic and Pereira (2005); Nawrot et al. (2008); Yang and Hazengerg (1991a), respectively, whereas the others are from this study. 
The heartwood formation rates (HFR) in this study were within the range reported in the literature (0.5 − 1.0 ring y^{−1}) (Björklund, 1999; Hazenberg and Yang, 1991; Knapic and Pereira, 2005; Pinto et al., 2004; Yang and Hazenberg, 1991a). The HFR was positively correlated to heartwood volume ratio (HVR) but negatively to sapwood ring longevity (SRL) (Tab. II), illustrated that the faster the heartwood formed, the more the heartwood contributed to the trunk volume, and the shorter the sapwood ring longevity was.
All trees start heartwood formation once the trees reach certain size or age, but the HIA or heartwood initiation xylem radius (HIXR) was speciesdependent (Tabs. III and IV). The estimated HIA varied substantially among species (from 4 y for the Japanese elm in this study to 21 y for maritime pine, Knapic & Pereira, 2005). However, few studies validated the extrapolated HIA. We measured the HIA of Japanese elm and Manchurian ash saplings ( ∼ 10 years old) in a natural forest in this region, and found that the measured HIA was consistent with the estimated.
4.2. Sapwood allometry
Unlike HRN, the sapwood ring number (SRN) was not significantly correlated with tree age or DBH, but strongly with heartwood formation rate (HFR) and sapwood ring longevity (SRL) (Tab. II). The significant polynomial relationship between SRL and SRN across the six species (Fig. 1) illustrated that the more sapwood rings were associated with the greater sapwood longevity. This model provided a simple and practical way to estimate the longevity of parenchyma cell and conducting time of vessel included in the sapwood. The Korean pine had the greatest SRL ( ∼ 13 y) among the six tree species in this study (Fig. 1), which was still considerable less than that of Picea abies (45 y, Longuetaud et al., 2006) and Pinus sylvestris (67 y, Mäkelä, 2002).
The SRN was positively correlated with the mean first decadal ring width (MFRW), but negatively with the mean last decadal ring width (MLRW) (Tab. II). This nonmonotonic curve between SRN and the ring growth rate helped trees to maintain relatively constant development of sapwood with tree aging. Nevertheless, the sapwood width (SW) was monotonically increasing with the radial growth rate for all the species (Tab. II); it was also more closely correlated with the radial growth rate than the SRN. This result suggested that the amount of transformed sapwood should be expressed with the SW or SA in tree physiology, better than with the SRN. Similar relationship has been observed in Pinus pinaster (Knapic and Pereira, 2005) and Picea abies (Longuetaud et al., 2006; Sellin, 1994).
Allometry of SA attracts many scientists in tree physiology and forestry, because SA is an important parameter for estimating tree transpiration, stem respiration and leaf area (e.g., Wullschleger et al., 1998). The SW was positively related to the DBH but not to CA probably because of the positive correlation between SW and radial growth rates across the seven species, which varied with trees development (Tab. II). This result is in agreement with previous studies on Pinus pinaster (Knapic and Pereira, 2005), Pinus ridiata(Carrodus, 1972), Picea abies (Sellin, 1994), and Eucalyptus globules (Morais and Pereira, 2007).
Commonly, power functions or logtransformed linear models (e.g. Meinzer et al., 2001) have been used for SA allometry against stem diameter. Enquist (2002) proposed a power function for scaling SA from stem diameter with a universal exponent of 7/3 (i.e. 2.33). However, Meinzer et al. (2005) found that the exponents could be divided into at least three distinct species groupings, varying from 1.42 to 1.90 for the 25 temperate and tropical species investigated. Our data showed the exponents varied from 1.32 for the Dahurian larch to 2.19 for the corktree (Tab. V), supporting the notion proposed by Meinzer et al. (2005) but with a wider exponent range. This conclusion seems plausible because there are divergences in morphological and physiological properties of water conducting system for diverse species (Hacke et al., 2006). For example, conifer tracheids and angiosperm vessels can be substantial different in water conducting capacity (Hacke and Sperry, 2001).
4.3. Heartwood and sapwood volumes
Logtransformed linear models of xylem volume (XV), heartwood volume (HV) and sapwood volume (SV) against DBH fitted well with our data (Tab. VI), in agreement with previous studies (Pérez Cordero and Kanninen, 2003; Climent et al., 2003). However, Pruyn et al. (2003) reported that a logtransformed polynomial model provided a good fit for four coniferous species in the central Cascade Range, Oregon, USA. The discrepancy may result from their much greater DBH range (cf. Tab. I vs. 11–157 cm).
Heartwood is preferred to sapwood for carpentry and wood use mostly because of its natural durability (Taylor et al., 2002), whereas sapwood is physiologically functional because it stores and conducts labile carbon (Ogle and Pacala, 2009) and water (Wullschleger et al., 1998) in trees. Thus, quantifying HV or SV is necessary for selecting silvicultural practices and understanding carbon metabolisms of various tree species. Standardizing the DBH to 20 cm, we found that the Korean pine had only half HV as much as the Dahurian larch (Fig. 3). This result implies that the silvicultural practice for timber production should aim at planting larger size pine trees than the larch trees, because the two species are the dominant conifers for timber production in this region and HVR was positively correlated to CA and DBH (Tab. II).
The SV is often used to scale up stem respiration and transpiration from chamberbased or sapflow measurements to stand level (e.g., Damesin et al., 2002; Pruyn et al., 2003; Wullschleger et al., 1998). The largest variations in the regression of log_{10}SV on log_{10}DBH among the wood volumetric components showed the greatest interspecific difference in SV (Fig. 2). For trees with 20 cm DBH, the SV of the larch was considerably greater than the others in this study (2–8 times larger, Fig. 3), and more than twice of that of Thuja plicata (Pruyn et al., 2003), but similar to that of Pinus canariensis (Climent et al., 2003), Abies amabilis, Pseudotsuga menziesii and Tsuga heterophylla (Pruyn et al., 2003). Using sapwood basal area (SBA) as the independent variable substantially reduced the variability in the regression of SV (Fig. 2d and Tab. VI), suggesting that the interspecific variations in SV mainly come from crosssectional variation in sapwood. The great interspecific differences in SV may reflect divergent strategies of trees for carbon metabolism and storage of labile carbon (Ogle and Pacala) and water (Wullschleger et al., 1998).
5. CONCLUSIONS
The allometry of sapwood and heartwood for the Chinese temperate tree species was speciesdependent. Transformation of sapwood to heartwood was closely correlated with tree age, but angiosperms and gymnosperms may have different heartwood formation patterns. Sapwood ring number provided a practical proxy to estimate sapwood longevity, while sapwood width or area provided more robust physiological assessment. Power function was suitable to scale sapwood area from DBH, but the exponent varied with species. The great interspecific variation in sapwood volume, mainly attributed to crosssectional variation in sapwood, may reflect divergent strategies of trees for carbon metabolism and storage of labile carbon and water.
Acknowledgments
This research was supported by grants from the National Natural Science Foundation of China (No. 30625010), the Ministry of Science and Technology of China (No. 2006BAD03A0703), and Special Research Program for Publicwelfare Forestry (No. 200804001) to C.K. Wang. We thank Dr. JeanMichel Leban and two anonymous reviewers for their comments.
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All Tables
Characteristics of the sampled trees for the seven tree species. DBH stands for stem diameter at breast height. The sample size for heartwood radius (HR), sapwood width (SW), heartwood ring number (HRN), and sapwood ring number (SRN) is provided. The age is the tree age at breast height.
Correlation coefficients between heartwood and sapwood parameters across the seven tree species. The parameters examined includes cambial age (CA, y), stem diameter at breast height (DBH, cm), heartwood radius (HR, cm), sapwood width (SW, cm), heartwood formation rate (HFR, rings y^{−1}), heartwood initiation age (HIA, y), heartwood volume ratio (HVR), sapwood ring number (SRN), sapwood ring longevity (SRL, y), mean first decadal ring width (MFRW, cm), mean last decadal ring width (MLRW, cm), and mean sapwood ring width (MSRW, cm). The HR, SW, SRN, and ring widths are all at breast height.
Allometric equations of heartwood ring number (HRN) against cambial age (CA, y) for the six tree species. The heartwood initiation age (HIA, y) is extrapolated from the equations. N and R^{2} are sample size and determination coefficient. The equations are all significant (P < 0.001).
Allometric equations of heartwood radius (HR, cm) against xylem radius (XR, cm) for the seven tree species. The heartwood initiation xylem radius (HIXR, cm) is extrapolated from the equations. N and R^{2} are sample size and determination coefficient. The equations are all significant (P < 0.001).
Allometric equations of sapwood basal area (SBA, cm^{2}) against stem diameter at breast height (DBH, cm) for the seven tree species. The equations are of the form log_{10}SBA = a(log_{10}DBH) + b. The sample size (N), coefficients (a and b), determination coefficient (R^{2}), standard error of the regression (SEE), P values, and the logarithmic correction factor (CF) are given.
Allometric equations relating xylem volume (XV, cm^{3}), heartwood volume (HV, cm^{3}), or sapwood volume (SV, cm^{3}) to stem diameter at breast height (DBH, cm) or sapwood basal area (SBA, cm^{2}) for the seven tree species. All slope coefficients are significant (P < 0.05). The sample sizes are 9, 6, 10, 10, 9, 10, and 6 for the pine, larch, elm, ash, walnut, corktree, and oak, respectively. The coefficients (a and b), determination coefficient (R^{2}), standard error of the regression (SEE), P values, and the logarithmic correction factor (CF) are given.
All Figures
Figure
1 Relationship between sapwood ring longevity (SRL) and sapwood ring number at breast height (SRN) across the six tree species. 

In the text 
Figure
2 Xylem volume (XV, cm^{3}) (a), heartwood volume (HV, cm^{3}) (b) and sapwood volume (SV, cm^{3}) (c) relating to stem diameter at breast height (DBH, cm), and SV relating to sapwood basal area (SBA, cm^{2}) (d) on a 10based logarithmic scale across the seven tree species. 

In the text 
Figure 3 Comparison of the xylem volume (XV), heartwood volume (HV) and sapwood volume (SV) among the seven tree species when standardizing the DBH to 20 cm. 

In the text 
Figure 4 Comparison of allometric model forms of heartwood ring number (HRN) against cambial age (CA) for diverse tree species. The models for Picea mariana, Picea abies, Pinus sylvestris, Pinus pinaster 1, Pinus pinaster 2, Larix decidua, Populus tremuloides are from Hazenberg and Yang (1991b), Longuetaud et al. (2006); Björklund (1999); Pinto et al. (2004); Knapic and Pereira (2005); Nawrot et al. (2008); Yang and Hazengerg (1991a), respectively, whereas the others are from this study. 

In the text 