Height-dependent changes in shoot structure and tree allometry in relation to maximum height in four deciduous tree species

Authors


Correspondence author. E-mail: osadada@kais.kyoto-u.ac.jp

Summary

1. Tree allometry often varies among coexisting species of different maximum height (Hmax) in forests. Although shoot growth patterns directly influence overall tree architecture, the structures of current-year shoots at the tops of crowns have not been directly related to differences in tree allometry across species.

2. I investigated height-dependent changes in structure and biomass allocation patterns in current-year shoots of four coexisting tree species differing in Hmax in a cool-temperate forest in Japan. The relative importance of total biomass, biomass allocation, shoot allometry, and shoot angle to vertical growth was quantified and compared with tree allometry.

3. Height-dependent changes in total biomass of current-year shoots varied across species. In contrast, stem length per unit mass, shoot angle, and total leaf area per unit stem cross-sectional area decreased, and leaf mass per unit area increased with height in all species. Vertical growth rate consequently declined with increasing height in all species. Sensitivity analyses revealed that the primary determinant of declining vertical growth rate was change in stem length per unit mass; shoot angle was a secondary determinant. In contrast, increases in total shoot mass with height modulated declining vertical growth rates.

4. Vertical growth rate was greater in two canopy species than in two sub-canopy species at given heights at the shoot level, and this pattern coincided with allometry between tree height and trunk diameter. In contrast, vertical growth rate was greater in sub-canopy species than in canopy species near their maximum heights. These patterns suggest that allometric differences between species may be useful for evaluating crown-development patterns, but not for estimating Hmax of species.

Introduction

Each tree species has its own maximum attainable height, and various tree species coexisting in a forest partition a vertical height gradient from small understorey species to large canopy species (e.g. Kohyama 1993; Thomas 1996; Poorter et al. 2005). Crown allometry reflects patterns of biomass allocation, height growth, leaf display, and light capture strategies of individual species. Consequently, differences in crown allometry among coexisting species have been related to differences in species position (i.e. niche) in forests (Kohyama 1987; King 1990, 1996; Aiba & Kohyama 1996; Thomas 1996; Poorter, Bongers & Bongers 2006). For example, vertical growth is considered more important for species of greater maximum height (Hmax), whereas lateral crown expansion is more important for species of smaller Hmax (King 1996). Various studies have indeed shown that tree height at a given dbh (diameter of trunk at breast height) tends to be greater for species with greater Hmax, at least for some ontogenetic stages (Aiba & Kohyama 1996; Thomas 1996; Kohyama et al. 2003; Poorter, Bongers & Bongers 2006; Aiba & Nakashizuka 2009).

Tree crowns develop through repetitive production of growth units (e.g. current-year shoots of temperate trees with an annual flush phenology) (Maillette 1982; Harper 1989; Room, Maillette & Hanan 1994; Barthelemy & Caraglio 2007), i.e. by changing the number, size, structure, position and orientation of growth units (Maillette 1982; Jones & Harper 1987; Koike 1989; Wilson 1989). The structure of growth units provides essential information about patterns of crown development over short time-scales that may not be detectable in tree-level measures, such as growth in trunk diameter, height and overall crown size (Passo, Puntieri & Barthelemy 2002; Heuret et al. 2006; Osada 2006). In trees with large crowns, analysis of growth unit structure is particularly useful for evaluating cost/benefit relationships during crown development; i.e. biomass investment and resulting light capture and growth at the shoot level (Falster & Westoby 2005). This approach expands our understanding of the process of crown development (Osada 2006).

The structure and allometry of growth units of a given species tend to change with tree height in both tropical and temperate tree species (Osada et al. 2002, 2004b; Osada 2006). Qualitative patterns are similar among the species examined; the diameters of growth units increased and lengths decreased with increasing tree height, resulting in shorter lengths per unit biomass in growth units of taller conspecific trees. Such patterns are noteworthy because, regardless of differences in developmental constraints between shoots and individual trees as described above, height-dependent changes in the diameter–length relationships of shoots are similar to the diameter–height relationships of individual trees. Moreover, the ratio of total leaf area to either stem cross-sectional area or shoot sapwood area decreases with height in a range of tree species (Osada et al. 2002, 2004b; Osada 2006; Beikircher & Mayr 2008; Ambrose, Sillett & Dawson 2009; Zhang et al. 2009). These changes in the architecture and allometry of shoots will necessarily affect crown growth patterns.

In addition to shoot allometry, shoot elevation angle is highly variable, both between and within species (King 2001; Kikuzawa 2003; Kawamura & Takeda 2004; Niinemets, Cescatti & Christian 2004), and directly influences patterns of crown development; i.e. vertical growth is reduced when a branch at the crown apex is inclined. Shoot angle indeed changed from vertical to horizontal with increasing tree height and influenced the vertical growth rate of the deciduous pioneer tree species Rhus trichocarpa (Osada 2006). Osada (2006) further quantified the relative effects of biomass, allometry, and angles of current-year shoots on vertical growth and found that height-dependent changes in shoot allometry and angle contribute similarly to a reduction in vertical growth with increasing height in R. trichocarpa. Evaluation of relative effects of various shoot traits on vertical growth might be of particular importance because height-dependent changes in shoot traits may be related to Hmax of a species; i.e. changes in traits with absolute height may be steeper for species with smaller Hmax. This is because shoot traits influence the rate of vertical growth, and vertical growth may become more costly as trees approach their maximum height. To my knowledge, however, no studies have related height-dependent changes in shoot traits to Hmax of multiple coexisting species.

Because of the above-mentioned variability in the relative importance of vertical growth and lateral crown expansion among species differing in Hmax, allometry and angles of shoots may be related to Hmax across a suite of coexisting species. I predicted that: (i) height-dependent changes in shoot allometry would be steeper for species with smaller Hmax; and (ii) species with greater Hmax would have shoots of larger elevation angles at given tree heights. Moreover, I predicted that (iii) vertical growth rate would be higher for species with greater Hmax at given heights, in accordance with differences in tree allometry.

Based on these predictions, I investigated height-dependent changes in the structure and biomass allocation patterns of current-year shoots in four coexisting tree species with different Hmax, Fagus crenata Blume (Fagaceae), Betula ermanii Cham. (Betulaceae), Sorbus commixta Hedl. (Rosaceae), and Acer tschonoskii Maxim. (Aceraceae), in a cool-temperate forest in Japan. By comparing these four species, I determined whether height-dependent changes in allometry and elevation angle of current-year shoots were similar across species differing in Hmax. The relative importance of total biomass, biomass allocation, shoot allometry, and angle to height growth were quantified for these four species, and differences in shoot growth patterns across species were related to differences in tree allometry.

Materials and methods

Study site and species

The study was conducted at Hakkoda Botanical Garden, Tohoku University (40°38′N, 140°51′E). Monthly mean temperature and rainfall during the growing season (June–October) are 13·9 °C and 179·6 mm, respectively, at the Sukayu meteorological station, about 200 m from the garden (890 m asl, 1979–2000). There is snow cover from November to May, with a maximum depth of >3 m at the station. This garden includes a cool-temperate forest, dominated by F. crenata, B. ermanii and Abies mariesii Mast. (Pinaceae) in the canopy layer (>10 m high); S. commixta, A. tschonoskii and Acanthopanax sciadophylloides Franch. et Sav. (Araliaceae) form a sub-canopy layer (6–8 m), while Ilex sugerokii Maxim. var. brevipedunculata (Maxim.) S.Y. Hu (Aquifoliaceae), Rhododendron brachycarpum D. Don ex G.Don and R. albrechtii Maxim. (Ericaceae) make up an understorey layer (3–5 m).

Four dominant deciduous tree species, F. crenata, B. ermanii, A. tschonoskii and S. commixta, were chosen as study species. Fagus crenata and B. ermanii are canopy species that grow to 12–13 m high. Sorbus commixta and A. tschonoskii are sub-canopy species reaching c. 8–9 m and 5–6 m maximum height, respectively, at this study site (N. Osada, unpublished data). Sorbus commixta produces compound leaves; the other three species produce single leaves.

Allometry of dbh and height

Trunk dbh and tree height were measured on 15, 15, 10 and 8 trees of F. crenata, B. ermanii, S. commixta and A. tschonoskii, respectively. All the chosen trees were in well-lit sites. The allometric relationship between dbh and height often becomes asymptotic because growth patterns differ between dbh and height; vertical growth levels off while diameter continues to increase (Aiba & Kohyama 1996; Thomas 1996). I first fitted quadratic regressions to the relationships between height and dbh to check whether these asymptotic patterns also occurred in the four selected species. There was no significant asymptotic relationship in the four species (= 0·13–0·93 for the quadratic regressions). I therefore fitted standard major axis regression to the relationships between dbh and height; the slopes and intercepts were compared among species using the smatr software (Falster, Warton & Wright 2006).

Measurement of current-year shoot structure

I selected 12, 10, 10 and 8 trees of F. crenata, B. ermanii, S. commixta and A. tschonoskii, respectively, from among the trees used for trunk allometry measurements. These individuals fell into a continuous range of height classes from small saplings to tall trees, and all were growing in high-light sites.

Photon flux density (PFD) was measured under overcast skies using quantum sensors (LI-190SA; Li-Cor, Lincoln, NE, USA). A sensor was fixed to the top of an extension pole (15-m long), and the pole was extended to insert the sensor horizontally at the crown tops. At the same time, PFD was measured in an open area. Relative PFD (PFD relative to PFD in the open area) was 64–100%. Light was thus considered to be well above light saturation points in all trees, regardless of height.

In July–September 2008, the leader crown (the leading section of the main trunk, 100 cm in length) was harvested from each tree. For tall trees, leader crowns were harvested with a pruning hook using ladders to reach the crowns. Each leader crown contained more than 10 current-year shoots. At the time of harvest, the leaves of all current-year shoots within these leader crowns were fully expanded and hardened, but had not yet become senescent. Average shoot angle was measured by positioning each leader crown in a natural orientation. Ten to 16 current-year shoots with no obvious damage were chosen randomly and cut from each leader crown. The lengths and basal diameters of current-year stems were measured shortly after harvesting. Three discs 1 cm in diameter were punched from each individual leaf. All stems, petioles and stalks, and leaf laminae were then oven-dried at 70 °C and the dry masses were measured. Leaf mass per unit area (LMA) was calculated as the ratio of mass to area in three leaf discs.

Analysis of current-year shoot structure

Total biomass, stem mass, total leaf mass, stem mass fraction (SMF: ratio of stem mass to total mass), and leaf mass fraction (LMF: ratio of leaf lamina mass to total biomass) were determined for each current-year shoot. Masses of leaf petioles and stalks were included in the total mass, but were not included in leaf mass and stem mass estimates. Total leaf mass was divided into leaf number and mean individual leaf mass; mean individual leaf mass and LMA determined mean individual leaf area.

Sensitivity analyses of vertical growth rate and total leaf area per shoot

Vertical growth of current-year shoots was calculated from total mass of current-year shoots, SMF, the allometric relationship between length and mass of current-year stems, and elevation angles of shoots. I then investigated the effects of height-dependent changes in these variables on vertical growth by simulating hypothetical shoots. Hypothetical shoots were computed by separately fixing the masses of current-year shoots (mass effect), SMF (allocation effect), stem allometries (allometry effect) and shoot angles (angle effect) to values for 2-m high trees of each species.

Similarly, total leaf area per current-year shoot was calculated from the total mass of current-year shoots, LMF and LMA. The effects of height-dependent changes in these variables on total leaf area were simulated by separately fixing the masses of current-year shoots (mass effect), LMF (allocation effect), and LMA (LMA effect) to values for 2-m high trees of each species. Based on these analyses, I quantified the relative effects of height-dependent changes in these variables on the rates of vertical growth and total leaf area of current-year shoots in the four species.

Results

Tree allometry and height-dependent changes in traits of current-year shoots

The allometric slope of SMA did not differ significantly (= 0·36) among the four species, but the intercept did (< 0·001; Fig. 1 and Table 1). The intercept was higher in canopy species (F. crenata and B. ermanii) than in sub-canopy trees (S. commixta and A. tschonoskii).

Figure 1.

 Relationships of tree height against trunk dbh in four species. See Table 1 for statistical results.

Table 1.   SMA regression analyses of allometric relationships between log (tree height) and log (trunk dbh) across four species, where tree height is given in m and dbh is in cm. (common slope = 0·548)
SpeciesnR2InterceptP-value of difference in intercept
Fagus crenataBetula ermaniiSorbus commixta
F. crenata150·9350·259   
B. ermanii150·9530·2840·21  
S. commixta100·8950·1810·00480·0001 
A. tschonoskii80·9270·1970·0160·00020·60

Total biomass of individual current-year shoots was quadratically related to height in B. ermanii (reaching a maximum in 6–7 m tall trees), linearly increased with height in F. crenata, and was not related to height in S. commixta or A. tschonoskii (Fig. 2 and Table S1 in Supporting Information). SMF decreased with height in F. crenata, but was not correlated with height in the three other species. Thus, stem mass was not related to height in any of the species (Table S1). Total leaf mass was quadratically related to height in B. ermanii and linearly related to height in F. crenata; there were no such correlations for S. commixta or A. tschonoskii (Table S1). Total leaf area was quadratically related to height in B. ermanii, but unrelated to height in the other species (Fig. 2).

Figure 2.

 Height-dependent changes in total mass and stem mass fraction (SMF), and total leaf area (TLA) of current-year shoots of leader crowns in four species. Note that the y-axis scales differ among species. Vertical bars indicate standard errors. Solid and dotted lines indicate regressions of significant and insignificant relationships, respectively.

In contrast to these variable patterns of biomass allocation, stem length per unit mass decreased and LMA increased with height in all species (Fig. 3). The slopes of the allometric relationship between stem length per unit mass and tree height did not differ among species, but intercepts did (Table 2). In contrast, slopes of the allometric relationship between LMA and height differed among species; the slope was steeper in F.crenata than in other species.

Figure 3.

 Height-dependent changes in stem length per unit mass (L/SM) and leaf mass per unit area (LMA) of current-year shoots in leader crowns of the four species. Note that the y-axis scales differ among species. Vertical bars indicate standard errors.

Table 2.   Analysis of covariance (ancova) for differences in various shoot traits among species and tree heights
Traits*Species × HeightSpeciesHeight
FPFPFP
  1. *L/SM, stem length per mass (cm g−1); LMA, leaf mass per area (g m−2); TLA/XA, total leaf area per stem cross-sectional area (cm2 cm−2); TLM/XA, total leaf mass per stem cross-sectional area (g cm−2).

  2. †Analysis was performed after log-transformation of height (x-axis) and traits (y-axis).

L/SM†0·600·6296·85<0·000188·28<0·0001
LMA†2·980·046    
TLA/XA†0·890·4682·13<0·000120·63<0·0001
TLM/XA†2·610·06876·42<0·00010·0140·91
Angle0·450·724·550·008621·20<0·0001

As a consequence, shoot length decreased with height in F. crenata and B. ermanii, but was not related to height in the other species (Fig. 4). Shoot angle decreased with height in all species; slopes did not differ, but intercepts did differ among species (Fig. 4 and Table 2). The allometric relationship of total leaf area per stem cross-sectional area against height decreased with height in all species; the slope did not differ among species but the intercept did (Fig. 4 and Table 2).

Figure 4.

 Height-dependent changes in stem length, elevation angle, and total leaf area per stem cross-sectional area (TLA/XA) of current-year shoots in leader crowns of the four species. Note that the y-axis scales differ among species. Vertical bars indicate standard errors. Solid and dotted lines indicate regressions of significant and insignificant relationships, respectively.

Sensitivity analyses of vertical growth rate and total leaf area per shoot

Vertical growth rate (calculated from total mass, SMF, stem length per unit mass and shoot angle) decreased concavely with height in F. crenata and A. tschonoskii, convexly with height in B. ermanii, and changed little with height in S. commixta (Fig. 5). With increase in height from 2 m to maximum height (13 m in F. crenata and B. ermanii, 9 m in S. commixta and 6 m in A. tschonoskii), vertical growth rate decreased from 70 to 15 mm per year in F. crenata, from 89 to 5 mm per year in B. ermanii, from 34 to 28 mm per year in S. commixta and from 57 to 31 mm per year in A. tschonoskii. Changes in stem allometry (stem length per unit mass) strongly reduced vertical growth rate with height in all species (39%, 48%, 59% and 58% of vertical growth was attained at the maximum height for F. crenata, B. ermanii, S. commixta and A. tschonoskii, respectively, compared with a simulation of constant allometry). Height-dependent changes in shoot angle slightly reduced vertical growth rates in all species (60%, 73%, 87% and 79% of vertical growth was attained at the maximum height compared with the constant-angle simulation, respectively). Also, changes in SMF weakly decreased vertical growth rates in F. crenata, B. ermanii and A. tschonoskii (53%, 91% and 93% of vertical growth was attained at the maximum height in comparison with the constant SMF simulation, respectively), but not in S. commixta (152%). In contrast, changes in total mass with height increased vertical growth rate in all species except B. ermanii (168%, 19%, 105% and 128% of vertical growth was attained at the maximum height compared with the constant mass simulation in F. crenata, B. ermanii, S. commixta and A. tschonoskii, respectively), because the total mass of current-year shoots was somewhat greater for the trees of maximum height than for those of 2-m tall in F. crenata, S. commixta and A. tschonoskii.

Figure 5.

 Sensitivity analyses of effects of changes in total mass, stem mass fraction (SMF), stem length per unit mass (L/SM), and shoot angle on vertical growth rates in the four species. Note that the y-axis scales in the upper panels differ among species. Closed circles, open circles, triangles, squares and crosses indicate simulations calculated from parameters for real shoots, shoots of constant total mass (total mass at 2 m height was fixed for the whole range of heights), constant SMF (SMF at 2 m height), constant shoot allometry (L/SM at 2 m height) and constant angle (shoot angle at 2 m height), respectively. Relative effects of height-dependent changes in total mass, SMF, L/SM, and angle are depicted in the lower panels.

Height-dependent changes in total leaf area per current-year shoot were smaller than those in vertical growth except in B. ermanii (Fig. 6). As trees grew from 2 m to their maximum heights, total leaf area changed from 111 to 99 cm2, 82 to 11 cm2, 382 to 279 cm2 and 15·3 to 15·1 cm2 in F. crenata, B. ermanii, S. commixta and A. tschonoskii, respectively. In all species, changes in total mass with height compensated for the negative effects of increased LMA, and the effect of LMF was small.

Figure 6.

 Sensitivity analyses of effects of changes in total mass, leaf mass fraction (LMF) and leaf mass per unit area (LMA) on total leaf area per shoot in the four species. Note that the y-axis scales in the upper panels differ among species. Closed circles, open circles, triangles and squares indicate simulations calculated from parameters for real shoots, shoots of constant total mass (total mass at 2 m height fixed across the whole range of heights), constant LMF (LMF at 2 m height) and constant LMA (LMA at 2 m height), respectively. Relative effects of height-dependent changes in total mass, LMF and LMA are depicted in the lower panels.

Discussion

Fine-scale analyses of growth patterns at the shoot level are useful to relate shoot traits to various constraints such as biomechanical stresses (Sterck, Vangelder & Poorter 2006; Anten & Schieving 2010; Larjavaara & Muller-Landau 2010), and provide information that complements the whole-tree patterns of allometry and biomass allocation (King 2005). In this study, various traits of current-year shoots in upper crowns changed with height in the four studied species (Figs 2–4). Depending on the trait, patterns of change were either similar or different among species (i.e. shoot mass and SMF changed with height differently among species, while stem length per unit mass, shoot angle and total leaf area per unit stem cross-sectional area changed similarly across species; Table 2). The predictions that changes in shoot allometry and shoot angle with height differ across species of different Hmax were not confirmed because of the non-significant interaction between species and height (Table 2). This outcome resulted from large differences in shoot mass and SMF among species, and these interacted with shoot allometry and angle to determine vertical growth patterns of the four species.

As a tree grows, biomass allocation to the trunk and branches inevitably increases due to the increasing proportions of these supporting tissues at the whole-tree level. From this viewpoint, the effects of tree allometry and biomass allocation on growth at the tree level have been investigated in a simulation model (King 2005), but the effects of shoot traits on height growth have not been considered in detail. Recent studies have related differences in biomass allocation and shoot allometry to height growth strategies of species (Falster & Westoby 2005) and to environmental factors such as water stress and altitude (Preston & Ackerly 2003; Westoby & Wright 2003; Sun, Jin & Shi 2006; Xiang et al. 2009). These works focused primarily on differences across species and sites, and did not consider height-dependent changes in shoot traits within species. In this study, four coexisting species exhibited similar height-dependent quantitative changes in shoot allometry; i.e. slopes did not differ significantly for the allometric relationships between stem length per unit mass and height (Table 2). This suggests that biomass per unit shoot extension increased similarly with increasing height in the four species. Moreover, total leaf area per unit stem cross-sectional area decreased similarly with height among species (Fig. 4). The nature of stem growth (sequential development by geometrical configuration, with annual increases in both diameter and length) may inevitably give rise to such patterns, regardless of species, shoot structure and leaf size (Osada 2006). Changes in environmental factors with height, such as water and mechanical stresses, may also affect shoot allometry. However, this may not be the reason for qualitatively similar height-dependent changes in shoot traits of the four species, as wood density differed largely across these species. This study further suggests that when shoots are compared for trees of different sizes across multiple species, differences in shoot traits among species may be confounded with height-dependent changes.

Consistent with previous studies (Niinemets & Kull 1995; King 1999; Cavender-Bares & Bazzaz 2000; Rijkers, Pons & Bongers 2000), LMA increased with height independently of light conditions in all species. In this study, the slope of the allometric relationship between LMA and height differed among species. In contrast to the prediction that ontogenetic changes in LMA are larger in shade-intolerant than in shade-tolerant species (Niinemets 2006), the highly shade-tolerant species F. crenata had greater ontogenetic changes in LMA than the other species.

Shoot elevation angle decreased with height in all species, as in R. trichocarpa (Osada 2006). The slopes of the relationship between shoot angle and height did not differ across species in this study, although there was large variation and a comparison of only four species may limit interpretation. This pattern contrasts with the within-crown branch angle patterns of growing trees, the branch angle of which is steeper in upper than in lower crowns (Osada & Takeda 2003; Sone, Noguchi & Terashima 2006). Moreover, branch orientation often shifts from plagiotropic in small trees to orthotropic in tall trees (Hallé, Oldeman & Tomlinson 1978; King & Maindonald 1999). Such changes are thought to result from changes in light availability within forests and may be related to effective growth and leaf display within crowns. In this study, all trees were selected from high-light sites and thus changes in light availability would not have been relevant. Shoot angles are indeed less steep in low-light saplings than in high-light saplings and in tall trees of F. crenata, S. commixta and A. tschonoskii (N. Osada, unpublished data). Complex crown architecture develops through reiteration from dormant buds in tall trees (Hallé, Oldeman & Tomlinson 1978; Edelin 1990; Barthelemy & Caraglio 2007). Shoot angle may thus become more variable within the crowns in taller trees. Regardless of this complexity of crown maintenance patterns in tall trees, shoot angles of leader crowns decreased with height in all four species, suggesting that shoot angle in leader crowns represents changes in the importance of vertical growth with increasing height.

Overall, vertical growth rate declined with increasing height in all species, but the rate of decline differed between species (Fig. 5). Sensitivity analyses revealed that declines in vertical growth rate were determined primarily by changes in stem allometry (stem length per unit mass) in all species (other than maximum-size trees of B. ermanii), and secondarily by changes in shoot angle (except in F. crenata). Effects of total mass were positive, and the increase in total mass compensated for declining vertical growth rate. On the other hand, height-dependent changes in total leaf area per current-year shoot were affected primarily by increases in LMA and total mass. The increase in total mass of current-year shoots with height modulated the negative effect of increasing LMA with height except in tall trees of B. ermanii. These results suggest that height-dependent increases in the costs of stem extension (stem length per unit mass) and of leaf area deployment (leaf area per unit mass) are key factors affecting vertical growth rate and shoot productivity in the four species.

It is noteworthy that the two canopy species with similar Hmax had quite different patterns of height-dependent change in shoot mass; shoot mass increased linearly with height in F. crenata, but convexly in B. ermanii. This suggests that productivity at the shoot level may not be limited even at near maximum height in F. crenata. Stem mass decreased, but leaf mass increased with height, and the increase in leaf mass compensated for the increase in LMA, resulting in constant leaf area per shoot in F. crenata. In contrast, reduction in total mass directly affected vertical growth rate and total leaf area in tall trees of B. ermanii, although changes in shoot allometry were predominant in trees of small-to-medium size. These results suggest that patterns of shoot structure and growth differed even for the species of similar Hmax.

Vertical growth rate was higher in the two canopy species than in the two sub-canopy species at given heights for the trees of 1–6 m in height. This pattern is consistent with the prediction based on differences in trunk allometry (Fig. 1); vertical growth of juveniles is more important for the survival and growth of canopy species than of sub-canopy species. This strongly suggests that differences in trunk allometry across species may be useful in evaluating patterns of crown development. On the other hand, vertical growth rate at near maximum height (13 m in F. crenata and B. ermanii, 9 m in S. commixta and 6 m in A. tschonoskii) was higher in sub-canopy species than in canopy species, suggesting that vertical growth rate of shoots cannot be used to estimate Hmax of a species. This may correspond to the non-asymptotic relationships and similar slopes of tree height against trunk diameter for all species in this study. In previous studies, the presence of species with non-asymptotic relationships of tree height against trunk diameter depended on the forests studied. For example, an asymptotic relationship was found for canopy species but not for understorey species in a Bolivian tropical forest (Poorter, Bongers & Bongers 2006), but was found for all species in a Japanese temperate forest (Aiba & Nakashizuka 2009).

Caution must be exercised in comparing the results of this study with previous studies. First, height and light generally interact within forests, and their effects have been confounded in previous studies of tree allometry; i.e. the light environment of saplings and small trees may differ among species and may also differ from tall conspecific trees. In this study, I selected only high-light trees to avoid such interactive effects, and this may have affected the outcome. For example, if tree height at a given trunk diameter is shorter in low-light saplings than in high-light saplings, the allometric relationship will be more quadratic with a convex shape when trees regenerating in the shaded understorey are included. Alternatively, relatively small differences in crown architecture between high- and low-light trees of small size may be obscured by large differences in crown architecture between large and small conspecific trees (Osada et al. 2004a). To better understand ontogenetic growth patterns of tree species, the effects of light and height should be distinguished as in this study, while the interactive effects of light and height should be included when the growth of tree species is evaluated in association with their regeneration patterns in the forests.

Second, the non-asymptotic relationship between trunk allometry of height and dbh may result from heavy snow cover in winter at this study site. If rapid turnover of leader shoots is the main factor affecting crown maintenance at maximum height, growth in trunk diameter may continue even when growth in height ceases. This would result in asymptotic patterns in the allometry of tree height and trunk diameter. Such patterns were, however, not observed in this study. The trees might not reach asymptotic size because severe stresses increase the mortality of tall trees. This suggests that, to integrate the crown allometry and dynamic patterns of shoot growth and shoot turnover in coexisting species, studies of maintenance mechanisms of crowns at Hmax and evaluation of the causes of mortality as trees approach maximum height will be important subjects of future studies (e.g. Van Pelt & Sillett 2008).

In conclusion, tree allometry reflected shoot traits of upper crowns in the studied species, suggesting that allometric differences between species may be useful for evaluating crown development patterns. Here, maximum height of canopy species was rather low in this study site, and they tended to have thicker trunks compared with trees of similar height in other allometric studies (e.g. Aiba & Kohyama 1996; Aiba & Nakashizuka 2009). The maximum tree heights for these species would be greater, and the relationship between trunk diameter and tree height may become asymptotic in more productive sites. Investigation of the relationship between shoot traits and tree allometry across forests of differing heights will be an important theme of future studies.

Acknowledgements

I thank Kouki Hikosaka, Satoki Sakai, Koji Yonekura, and Naoko Tokuchi for their valuable suggestions. I also thank Niels Anten and Kaoru Kitajima for their critical comments on the manuscript. This study was partly supported by a grant of from the Ministry of Education, Science, Sports and Culture of Japan (18770011 and 21780140), and Nissan Foundation (08336).

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