| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
|
|
|
|||||||
|
|||||||||
Ecology |
Department of Biology and 3Department of Physics, Universiti Brunei Darussalam, Jalan Tungku Link, Bandar Seri Begawan, Brunei Darussalam, Borneo
Received for publication April 15, 2007. Accepted for publication October 16, 2007.
ABSTRACT
In rainforests, trunk size, strength, crown position, and geometry of a tree affect light interception and the likelihood of mechanical failure. Allometric relationships of tree diameter, wood density, and crown architecture vs. height are described for a diverse range of rainforest trees in Brunei, northern Borneo. The understory species follow a geometric model in their diameter–height relationship (slope, β = 1.08), while the stress–elasticity models prevail (β = 1.27–1.61) for the midcanopy and canopy/emergent species. These relationships changed with ontogeny, especially for the understory species. Within species, the tree stability safety factor (SSF) and relative crown width decreased exponentially with increasing tree height. These trends failed to emerge in across-species comparisons and were reversed at a common (low) height. Across species, the relative crown depth decreased with maximum potential height and was indistinguishable at a common (low) height. Crown architectural traits influence SSF more than structural property of wood density. These findings emphasize the importance of applying a common reference size in comparative studies and suggest that forest trees (especially the understory group) may adapt to low light by having deeper rather than wider crowns due to an efficient distribution and geometry of their foliage.
Key Words: adaptation • comparative studies • standardized major axis regression • tree adult stature • tree architecture • wood density
The relationship between size and shape (allometry) is influenced by the age of an organism (ontogeny) and has profound effects on species fitness, and consequently on ecosystem structure (McMahon, 1973
; Niklas, 1994
, 1995
; Poorter et al., 2003
). In rainforests, vertical stratification of light is well pronounced, with the lower stratum receiving irradiation as low as 1.5% of open sunlight (Osunkoya and Ash, 1991
; Osunkoya et al., 1992
). For establishment, plants in this layer often depend on sun flecks, which are unpredictable both in time and space, and thus success in such a low light environment can be expected to rely on tree size, leaf geometry, and crown architecture and position. The thickness (height–diameter quotient) and structural properties (as measured by wood density and/or modulus of elasticity) of a tree trunk influence the likelihood of mechanical damage from lianas and fallen debris or trunk snapping from wind stress. Thus, natural selection should favor trees with a height–diameter relationship that permits growth in height (to harvest more light, which becomes exponentially more available at higher levels in the forest) and/or horizontal crown expansion (to decrease leaf self-shading and to increase the probability of intercepting light, especially sun flecks) without compromising mechanical stability (Sterck and Bongers, 1998
; Sposito and Santos, 2001
). Height growth has often been shown to be at the expense of investment in safety margin against (static) self-loading and (dynamic) wind pressure or at the costs of investment in horizontal crown expansion (e.g., Bongers and Sterck, 1998
; Alves and Santos, 2002
; Alves et al., 2004
; Poorter et al., 2005
), but how height growth or investment in mechanical safety vary with tree adult stature (understory vs. midcanopy vs. canopy vs. emergent) or tree successional status (early vs. late successional species) remains controversial (see Sterck and Bongers, 1998
; Bongers and Sterck, 1998
; Poorter et al., 2003
, 2005
, 2006
; Bohlman and O'Brien, 2006
). For example, some studies on rain forests have shown that low stature (and by inference, shade tolerant) tree species may exhibit more self-shading and smaller relative crown width (e.g., King, 1981
; Shukla and Ramakrishnan, 1986
; Kuppers, 1989
; Sterck, 1999
; Sterck et al., 2001
) than high stature (shade-intolerant) species, while others have documented the opposite trend or even no difference (e.g., Kohyama and Hotta, 1990
; O'Brien et al., 1995
; Aiba and Kohyama, 1996
; Poorter et al., 2003
, 2006
). This inconsistency in direction and magnitude of the linkage between growth form and trait associations (e.g., height vs. crown allometry) has been attributed to the fact that analyses are seldom done at a standardized reference height or diameter for all the species under investigation (Poorter et al., 2005
, 2006
).
To explain the mechanical design of trees, researchers have invoked three models of engineering principles derived from cantilevered beams (McMahon, 1973
; Niklas, 1994
; Henry and Aarssen, 1999
). The elastic similarity model assumes that for trees to resist buckling (falling) under their own mass (i.e., to stay upright), longer stems need to be proportionally thicker than shorter ones, and hence diameter (D) should scale at 3/2 (1.5) to the power of trunk height (H) (alternatively, H·
·D2/3). The constant stress similarity model dictates that to efficiently transmit wind pressure generated above the forest canopy down a tree trunk and thus minimize damage, diameter should scale to two to the power of height (or H·vD1/2) (Dean and Long, 1986
). The geometric self-similarity model is based on the notion that, whenever wind loading is not the dominant controlling factor in tree mechanical design such that the wind forces are resisted with a minimal biomass investment in branches, stem length will scale in direct proportion to stem diameter (i.e., H··D) (King and Loucks, 1978
; Norbeg, 1988
). In a detailed work on Robinia pseudoacacia, Niklas (1995)
showed that a single optimal design principle neither held true throughout ontogeny nor governed the taper of a trunk throughout its entire length. Based on this, Niklas (1995)
suggested that geometric self-similarity might occur early in the ontogeny of a tree, while elastic or stress self-similarity would be reached toward the end of a tree's life. Such changes in the scaling component of the diameter–height (D–H) relationship with ontogeny have since been found for tropical forest trees of differing adult stature or successional status (Kohyama and Hotta, 1990
; Alvarez-Buylla and Martinez-Ramos, 1992
; Fansworth and Niklas, 1995
; O'Brien et al., 1995
; King, 1996
; Sposito and Santos, 2001
; Alves and Santos, 2002
; Bohlman and O'Brien, 2006
).
In general, there is no reason we should expect intraspecific trends in tree allometry and mechanical design to differ from that observed between species or between adult stature groups. We therefore hypothesized that (1) although crown width, diameter, or area might increase with increasing tree height, relative crown depth (RCD) and relative crown width (RCW) should increase and decrease, respectively, with tree height and by inference with adult stature groups (we expect this relationship because increasing RCD and decreasing RCW as tree height increases should reduce shading, especially under low light conditions); (2) tree slenderness should be positively correlated with wood strength (e.g., wood density) because mechanical safety against snapping in slender stems calls for greater structural reinforcement; and (3) tree overall safety factor against buckling—a proxy of tree stability—should decrease with increasing tree height and adult stature because of upward displacement of the center of gravity of a tree trunk with increasing height and because of the need by taller trees to allocate less to crown expansion but more to height gain before becoming reproductive (Thomas, 1996
; Sterck and Bongers, 1998
).
Using 22 tree species from the tropical mixed dipeterocarp rainforest of Kuala Belalong, Brunei, northern Borneo, we examined intra- and interspecific patterns of variation in stem and crown allometry, growth increment in diameter at breast height (DBH), and wood density. These trees come from a diverse group of families and vary widely in adult stature and or succession status. Specifically, using tree height as the independent variable, we looked for allometric relationships within and between species in tree height–diameter, height–crown architecture, and height–safety margin to minimize self-buckling. In all cases, we determined whether a particular (null) model can exclusively describe the D–H allometric relationships in a rainforest setting. Detection of these allometric relationships also allowed us to study whether rainforest tree species with inherently slow growth (and by inference, short adult stature) that establish predominantly in the low-light understory have flatter but wider crowns and thinner stems than do species with taller stature that tend to occupy the high-light overstory.
MATERIALS AND METHODS
Study site
Data were collected from trees of Kuala Belalong, a mixed dipterocarp, lowland rainforest, which is part of the Ulu Temburong National Park, Brunei Darussalam, Borneo in SE Asia (4°30' N, 115°10' E). Mixed dipterocarp forests (MDF) with emergent trees up to 40–60 m tall are a well-represented forest type in Brunei, with Anacardiaceae, Euphorbiaceae, Dipterocarpaceae, Lauraceae, Myrtaceae, and Rubiaceae being the dominant families (Ashton and Hall, 1992
; Ashton et al., 2004
). The tropical forest of Belalong is extraordinarily species-rich (256 species per ha; Cranbrook and Edwards, 1994
; Small et al., 2004
) and is similar in community structure to other lowland MDF in Borneo in its lack of dominant species and in the tendency towards localized distributions of many main canopy/emergent species (often >40 m high). In addition, many species are locally rare, with <5 individuals per ha. The soils of the area are of orthic acrisols derived from shale parent materials. They are relatively porous in bases and have clay enriched B-horizon with deep profiles (up to 2 m). Mean annual rainfall is 
5080 mm, and there is no distinct dry season. Typical of an equatorial climate, the temperature varies little, with the daily maximum between 30.5°C (January) and 35.0°C (March) and the minimum around 25°C.
In September 1995, a 1-ha unlogged MDF plot was set up in a low to midslope valley position, west of the Belalong River in Kuala Belalong by the Earthwatch Institute and the Universiti Brunei Darussalam (UBD) Kuala Belalong Field Studies Centre; the purpose of the plot was to study long-term dynamics of tree populations (see Small et al., 2004
). All trees 
5 cm DBH were taxonomically identified, mapped (using x and y coordinates), numbered with aluminum tags, and measured for their DBH at a red-paint mark usually 1.3 m above the forest floor; for trees with buttresses, DBH was measured 20 cm above the top of the buttress. Voucher specimens of all species identified were deposited in the herbaria of the UBD Biology Department and the Brunei Forestry Department. The topography is gently undulating in about half of the plot but is quite rugged in the remaining portion; the rugged portion has an elevational gradient of 20–30 m and is dissected by two floodstreams and extensive ridge systems. Within the plot, 1019 individual trees >5 cm DBH were identified (278 species). Mean stem diameter of trees 5 cm DBH in this plot was 12.8 cm, with the upper range at 97.5 cm. The plot was dominated by lower understory and midcanopy species with an average height of 11 m. The plot also contained a few emergents, including Koompassia excelsa (Caesalpiniaceae) and Crypteronia griffithii (Crypteroniaceae), that were tall (>45 m) and hence with large DBH (>60 cm). For more details on the floristics of this plot, see Small et al. (2004)
.
Sampling procedure: determining tree height, diameter, stem growth, crown architecture, wood density, and tree stability safety factor
The 1-ha permanent plot was revisited in September 2004—nine years after the initial set up—to document tree mortality, tree height, crown geometry, and changes in DBH for all 1019 plants previously tagged and identified. The procedures have been fully reported elsewhere (Osunkoya et al., 2007
). Briefly, tree heights and fork (branch) heights were determined with clinometers for stems with less than 10° lean and with no evidence of past crown or stem damage or disease. For tree height (H), the highest foliage point was considered the top of the stem. Fork height (Hf) was defined as the vertical distance between the stem base and the lowest major branch, which in itself is defined as a branch that is at least half as thick as the main stem at the same height. Crown depth was then calculated as the difference between tree height and fork height. From the base of the trunk, four horizontal ground projections of the crown (i.e., four radii at 90° angles) were measured for each tree. Crown width (W) was calculated as two times the mean of the four radii. Crown projection area (m2), assuming an ellipsoidal shape, was then derived as S = 
[
W(H – Hf)]. Relative crown width and depth (RCW and RCD) were estimated as ratio of tree crown width or depth to tree height, respectively. From the diameter measurements, tree diameter increment (
d) was calculated as: d = (Dt – D0)/t, where t = number of years between measurements (9 yr), D0 = tree DBH at first recording (1995), Dt = tree DBH at t years (2004).
For estimating wood density (WD), cylindrical cores were taken at breast height from the trunks of the tagged trees; the cores were made with a 5-mm-wide increment borer (SUUNTO, Vantaa, Finland) and were 30–100 mm long, excluding the bark. Representative trees, spanning the observed height range, of each common species (N 4; range: N = 4–22, Table 1) were sampled. WD was empirically derived using the ratio of dry mass to fresh volume (see Osunkoya et al., 2007
for details of the procedure).
|
; Sposito and Santos, 2001
). Note that the SSF calculated here is an approximate estimate of a more accurate determination of McMahon's buckling limit that incorporates stem tapering and bulk tissue properties, such as wood density and modulus of elasticity (see King and Loucks, 1978
; King, 1996
; Niklas and Spatz, 2004
).
Tree classification into adult stature groups
The present study focused on 22 species (from 12 families) whose individuals were abundant (N > 10 individuals) in the 1-ha plot. For these selected species, maximum (potential) plant height (Hmax) was estimated from H = Hmax x [1 – exp(–aDb)], where H is tree height in m, D is DBH in cm, and a and b are allometric coefficients that approach values of standard allometric constants for small values of H (see Thomas, 1996
; Osunkoya et al., 2007
). The species were then categorized into three adult stature groups of understory (Hmax 
15–20 m), midcanopy (Hmax 20–30 m), and canopy/emergent (Hmax > 30 m) tree species. These species are listed in Table 1, together with their adult stature forms. Taxonomy follows Coode et al. (1996)
. The present study did not consider the other axis of rainforest plant regeneration—that of successional/light-demand status of our study species. This functional grouping would be informative (see Falster and Westoby, 2005
; Poorter et al., 2006
; van Gelder et al., 2006
), but we lack data to unequivocally assign species to different successional/light-demand groups. As far as we know, there are no standards or procedures outlining how this grouping is determined or what exactly is to be measured (see Falster, 2006
; Bohlman and O'Brien, 2006
).
Allometry relationships
Data analyses for the allometric trends consisted of calculating linear regressions using standardized major axis (SMA) of log 10 height—the independent variable—on the log 10 of the other traits (DBH, growth increment, fork height, crown shape [area, depth and width], RCW, RCD and SSF); (S)MATR 2.0 software was used (Falster et al., 2003
; Warton et al., 2006
). Plant height was used as the independent trait because height influences the light environment and the space available for plant growth. SMA estimates of lines summarizing relationship between two variables are superior to ordinary least square linear regression and have been advocated in the literature because residual variance is minimized in both the X and Y dimensions rather than in the Y dimension only (McArdle, 1988
; Niklas, 1994
; Falster and Westoby, 2005
; King et al., 2005
). When comparing regressions, differences can occur in either exponent of a (Y intercept) and/or b (regression slope). If b differs among species, species with larger b will have greater increase in Y per increment of X. If a differs, but b does not, species with larger a will have a consistently larger amount of Y at any given value of X (Kohyama and Hotta, 1990
; Sposito and Santos, 2001
).
In testing for statistical differences in allometric slope values among species or between adult stature forms (using the S(MATR) software), a common slope was first estimated following Warton and Weber (2002)
, using a maximum likelihood ratio method (analogous to 
2 analysis); the significance of the common slope was determined by permutation (Manly, 1997
). The calculation of a common slope also allowed us to test elevation (intercept) differences among species or adult stature forms, as in standard analyses of covariance (ANCOVA) that requires the calculation of F statistics. Shifts in elevation were tested by transforming the data such that the common slope was set to zero (Wright et al., 2001
) and then testing for the differences in species or tree adult stature form of y' and x' using one sample ANOVA (where y' and x' are y and x after data transformation by an amount corresponding to the common slope β; y' = y – βy and x' = x – βy). This procedure also allows testing for differences in trait values across species or between adult stature forms at a common (e.g., low) tree height (see Warton et al., 2006
).
For determining how our data fit each of the three D–H allometric growth models (elastic, geometric, and stress), 95% confidence limits of the slopes of the relationship between DBH and tree height were fitted for each species and for each of the three adult stature forms; we then tested statistically whether the limits bracketed the expected slope values (see the introduction). To explore possible dimensional changes in the D–H allometry through ontogeny, we calculated separate regressions in two height ranges: one for trees <13 m and the other for trees >13 m. These size delimitations were chosen based on observed vertical forest structure at the study site (see also Alves and Santos, 2002
). Last, cross-species correlation analyses between each pair of the traits examined were carried out in which each species contributed a single data point obtained by averaging values over all individuals of that species.
RESULTS
Overall trend
Mean values of tree height, crown architectural traits, DBH growth, and wood structural and mechanical properties are shown in Table 1. For most of the 22 species, within-species trait values varied significantly with plant height, except for stem slenderness, RCD, and stem DBH growth (intraspecific statistical test results not shown). Overall, tree diameter, stem DBH growth, fork height, wood density, and crown shape (width, depth, and area) increased linearly while RCW and SSF decreased exponentially and significantly with increasing plant height (Figs. 1 and 2).
|
|
0.47–0.49); moderate in Aporusa elemeri, A. grandistipula, and Diospyros borneensis (0.60); and high in the remaining species (>0.70) (Table 2). The D–H scaling relationships differed significantly among species as judged by differences in slope values (2 = 86.68, df = 21, p = 0.001; Tables 2 and 3). Test for shift in elevation using ANCOVA also indicated significant differences among species, suggesting differences in intercept values (F21,389 = 4.61, P = 0.001); differences appeared to be caused mainly by the subcanopy Dillenia excelsa, the two understory Fordia species, and Mallotus wreyi (Table 2). The D–H scaling exponent (β) of the regression was highest for the two emergent Syzygium species (β = 2.03, 1.74) and the canopy Payena (β = 1.88) species, indicating thicker trunks with increasing height for these species, and conformity with the constant stress model of McMahon (1973)
. Three understory species (Mallotus wreyi, Fordia sp.3, and F. splendidissima) and one midcanopy species (Dillenia excelsa) had slope values well below but not significantly different from unity, except in the case of Fordia sp.3. Also, their 95% confidence interval (CI) did not overlap with values expected of an elastic or stress similarity exponent, and we therefore inferred that data from these species fit the geometric growth model (Table 2). The remaining species had slope values between 1.10–1.60, but can be said, judging from their 95% CI and rejection of the null hypothesis of β = 1, to follow the scaling exponent predicted by the elastic similarity model. Considering tree adult stature forms, significant differences existed in their D–H allometry (Fig. 2, Tables 2 and 3) as indicated by the scaling exponents (2 = 54.4, df = 2, p = 0.001). The understory species, though, did not fall exactly on but were close to the line of the geometric similarity model (pooled data: β = 0.94; Table 2). The midcanopy species had a much higher scaling exponent (pooled data: β = 1.27) and were closest to the elastic similarity model, though they were still significantly different from it (Table 2), while the data for the canopy species fit clearly the elastic similarity model (pooled data: β = 1.60). Overall and irrespective of species and tree height, the elastic similarity rule prevailed (β = 1.31, 95% CI: 1.23–1.58). To examine whether these scaling components remain constant irrespective of ontogeny, the data were split into two sets to reflect trees in the lower (<13 m) and upper stratum (>13 m) of the forest (Fig. 2). The pattern remained consistent for the canopy/emergent and the midcanopy species because the elastic-stress models (β = 1.27–1.92; 95% CI: 1.22–2.31; Fig. 2b, c) still prevailed at the two height ranges. The pattern changed significantly for the understory species: for trees <13 m, the understory species operated close to the geometric scaling (β = 0.76; 95% CI: 0.66–1.03; Fig. 2d), while above this height, the trees became more robust per unit change in stem length and thus the data best fit the elastic-stress models (β = 2.18; 95% CI: 1.48–2.31), as did the data from the other two groups of species.
|
|
midcanopy > canopy species (Fig. 1c). Overall, SSF-height scaling exponent varied significantly between adult stature forms (P < 0.05; Table 3); analysis at a common (low) height gave similar results with a tendency for higher SSF value for the canopy/midcanopy compared to the understory species (Table 4, Fig. 3a). The scaling exponents for the slenderness–height relationship did not vary across species or amongst adult stature forms (Fig. 1j; Table 3). However, analysis at a common (low) height showed that slenderness differed significantly between adult stature forms with the understory species having the highest slenderness ratio (Fig. 3j; Tables 3 and 4). No significant difference in the scaling exponent of the WD–height relationship was detected across species (Table 3). Analyses at a common (low) height also indicated that the structural trait of WD did not differ between adult stature forms (P > 0.05; Tables 3 and 4; Fig. 3d).
|
|
Cross-species bivariate relationships
Cross-species correlation values between each pair of the 11 traits examined are given in Table 5. When mean values of the species traits were used, of the 55 possible pairwise bivariate relationships, 26 were significant at P < 0.05 with an additional two emerging as marginally significant at P < 0.10 (Table 5a). Across species, the measure of adult stature—Hmax—was positively correlated with crown traits (width, depth, and area), DBH growth, and the D–H scaling exponent, and negatively correlated with RCD. Decrease in slenderness appeared to allow a much higher Hmax to be attained. Contrary to expectation, WD was not significantly related to Hmax. SSF increased with increasing RCW but decreased significantly with increasing tree slenderness. Increase in DBH growth was accompanied by significant increase in crown area and its associated determinants (crown depth and width), though such increase in DBH growth appeared to be at the expense of RCD. Trade-offs existed between slenderness and crown architectural traits (RCW, RCD, crown area, width, and depth), suggesting that increase in crown expansion necessitates a robust trunk. Species with faster increase in diameter relative to height (i.e., higher D–H scaling exponent) also significantly increased their RCD.
|
0.10) (Table 5b). Figure 3 summarizes how the predicted trait values change with Hmax—a known correlate of many demographic and architectural traits in rainforest settings. At a common (low) height, the magnitude and direction of the links between Hmax and most traits examined were similar to those obtained using species mean values. However, it is now noteworthy that the correlations between Hmax and stem DBH growth and between Hmax and crown width were not significant any more (Fig. 3c, e). Hmax was significantly and positively correlated with SSF, while its links with crown depth and area were now negative (Fig. 3a, f, g). The negative Hmax–crown area/depth trends confirmed earlier analyses based on adult stature form (Table 4) and thus suggests that at a lower tree height, taller stature tree species have smaller crown areas and shallower crown depths than do shorter stature tree species (Table 4, Fig. 3). Crown area relationships with other traits, except with its own derivatives (i.e., crown depth and width), also changed direction when compared to results obtained using species mean values—notably with slenderness and D–H scaling exponent. We could still not detect any significant link between WD and Hmax (Fig. 3d). Increase in diameter relative to height (i.e., higher D–H scaling exponent) was achieved with lower WD value (r = –0.64; P < 0.05). In summary, the magnitude of the correlations for most trait associations examined differed depending on whether the data used were obtained at a common (low) tree height or came form species mean response. Also fair to say is that a reasonable number of the relationships that were significant using mean values changed directions at a common (low) reference height (nine of 30 or about 30%). DISCUSSION
Tree diameter–height allometry and mechanical stability
The slopes of the D–H allometric relationship differ significantly between the species under investigation but are within the range reported for other studies, especially in rainforest settings (e.g., King, 1990
; Claussen and Maycock, 1995
; Thomas, 1996
; Alves and Santos, 2002
). The analyses showed that roughly equal numbers of species follow exclusively the geometric and elastic similarity growth patterns in their D–H relationship (4/22 in each type)—a proportion greater than that observed for the stress type (1/22). The majority of the remaining 22 species fall within two of the three predicted allometric exponents. Thus, none of the three models can exclusively describe the allometric patterns observed for optimal mechanical design (see also Niklas, 1994
; Niklas and Spatz, 2004
). However, pooled or mean data suggest that geometric similarity is the closest approximation to the growth pattern observed for smaller trees (β = 1.01) and stress-elastic similarity for larger ones (β = 1.91; Fig. 2a). Hence, size-dependent changes do seem to exist in the scaling exponents of D–H relationships among tropical rainforest trees. Some authors have documented similar findings of scaling close to the McMahon elastic similarity model, especially for emergent trees (e.g., Fansworth and Niklas, 1995
; O'Brien et al., 1995
), while others have detected an isometric (geometric) relationship, especially for the understory species (e.g., King, 1990
, 1996
; Kohyama and Hotta, 1990
; Sposito and Santos, 2001
), as was also detected for the same groups of species in this study. Nonetheless, it has to be recognized that species-specific growth/allocation patterns and hydraulic constraints as well as physical changes occurring during tree development (e.g., changes in light resource and neighboring plant density) can significantly alter the scaling exponent but are rarely considered in explaining the dimensional design of trees. Indeed, Niklas and Spatz (2004)
have shown that the elastic-similarity rule is violated by small and intermediate size trees and even suggested that scaling based on growth and hydraulic properties of trees provides more accurate and biologically realistic predictions of the D–H scaling than does the mechanical stability model. Causes of the scaling have not been fully understood, though numerous functional hypotheses have been proposed. These include resistance to elastic buckling (as assumed in this study), mass transfer, and the influence of fractal-like branching patterns within the body parts of all organisms. All these hypotheses emphasize that the scaling is in response to the need to conduct and distribute fluid efficiently (see McMahon, 1973
; West et al., 1997
; Niklas and Spatz, 2004
).
As in other studies (e.g., Niklas, 1994
; Thomas, 1996
; Davies et al., 1998
; Kohyama et al., 2003
; van Gelder et al., 2006
), estimated Hmax in the current study was positively correlated with the D–H scaling exponent values (Table 5, Fig. 3b), suggesting that small tree species achieve a greater height gain relative to diameter gain and consequently are more slender than large species. This higher height gain has often been interpreted as a response to the low light typical of the environment where small stature treespecies spend most of their lives. Because light intensity can be up to fourfold greater at 6 m height than at the forest floor (Osunkoya et al., 1992
), greater growth in height relative to growth in diameter may be advantageous for small stature trees, as relatively small increases in plant height may have important consequences for the whole carbon balance. Like Thomas (1996)
, we had hypothesized (see introduction) that the slender stem of small trees may be accounted for by their generally greater wood density and hence strength, but our data did not support this hypothesis because wood strength was not significantly greater in the understory species than in the midcanopy and canopy/emergent ones, even at a common (low) reference height (Table 4).
We found also that the SSF for trees in the lower stratum (<10 m), irrespective of species or adult stature, is high (mean 3.11; Fig. 1c), suggesting that they are almost one-third shorter than their potential maximum (see Niklas, 1994
, 1995
for a full discussion of this topic). High SSF at the lower forest stratum has been attributed to the need for plants in this condition for stability and survival as opposed to rapid growth in height, which can only be attained in the high light environment above the canopy. Fallen debris (from trees and branches) and liana infestations may also greatly damage trees in this stratum; such a negative effect can be counterbalanced by selection for higher SSF together with high wood density. For trees >10 m, the SSF is expected to decrease dramatically, as it did for most species in this study. Trees in the midcanopy (10–20 m high) are well buffered from strong wind and falling debris (Bongers and Sterck, 1998
; Sterck and Bongers, 1998
), and may account for decreasing SSF values at this height range. Above the canopy (>20 m), the SSF may increase again as in most emergent/canopy species to counter the stress imposed by high wind speed (Claussen and Maycock, 1995
; Sterck and Bongers, 1998
), but we lacked the power in this size range to detect this last generalization. In terms of adult stature, understory trees had the greatest decrease in the SSF with increasing plant height, suggesting that the species in this group approach their potential maximum height faster with age, which may have led directly to their greater slenderness relative to the other two groups of species (Tables 1 and 4). Across species, the positive relationship between the SSF and Hmax, especially at a common (low) height (Fig. 3a), is in contrast with our initial hypothesis of lower mechanical stability with increasing potential height and adult stature. Thus, this relationship requires more investigation, though it appears that trunk slenderness and expanding crown geometry but of a low RCW may play indirect but influential roles in lowering SSF values in smaller tree species (Table 4) relative to the taller ones (see also Sterck and Bongers, 1998
). Indeed, the significant and positive SSF–Hmax relationship becomes neutral when a partial correlation between the two traits is carried out using slenderness as a control factor (r = –0.13; N = 21; P = 0.59). None of the crown shape traits had a similar damping effect on the SSF–Hmax relationship. Hence, the increase in the SSF value with increasing Hmax at a common (low) height may be an artifact of increasing robustness rather than a real increase in mechanical safety.
Overall, it is interesting that crown architectural traits, especially RCW and height to diameter ratio (tree slenderness), influence SSF more than does the structural trait of WD. The SSF was also weakly linked to tree stiffness measured as the modulus of elasticity (O. O. Osunkoya, unpublished data), in line with a similar finding by van Gelder et al. (2006)
for 30 rain forest tree species in Santa Cruz, Bolivia, South America. The significant positive trend between RCW and SSF is a further indication of the large influence of crown architectural traits in minimizing tree buckling under its own weight, perhaps via a better dissipation of wind stresses and a more efficient mass distribution (overall moment of inertia) about the vertical axis of the trunk as RCW increases.
Crown architecture
In most cases, architectural traits change significantly with plant height both within and across species (Fig. 1, Tables 2 and 3) to deal with increasing availability of light and larger respiration load as trees move up the vertical ladder. Trees were predicted to have deeper and wider crowns with increasing height. This hypothesis is upheld (Fig. 1) and is consistent with findings in other tropical forest around the globe (e.g., King, 1996
; Sterck and Bongers, 1998
; Sterck et al., 2001
). That within species, RCD did not vary significantly with height (for 21/22 species), but RCW did vary (for 11/22 species) (see also Fig. 1h, i) is a strong indication that with respect to intraspecific competition, horizontal search for light may be much more advantageous than the development of a large surface leaf area on a vertical column, especially in the gloom of the forest interior. This result shows that in the lower stratum environment, irrespective of tree stature or species, trees need to have a high RCW so as to intercept light by extensive horizontal crown growth at the cost of height growth. King (1991)
, Horn (1971)
, and Kohyama and Hotta (1990)
argued that such high RCW growth should be more pronounced in the understory species (because they spend their entire lives there) than other guilds, but like O'Brien et al. (1995)
, Sterck and Bongers (1998)
, and Poorter et al. (2003
, 2006
), we found, using mean data, no difference in this trait among the three adult stature forms (Table 1) and even a significant opposite trend at a common (low) tree height (Table 4, Fig. 3h). At the interspecific or adult stature comparative levels, this hypothesis of extensive crown extension for trees in the understory level may be upheld, but the strategy now shifts toward increasing crown depth rather than crown width (Fig. 3f, Tables 3–5). In other words, across species, the link between RCW and Hmax is weak (Table 5). Also interesting is that at a common (low) height, the RCD of the smaller (understory) species is almost equal to that of the taller (canopy/midcanopy) species (Fig. 3i, Table 4). Thus, it appears as if many of the understory species in this study adapt to low light by investing more in crown depth than in crown width. If true, this begs the question: what happens to the problem of self-shading at low light if so much foliage is packed on the vertical stem? Perhaps most of the irradiance in the lower stratum of the site we studied comes from the side rather than from above, and thus the strategy has shifted toward changes in crown depth rather than changes in crown width (see also Sterck et al., 2001
). Indeed, Poorter et al. (2003
, 2006
) stated that a deep crown does not necessarily imply a high number of leaf layers and that the distribution and geometry (shape, size, and orientation) of the foliage may play a crucial role in light interception. Additionally, most short species have leaves that can operate at a lower light compensation point than leaves of their overstory counterparts (Osunkoya et al., 1992
), and hence, reduction in self-shading might not be that important. Lastly, the shallow crown depth of many large tree species may result from the short lifespan of their spaces (i.e., petioles, rachae, or branches). This finding is also partially in line with the crown width/depth vs. height hypothesis (in the introduction) that taller trees by virtue of higher investment in height growth have less expansion of the crown than do smaller trees (Table 4).
In summary, across species, the lack of significant changes in RCW with increasing Hmax, coupled with significantly lower RCW values for small trees when comparisons were made at a common (low) height, suggests that horizontal crown expansion plays less of a role in vertical niche/ecological differentiation among species, at least in the forest studied herein; ordination of the entire data set supported the same conclusion (data not shown).
Conclusion
The D–H scaling relationships varied among species and adult stature growth forms. However, most species fit into one (though not exclusively) of the three mechanical design models in the literature; the data from most species fit the elastic similarity model. Niklas (1995)
showed that in most cases geometric self-similarity might occur early in the ontogeny of a tree while elastic or stress self-similarity would be reached toward the end of a tree's life. This concept appears to be supported in this study because the scaling exponents did change significantly with ontogeny, especially for the understory and midcanopy species (Fig. 2). Nonetheless, alternative hypotheses that do not invoke a mechanical constraint effect may also explain such a scaling relationship (Niklas, 1995
; Henry and Aarssen, 1999
; Niklas and Spatz, 2004
).
We have also shown that species cope with space limitation and vertical light stratification by changing their crown architecture. Most species increase their RCW with decreasing tree height so as to intercept more light, thus indicating that species or adult stature group cannot be differentiated with this trait. When the data are analyzed at a common/standardized reference point and in line with some recent findings (e.g., Kohyama et al., 2003
; Poorter et al., 2003
, 2006
), crown depth rather than crown width seems to be the trait under intense interspecific selection for coping with changes in forest light. The small species have a higher crown depth than those of overstory species at a common (low) tree height; and even under this condition, though RCW of smaller trees are significantly lower, their RCD is roughly equal to that of the canopy/midcanopy species. The changes in crown width and crown depth indicate the importance of these traits for morphological adaptation of forest trees to deep shade. Also, when a common height reference point is used rather than species mean values, some trait relationships (especially those associated with crown area) changed direction and/or significance, just as suggested by Poorter et al. (2006)
. These results might indicate that competition for light rather than inherited developmental constraints of the species may be the more proximate cause of trait associations or coordinations. Future research must partition the relative influence of competition for light and inherited developmental constraints to better explain growth allometry and species coexistence among rainforest trees (see Poorter et al., 2005
).
FOOTNOTES
1 The authors thank the staff of the UBD Kuala Belalong Field Studies Centre for granting access to the permanent plot and for logistic support. D. Falster and I. Wright provided freely and online the SMA regression software used. Thanks also go to A. Olofinjana for thoughtful discussion on wood strength and tree mechanical design. 
4 Author for all correspondence (e-mail: osunkoya{at}fos.ubd.edu.bn
or Zegler_au{at}yahoo.com.au
), present address: Department of Biology, Faculty of Science, Universiti Brunei Darussalam, Jalan Tungku Link BE 1410 Bandar Seri Begawan, Brunei Darussalam, phone: +673-2463001 ext. 1374, fax: +673-2461502.
LITERATURE CITED
Aiba S. I. Kohyama T.. 1996. Tree species stratification in relation to allometry and demography in a warm-temperate rainforest. Journal of Ecology 84: 207-218..[CrossRef][ISI]
Alvarez-Buylla E. R. Martínez-Ramos M.. 1992. Demography and allometry of Cecropia obtusifolia, a neotropical pioneer tree—an evaluation of the climax-pioneer paradigm for tropical rainforests. Journal of Ecology 80: 275-290..[CrossRef][ISI]
Alves L. F. Fernando R. M. Santos F. A. M.. 2004. Allometry of tropical palm, Euterpe edulis Mart. Acta Botanical Brazil 18: 369-374..
Alves L. F. Santos F. A. M.. 2002. Tree allometry and crown shape of four tree species in Atlantic rainforest, south-east Brazil. Journal of Tropical Ecology 18: 245-260..[CrossRef][ISI]
Ashton P. S. Hall P.. 1992. Comparisons of structure among mixed dipterocarp forests of north-western Borneo. Journal of Ecology 80: 459-481..[CrossRef][ISI]
Ashton P. S. Kamriah A. S. Said I. M.. 2004. A field guide to the forest trees of Brunei Darussalam. Universiti Brunei Darussalam, Bandar Seri Begawan, Brunei, Borneo..
Bohlman S. O'Brien S.. 2006. Allometry, adult stature and regeneration requirement of 65 tree species on Barro Colorado Island. Journal of Tropical Ecology 22: 123-136..[CrossRef][ISI]
Bongers F. Sterck F. J.. 1998. Architecture and development of rainforest trees: responses to light variation. In D. M. Newbery, H. H. T. Prins, N. D. Brown [eds.], Dynamics of tropical communities—the 37th Symposium of the British Ecological Society, 125-161. Blackwell, London, UK..
Claussen J. W. Maycock C. R.. 1995. Stem allometry in a northern tropical rainforest. Biotropica 27: 421-426..[CrossRef][ISI]
Coode M. J. E. Dransfield J. Forman L. L. Said I. M.. 1996. A checklist of the flowering plants and gymnosperm of Brunei Darussalam. Ministry of Industry and Primary Resources, Bandar Seri Begawan, Brunei Darussalam, Borneo..
Cranbrook E. Edwards D. S.. 1994. Belalong—a tropical rainforest. Royal Geographical Society, London, UK and Sun Tree Publishing, Singapore..
Davies S. J. Palmiotto P. A. Ashton P. S. Lee H. S. Lafrankie J. V.. 1998. Comparative ecology of 11 sympatric species of Macaranga in Borneo: tree distribution in relation to horizontal and vertical resource heterogeneity. Journal of Ecology 86: 662-673..[CrossRef][ISI]
Dean T. J. Long J. N.. 1986. Validity of constant-stress and elastic–instability principles of stem formation in Pinus contorta and Trifolium pretense. Annals of Botany 58: 833-840..
Falster D. S.. 2006. Sapling strength and safety: the importance of wood density in tropical forests. New Phytologist 171: 237-239..[CrossRef][ISI][Medline]
Falster D. S. Warton D. I. Wright I. J.. 2003. (S)MATR: standardized major axis tests and routines http://www.bio.mq.edu.au/ecology/SMATR [accessed 5 April 2007]..
Falster D. S. Westoby M.. 2005. Alternative strategies among 45 dicot rain forest species from tropical Queensland, Australia. Journal of Ecology 93: 521-535..[CrossRef][ISI]
Fansworth K. D. Niklas K. J.. 1995. Theories of optimization, form and function in branching architecture in plants. Functional Ecology 9: 355-363..[CrossRef]
Henry H. Aarssen L. W.. 1999. The interpretation of stem diameter–height allometry in trees: biochemical constraints, neighbour effects, or biased regressions?. Ecology Letters 2: 89-97..[CrossRef][ISI]
Horn H. S.. 1971. The adaptive geometry of trees. Princeton University Press, Princeton, New Jersey, USA..
King D. A.. 1981. Tree dimensions: maximizing the rate of height growth in dense stands. Oecologia 51: 351-356..[CrossRef][ISI]
King D. A.. 1990. Allometry of saplings and understorey trees of a Panamanian forest. Functional Ecology 4: 27-32..[CrossRef]
King D. A.. 1991. Tree size. National Geographic Research and Exploration 7: 342-351..
King D. A.. 1996. Allometry and life history of tropical trees. Journal of Tropical Ecology 12: 25-44..[ISI]
King D. A. Davies S. J. Supardi N. Tan S.. 2005. Tree growth is related to light interception and wood density in two mixed dipterocarp forests of Malaysia. Journal of Ecology 19: 445-453..[ISI]
King D. A. Loucks O. I.. 1978. The theory of tree bole and branch form. Radiation and Environmental Biophysics 15: 141-165..[CrossRef][ISI][Medline]
Kohyama T. Hotta M.. 1990. Significance of allometry in tropical saplings. Functional Ecology 4: 515-521..[CrossRef]
Kohyama T. Suzuki E. Parthomhardjo T. Yamad T. Kubo T.. 2003. Tree species differentiation in growth, recruitment and allometry in relation to maximum height in a Bornean mixed dipterocarp forest. Journal of Ecology 91: 797-806..[CrossRef][ISI]
Kuppers M.. 1989. Ecological significance of above ground architectural patterns in woody plants: a question of cost-benefit relationships. Trends in Ecology and Evolution 4: 375-379..[CrossRef]
Manly B. F. J.. 1997. Randomization, bootstrap and Monte Carlo methods in biology, 2nd ed. Chapman and Hall, London, UK..
McArdle B. H.. 1988. The structural relationship: egression in biology. Canadian Journal of Zoology 66: 2329-2339..
McMahon T.. 1973. Size and shape in biology. Science 79: 1201-1204..
Niklas K. J.. 1994. Interspecific allometries of critical buckling height and actual plant height. American Journal of Botany 81: 1275-1279..[CrossRef][ISI]
Niklas K. J.. 1995. Size-dependent allometry of tree height, diameter and trunk taper. Annals of Botany 75: 217-227..
Niklas K. J. Spatz H. C.. 2004. Growth and hydraulic (not mechanical) constraints govern the scaling of tree heights and mass. Proceedings of National Academy of Sciences, USA 101: 15661-15663..
Norberg R. A.. 1988. Theory of growth of plants and self-thinning of plant populations: geometric similarity, elastic similarity and different modes of plant parts. American Naturalist 131: 220-256..[CrossRef][ISI]
O'Brien S. T. Hubbel S. P. Spiro P. Condit R. Foster R. B.. 1995. Diameter, height, crown and age relationships in eight neotropical tree species. Ecology 76: 1926-1939..[CrossRef][ISI]
Osunkoya O. O. Ash J. E.. 1991. Acclimation to a change in light regime in seedlings of six Australian rainforest tree species. Australian Journal of Botany 39: 591-605..[CrossRef][ISI]
Osunkoya O. O. Ash J. E. Graham A. W. Hopkins M. S.. 1992. Factors affecting survival of tree seedlings in north Queensland rainforests. Oecologia 91: 569-578..[CrossRef][ISI]
Osunkoya O. O. Sheng T. K. Mahmud N. A. Damit N.. 2007. Variation in wood density, wood water content, stem growth and mortality amongst 27 tree species in a tropical rainforest on Borneo Island. Austral Ecology 32: 191-201..[CrossRef][ISI]
Poorter L. Bongers F. Sterck F. J. Woll H.. 2003. Architecture of 53 rainforest tree species differing in adult stature and shade tolerance. Ecology 84: 602-608..[CrossRef][ISI]
Poorter L. Bongers F. Sterck F. J.. 2005. Beyond the regeneration phase: differentiation of height-light trajectories among tropical tree species. Journal of Ecology 93: 256-267..[CrossRef][ISI]
Poorter L. Bongers L. Bongers F.. 2006. Architecture of 53 rainforest tree species: traits, trade off and functional groups. Ecology 87: 1289-1301..[ISI][Medline]
Shukla R. P. Ramakrishnan P. S.. 1986. Architecture and growth strategies of tropical trees in relation to successional status. Journal of Ecology 74: 33-46..[CrossRef][ISI]
Small A. Martin T. G. Kitching R. L. Wong K. M.. 2004. Contribution of tree species to the diversity of a 1 ha Old World rainforest in Brunei, Borneo. Biodiversity and Conservation 13: 2067-2088..[CrossRef][ISI]
Sposito T. C. Santos F. A. M.. 2001. Scaling of stem and crown in eight Cecropia (Cecropiaceae) species of Brazil. American Journal of Botany 88: 939-949..
Sterck F. J.. 1999. Crown development in tropical rainforest trees in gaps and understorey. Plant Ecology 143: 89-98..[CrossRef][ISI]
Sterck F. J. Bongers F.. 1998. Ontogenetic changes in size, allometry and mechanical design of tropical rainforest trees. American Journal of Botany 85: 266-272..[Abstract]
Sterck F. J. Bongers F. Newbery D. M.. 2001. Tree architecture in a Bornean lowland rainforest: intraspecific and interspecific patterns. Plant Ecology 153: 279-292..[CrossRef][ISI]
Thomas S. C.. 1996. Asymptotic height as a predictor of growth and allometric characteristics in Malaysian rainforest trees. American Journal of Botany 83: 556-566..[CrossRef][ISI]
van Gelder H. A. Poorter L. Sterck F. J.. 2006. Wood mechanics, allometry and life history variation in a tropical rain forest tree community. New Phytologist 171: 367-378..[CrossRef][ISI][Medline]
Warton D. I. Weber N. C.. 2002. Common slope tests for bivariate structural relationships. Biometrical Journal 44: 161-174..[CrossRef][ISI]
Warton D. I. Wright I. J. Falster D. S. Westoby M.. 2006. Bivariate line fitting methods for allometry. Biological Reviews 81: 259-291..[Medline]
West G. B. Brown J. H. Enquist B. J.. 1997. A general model for the origin of allometric scaling in biology. Science 276: 121-126..
Wright I. J. Reich P. B. Westoby M.. 2001. Strategy shifts in leaf physiology, structure and nutrient content between species of high and low rainfall and high and low nutrient habitats. Functional Ecology 15: 423-434..[CrossRef]
| ||||||||||||
, P < 0.10; *, P < 0.05; **, P < 0.01; ***, P < 0.0001. See