Evergreenness and wood density predict height–diameter scaling in trees of the northeastern United States

Forest Ecology and Management 279 (2012) 21–26

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Evergreenness and wood density predict height–diameter scaling in trees of the northeastern United States Mark J. Ducey ⇑ University of New Hampshire, Department of Natural Resources and the Environment, Durham, NH 03824, USA

a r t i c l e

i n f o

Article history: Received 13 March 2012 Received in revised form 27 April 2012 Accepted 30 April 2012 Available online 23 June 2012 Keywords: Allometric scaling theory Metabolic scaling Metabolic theory of ecology Tree growth Wood specific gravity North American forests

a b s t r a c t Several tree height–diameter scaling rules have been proposed based on mechanical considerations or metabolic scaling. I used data on 202,950 trees of 86 species from the northeastern United States to examine height–diameter scaling patterns, and to determine whether they were sensitive to phylogeny (angiosperm vs. gymnosperm), shade-, drought-, and waterlogging tolerance, evergreenness, and wood density. Mixed effects models were used to estimate average scaling relationships and to quantify variability due to species and site attributes. Results did not support the invariant 2/3 scaling exponent assumed by the Metabolic Ecology Model. Evergreenness and wood density emerged as the primary predictor of height–diameter scaling in this assemblage, with considerable variation remaining at the species and location level. The results suggest that greater ecological and ontogenetic variability must be incorporated into scaling theories if height–diameter scaling is to be predicted successfully. Ó 2012 Elsevier B.V. All rights reserved.

1. Introduction Tree architecture influences the ability of trees to capture light, and to remain stable in the face of wind, ice, and other mechanical disturbances. As such it is a key factor in the vertical structure and temporal dynamics of forest ecosystems (Poorter et al., 2006). Relationships between tree height and diameter are important for understanding fundamental physiological tradeoffs within individual trees, and how these may impact communities and ecosystems (Givnish, 1995; O’Brien et al., 1995). Improved understanding of height–diameter relationships is also critical for improving regional and global estimates of forest biomass and carbon storage, as many large-scale studies rely on allometric equations that depend on tree diameter alone (Jenkins et al., 2004; Zianis et al., 2005; Feldpausch et al., 2011). Within a timber inventory framework, predictive relationships between height and diameter have long been used to simplify the measurements needed to estimate timber volume, to project growth and yield, and to describe stand development trajectories (e.g. Curtis, 1967). More recently, tree architecture has been scrutinized in the context of general theories of metabolic scaling (West et al., 1997, 1999; Enquist and Niklas, 2002). Several factors have been suggested as constraints on or predictors of height–diameter scaling in trees. Ultimately, tree height is constrained by basic physics: beyond a certain height, a columnar ⇑ Tel.: +1 603 862 4429; fax: +1 603 862 4976. E-mail address: [email protected] 0378-1127/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.foreco.2012.04.034

structure of given strength and density will buckle under its own weight (Greenhill, 1881; McMahon, 1973). Maximum buckling height considerations and elastic self-similarity suggest that height should scale approximately as a power function of diameter, e.g.

H ¼ aDb

ð1Þ

where H is tree height, D is diameter at breast height, a is a scaling constant, and b = 2/3 is the scaling exponent (Greenhill, 1881; McMahon, 1973; Dean and Long, 1986). Different mechanical assumptions can yield different values for b. Stress-similarity implies b = 1/2 (McMahon and Kronauer, 1976), while minimization of biomass allocation in stems subject to lateral stress implies geometric similarity with b = 1 (King and Loucks, 1978; Niklas, 1993). Although mechanical considerations predict an envelope of the height–diameter relationship, some authors (e.g. Niklas, 1994; King et al., 2009) have found that average scaling exponents for some species are indeed close to 2/3. The Metabolic Ecology Model or MEM (West et al., 1997, 1999; Enquist and Niklas, 2002) also predicts that height should scale as diameter to the 2/3 power, based partly on the assumption that branching networks in trees are efficient, space-filling fractals. Niklas and Spatz (2004) suggest that even though the implied scaling exponents are similar, metabolism and hydraulic transport rather than buckling height drive observed patterns of height–diameter scaling. However, several recent studies have reported results that contradict one or more predictions of the MEM (e.g. Muller-Landau et al., 2006; Russo et al., 2007). Even if the MEM holds under some circumstances, other factors might also limit or modify height–diameter scaling relationships, including

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hydraulic limitation (Ryan and Yoder, 1997; Ryan et al., 2006) and competition (Assmann, 1970; Oliver and Larson, 1996, Henry and Aarsen, 1999). Given the number of factors potentially influencing the relative rates of height and diameter growth, and hence height–diameter scaling relationships, it would not be entirely surprising if multiple tree attributes impacted the scaling constant a, the scaling exponent b, or both, perhaps interactively. For example, Poorter et al. (2006) suggested that light demand should be a key predictor of tree architecture, while hydraulic limitation theory (Ryan and Yoder, 1997; Ryan et al., 2006) suggests drought-tolerance might play a role, with drought-tolerant trees showing greater hydraulic conductance (reflected in greater stem diameter) at a given height. A similar effect might be seen in tree species that are tolerant to waterlogging, if waterlogging is associated with rooting depth restrictions. To the degree that stem architecture reflects fundamental tradeoffs in carbohydrate allocation between height and diameter growth, other attributes associated with the carbohydrate economy of trees (such as evergreenness) might also be correlated with height–diameter scaling parameters. Any or all of these factors might interact with basic stem mechanical considerations (cf. King et al., 2009) to determine stem architectural phenotypes. One species attribute of potential interest in understanding height–diameter scaling is wood density. Wood density is correlated with a wide range of structural and functional characteristics of trees, and represents a key variable in a hypothesized ‘‘wood economics spectrum’’ that describes functional tradeoffs and constraints for woody plants (Chave et al., 2009). Wood density is often interpreted as reflecting a life history tradeoff: higher density is associated with resistance to breakage or hydraulic cavitation, but also with higher construction costs, leading to a fundamental tradeoff between growth rate and longevity (van Gelder et al., 2006). For example, Chou et al. (2008) found that low wood specific gravity was positively correlated with mortality risk in two Amazonian forest regions. However, recent authors have questioned the basic mechanical foundation of this hypothesis, as low-density stems can be larger in diameter and hence stronger for an equivalent mass investment (Anten and Scheiving, 2010; Larjavaara and Muller-Landau, 2010). Observed relationships between wood density and other functional traits may not be causal, but correlative and complex (Larjavaara and Muller-Landau, 2010; Russo et al., 2010). Nonetheless, wood density data are widely available for many tree species (Chave et al., 2009), and wood density seems to have some predictive power for ecological relationships, including those at the stand level (e.g. Dean and Baldwin, 1996; Woodall et al., 2005, 2006; Ducey and Knapp, 2010). The objectives of this paper are (1) to test whether observed height–diameter scaling conforms to the predictions of the stem mechanics and Metabolic Ecology Models, (2) to determine what broad functional characteristics of a species, if any, influence the scaling constant or exponent, and (3) to parse any explained departures from central trends into species- and site-level components.

Table 2 Species frequencies for height measurements used in this study. Species

Number of trees

Percent of total

Acer rubrum Acer saccharum Abies balsamea Picea rubens Tsuga canadensis Pinus strobus Fagus grandifolia Betula alleghaniensis Thuja occidentalis Betula papyrifera Quercus rubra Fraxinus americana Populus tremuloides Prunus serotina Picea mariana Betula lenta Picea glauca 69 Other species Total

32,817 20,332 18,277 16,246 15,517 13,491 10,483 9129 8417 7478 7336 7062 4310 3375 3041 2639 2402 20,598 202,950

16.2 10.0 9.00 8.00 7.6 6.6 5.2 4.5 4.1 3.7 3.6 3.5 2.1 1.7 1.5 1.3 1.2 10.1 100.0

Data are from a region of the northeastern United States that is dominated by naturally regenerated, mixed-species forests. The focus is on the regional scale because general scaling approaches such as the MEM are believed to provide better prediction over large scales than at micro-scales, such as the plot or stand scale of typical forest community investigations (cf. Tilman et al., 2004).

2. Methods 2.1. Data Data for this study come from the Forest Inventory and Analysis (FIA) program of the United States Forest Service, and were collected in the states of Connecticut, Maine, Massachusetts, New Hampshire, New York, Rhode Island, and Vermont. The FIA program collects tree measurements on one plot cluster per approximately 2400 ha of forested land across all ownership types in an annualized panel design. Each cluster consists of four plots. Trees with diameter at breast height (DBH) greater than 12.7 cm are tallied on a 0.0168 ha circular plot, while those with DBH between 2.54 and 12.7 cm are tallied on a nested 0.00135 ha circular plot. Further details of the field procedures can be found in USFS (2007), while additional detail on the design and associated statistical estimators can be found in Bechtold and Patterson (2005). All data were downloaded from the FIA database (Woudenberg et al., 2010) on November 26, 2010. Because the current FIA design was implemented beginning in different years in different states, the number of plots by state varies over time (Table 1). The raw tree measurement data were screened to include only live, unbroken trees with directly measured heights, and converted from their original English units to metric. Each tree was assigned a wood

Table 1 Number of plots with measured tree heights, by state and year. State

Connecticut Maine Massachusetts New Hampshire New York Rhode Island Vermont

Year 1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

0 610 0 0 0 0 0

0 616 0 0 0 0 0

0 603 0 0 0 0 0

0 575 0 113 650 0 0

50 563 92 133 652 14 100

48 543 83 127 337 17 131

51 590 88 137 355 18 148

78 612 133 167 565 30 242

79 616 142 186 608 52 245

66 618 111 159 658 32 155

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M.J. Ducey / Forest Ecology and Management 279 (2012) 21–26

specific gravity based on its species; specific gravities were taken from Miles and Smith (2009). In addition, each tree was assigned a dummy variable to indicate whether it was an angiosperm (0) or gymnosperm (1), and another dummy variable to indicate whether it was deciduous (0) or evergreen (1). Drought tolerance, shade tolerance, and waterlogging tolerance values (on ordinal scales from 1 to 5, but with some intermediate values) were taken from Niinemets and Valladares (2006). Of the original 204,146 tree records, 1196 were not identified to species or were of exceedingly rare species for which no specific gravity or tolerance values could be identified. Those trees were excluded, leaving 202,950 trees of 86 species from 9027 unique plot clusters in the data set. The species composition of the trees in the data is summarized in Table 2. 2.2. Statistical analysis Following log-transformation, the basic scaling model (Eq. (1)) becomes

lnðHÞ ¼ lnðaÞ þ b lnðDÞ þ ei

ð2Þ

Fitting Eq. (2) with ordinary least squares would involve assuming log-normally distributed individual-tree residuals in the original variable space of Eq. (1) (cf. Russo et al., 2007; Mascaro et al., 2011). Fitting (2) in this fashion requires post hoc adjustment of the scaling constant a, but not the scaling exponent b, to obtain unbiased predictions in the original untransformed variables (Baskerville, 1972). Although some authors have argued for other approaches (e.g. reduced major axis regression; Henry and Aarsen, 1999) measurement errors in height are likely to be much greater than those for diameter, so least squares is a reasonable approach. However, at least two additional sources of variation should be accounted for in the basic model. First, factors associated with site quality, climate, or stand history might affect the height–diameter scaling of all trees at an individual FIA plot cluster. Second, unmeasured factors associated with a particular species could affect the height–diameter scaling of all trees of that species. In other words, even if we account for other salient features of species biology, we would still expect individual species to vary around typical height– diameter scaling relationships. Both of these sources of variation can be modeled as random effects, which may either impact the scaling constant or the scaling exponent:

lnðHÞ ¼ lnðaÞ þ b lnðDÞ þ as þ bs lnðDÞ þ cp þ dp lnðDÞ þ ei

ð3Þ

where as and bs are random effects of species that modify the scaling constant and exponent, respectively, and cp and dp are random effects of plot that modify the scaling constant and exponent, respectively. The effects as, bs, cp and ds are defined to be normal with zero mean. The fixed effects [ln(a) + b ln m(D)] thus model the expected scaling relationship of an average species at an average plot. Model fitting and selection followed an information-theoretic approach using the Akaike Information Criterion (AIC) (Burnham and Anderson, 2002). To avoid numerical convergence challenges associated with divergent scales of measurement, D, wood specific gravity, and tolerance scores were normalized to zero mean and unit variance for fitting purposes. Using Eq. (3) as a base model, I attempted to add the gymnosperm and evergreen dummy variables, wood specific gravity, and shade, drought, and waterlogging tolerance scores as additional fixed effects, either alone (which would impact the scaling constant) or in interaction with D (which would impact the scaling exponent). All models were fit initially using maximum likelihood so that the calculated AIC would be valid and could be used to compare models. Factors were added in forward stepwise fashion so long as they led to an improvement (i.e. reduction) in AIC. Once a minimum AIC value was reached,

the final model was refit using restricted maximum likelihood to provide more efficient parameter estimates (Faraway, 2006). The final model (including random effects) was then transformed back to the space of the original variables for inspection and interpretation. All statistical analyses were performed using the lme4 package within R (Bates and Maechler, 2010; R Development Core Team, 2010). 3. Results Values of the variables used in this analysis for the 202,950 trees used in the data set are shown in Table 3. Only one species (Ilex opaca, 4 trees) was an evergreen angiosperm. Likewise, only one species (Larix laricina, 924 trees) was a deciduous gymnosperm. As a result, the gymnosperm and evergreen dummy variables were nearly collinear and at most one of those two variables was allowed to be included in any subsequent models. The best fitting model, as judged using AIC, included terms for evergreenness and wood specific gravity. Following transformation from standardized predictors to the original predictor variables, the fixed effects are described by the equation

lnðHÞ ¼ lnðaÞ þ b lnðDÞ lnðaÞ ¼ 1:0653ð0:2059Þ  0:5391ð0:0754ÞEV þ 0:5541ð0:2807ÞSG b ¼ 0:5411ð0:0491Þ þ 0:1382ð0:0229ÞEV  0:1790ð0:0907ÞSG ð4Þ where EV is the dummy variable for evergreenness, SG is wood specific gravity, and standard errors for each parameter are given in parentheses. DAIC = 43.6 was between the best model and the base model, and DAIC = 1.96 between the best model and the next best model, which omitted specific gravity and contained no additional variables. (From a traditional frequentist perspective, all fixed effects in the model were associated with significant t values in both the transformed and original variable spaces, with p < 0.05 for all individual fixed effects.) Fig. 1 depicts the model predictions using fixed effects only for evergreen and deciduous trees. The model also included substantial random effects of species and location on both the scaling constant a and on the scaling exponent b. In terms of the species effects, following transformation back to the original variables, as had a standard deviation of 0.2043, while bs had a standard deviation of 0.0535, and these effects were negatively correlated (r = 0.87). For the plot or location effects, cs had standard deviation equal to 0.3927, while ds had a standard deviation of 0.1093. The plot effects were also negatively correlated (r = 0.94). Fig. 2 shows the predicted values of the scaling parameters with and without the species random effects (values including the random effects for each species are given in Appendix Table A1). Notwithstanding the random effects, the evergreen and deciduous species are nearly disjunct when viewed in this plot (only two evergreens, Pinus rigida and Pinus sylvestris, Table 3 Characteristics of the n = 202,950 trees in the dataset. Variable

Minimum

Median

Maximum

Mean

Std. dev.

H (m) D (cm) Wood specific gravity Shade tolerance score (1–5) Drought tolerance score (1–5) Waterlogging tolerance score (1–5) Gymnosperm Evergreen

1.5 2.5 0.27 1.0

15.9 21.6 0.54 3.4

43.0 127.0 0.72 5.0

16.2 23.9 0.51 3.7

4.8 10.1 0.11 1.1

1.0

2.3

5.0

2.1

0.7

1.0

1.5

4.7

1.8

0.7

120,966 yes, 81,894 no 121,888 yes, 81,062 no

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M.J. Ducey / Forest Ecology and Management 279 (2012) 21–26

small number of relatively low-density evergreen species approach or exceed the predicted scaling exponent of 2/3. The scaling exponents in Fig. 2 reflect average plot conditions, and do not include the random effects of plot, which predict how observed scaling exponents would vary from location to location. Because the plot effect is normally distributed, the proportion of plots on which a species would be expected to reach or exceed b = 2/3 can be calculated as 1  F(z), where F is the normal cumulative density function and 2

z¼3

 ð0:5541 þ 0:1382EV  0:1790SG þ bs Þ 0:0535

ð5Þ

For example, the species most likely to reach or exceed b = 2/3 is Picea glauca, which would be expected to do so on 73% of plots. 13 species would be expected to achieve b = 2/3 on at least 10% of plots. All of these species are evergreen. The deciduous species most likely to achieve b = 2/3, Nyssa sylvatica, would be expected to do so on less than 1.5% of plots. 4. Discussion

Fig. 1. Predicted height–diameter allometry of evergreen and deciduous trees, using fixed effects only, at the average specific gravity (solid line) and maximum and minimum specific gravity (dashed lines) for each group.

Fig. 2. Height–diameter scaling parameters based on fixed effects only, and including the random effects associated with each species. Prediction of the Metabolic Energy Model is shown as a dotted line for comparison.

fall within the deciduous grouping). The mean scaling exponent of a deciduous species under average plot conditions was b = 0.45, while that of an evergreen species was b = 0.61. The mean over both groups combined, b = 0.49, falls at the upper extreme for the deciduous cluster. The deciduous gymnosperm Larix laricina is to be found amid the other deciduous species [ln(a) = 1.41, b = 0.46] while the evergreen angiosperm Ilex opaca is well within the range of the other evergreens [ln(a) = 0.51, b = 0.62]. Only a

Broadly speaking, height–diameter scaling among trees in this study region does not reflect the predictions of the MEM (West et al., 1997, 1999; Enquist and Niklas, 2002) or of the most commonly invoked theories of structural limitation (Greenhill, 1881; McMahon, 1973). The height–diameter scaling exponent was not invariant, as predicted by the MEM, but varied due to species attributes (evergreenness, wood specific gravity), random effects due to species, and random effects due to location. The latter could include climate, site quality, and current and past competition. Moreover, typical scaling exponent values for deciduous species were quite far from the 2/3 predicted by MEM. Some evergreens are predicted to approach the MEM prediction at least some of the time, however. In some ways, the failure of the MEM to predict height–diameter scaling is understandable: several authors have suggested that competition for light and nutrients, local demographics, and disturbance might overwhelm the underlying scaling trends predicted by MEM (Tilman et al., 2004; Coomes, 2006; Muller-Landau et al., 2006). Nonetheless, the MEM hypothesis remains controversial (Coomes and Allen, 2009; Duursma et al., 2010; Stark et al., 2010; Price et al., 2010; Coomes et al., 2011). For example, Stark et al. (2010) argue that while Russo et al. (2007) found interspecific variability in scaling parameters, the broad average across species conformed approximately to MEM predictions. The same cannot be said of the results of this study. To the degree that the results of this study do not match well with the MEM, how about competing scaling theories based on mechanical principles? Certainly the mean scaling exponent over all species (b = 0.49) corresponds quite well to the predictions of the stress similarity hypothesis (King and Loucks, 1978). Unfortunately, these results present a situation in which the mean is hardly typical: the distribution of scaling exponents quite broad, with evergreens clustered intermediate between the scaling exponents predicted by MEM or the elastic similarity hypotheses, and deciduous species tending to fall below that predicted by stress similarity. Low values of the scaling exponent do not appear uncommon: Russo et al. (2007) report an average value of b = 0.45 for New Zealand forests, while Feldpausch et al. (2011) report b = 0.53 for their pan-tropical analysis. However, both between-species and between-location variability are evident, and the results here do not correspond neatly to those predicted by any single scaling rule. Competition between trees is a critical factor that could drive departures from the relatively simple MEM model or any simple mechanically-derived rule (Mäkelä and Valentine, 2006). Likewise,

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M.J. Ducey / Forest Ecology and Management 279 (2012) 21–26 Table A1 Scaling constants and exponents for all species, incorporating both fixed and random effects from the model. Species

ln(a)

b

Abies balsamea Abies fraseri Acer negundo Acer nigrum Acer pennsylvanicum Acer platanoides Acer rubrum Acer saccharinum Acer saccharum Acer spicatum Aesculus glabra Ailanthus altissima Amelanchier arborea Betula alleghaniensis Betula lenta Betula nigra Betula papyrifera Betula populifolia Carya cordiformis Carya glabra Carya laciniosa Carya ovata Castanea dentata Catalpa speciosa Celtis occidentalis Chamaecyparis thyoides Cornus florida Fagus grandifolia Fraxinus americana Fraxinus nigra Fraxinus pennsylvanica Gleditsia triacanthos Ilex opaca Juglans cinerea Juglans nigra Juniperus virginiana Larix laricina Liquidambar styraciflua Liriodendron tulipifera Magnolia cuminata Morus alba Nyssa sylvatica Ostrya virginiana Picea abies Picea glauca Picea mariana Picea pungens Picea rubens Pinus banksiana Pinus nigra Pinus resinosa Pinus rigida Pinus strobus Pinus sylvestris Pinus virginiana Platanus occidentalis Populus balsamifera Populus deltoides Populus grandidentata Populus tremuloides Prunus persica Prunus serotina Prunus virginiana Pseudotsuga menziesii Quercus alba Quercus bicolor Quercus coccinea Quercus macrocarpa Quercus muehlenbergii Quercus palustris Quercus prinus Quercus rubra Quercus stellata

0.563310 0.884362 1.287901 1.102923 1.224640 1.378349 1.501424 1.391696 1.578680 1.155387 1.222592 1.100026 1.368907 1.588783 1.519973 1.311029 1.507150 1.370103 1.476039 1.274864 1.416760 1.404015 1.184987 1.377692 1.058600 0.801018 1.199312 1.252189 1.589726 1.430213 1.348849 1.453910 0.506555 1.193342 1.077321 0.643276 1.412731 1.364088 1.327860 1.411190 1.330896 1.049334 1.624877 0.723078 0.513128 0.737308 0.403423 0.681018 0.781255 0.758510 0.895269 1.285323 0.816870 1.038030 0.851467 1.421029 1.277420 1.478265 1.685232 1.458955 1.327170 1.253850 1.341929 0.863201 1.269595 1.370124 1.281888 1.286673 1.171735 1.161797 1.515024 1.585060 1.409946

0.692443 0.605802 0.421796 0.464813 0.466459 0.432019 0.419500 0.450118 0.396229 0.492753 0.457199 0.518652 0.428896 0.368108 0.411188 0.459985 0.411957 0.456659 0.454305 0.510998 0.432477 0.475286 0.474087 0.453777 0.474762 0.586743 0.439080 0.467991 0.412552 0.421177 0.484402 0.431355 0.616962 0.480353 0.524240 0.588517 0.459211 0.447771 0.488413 0.458307 0.450371 0.549546 0.335627 0.647519 0.700039 0.649916 0.679207 0.645932 0.626824 0.600970 0.572902 0.449537 0.600201 0.514140 0.603153 0.453972 0.488970 0.447654 0.385507 0.454937 0.457213 0.487680 0.427269 0.559746 0.472670 0.427226 0.484074 0.465015 0.439782 0.497642 0.400422 0.393031 0.431506

Table A1 (continued) Species

ln(a)

b

Quercus velutina Robinia pseudoacacia Salix alba Salix nigra Sassafras albidum Sorbus americana Thuja occidentalis Tilia americana Tsuga canadensis Ulmus americana Ulmus pumila Ulmus rubra Ulmus thomasii

1.452319 1.452843 1.330181 1.300174 1.114194 1.367019 0.685248 1.145385 0.431364 1.111892 1.337829 1.416124 1.432381

0.427099 0.451353 0.422000 0.447298 0.515347 0.389490 0.579537 0.522704 0.663990 0.523212 0.427961 0.433793 0.437215

self-shading may influence the allocation of biomass to branches within a crown, and hence drive departures from scaling relationships predicted by MEM (Duursma et al., 2010). Competition is almost certainly a factor influencing the random variability in scaling parameters at the plot scale (Henry and Aarsen, 1999), and indeed the use of height–diameter ratios as diagnostic tools by foresters and manipulation of those ratios through density management argues for a strong competitive influence (e.g. Wonn and O’Hara, 2001). Thus it was somewhat surprising that shade tolerance – the capacity to grow in the shade, whether shade is due to competition or self-shading (Niinemets and Valladares, 2006) – did not emerge as a predictor of height–diameter scaling patterns among these species. Among the species attributes that were considered in this study, evergreenness emerged as a strong predictor and wood density as a considerably weaker one. The sensitivity of height–diameter scaling to wood density is consistent with the recent analysis by Anten and Scheiving (2010), who suggest that low wood density is carbohydrate-efficient for maximization of height growth while high wood density is more efficient for mechanically stable branches. Although wood density appears to be an important element of a broader resource efficiency spectrum (Chave et al., 2009), one should be cautious about asserting a mechanistic basis for its association with scaling properties, as correlations between wood density and other ecophysiological attributes, including mechanistic attributes of wood and emergent properties such as tolerance and longevity, can be highly variable (Larjavaara and Muller-Landau, 2010; Russo et al., 2010). For our species, wood density was correlated with drought tolerance (Spearman’s q = 0.38, n = 86, p < 0.001) but not shade tolerance (q = 0.02, p = 0.88) or waterlogging tolerance (q = 0.09, p = 0.43). The results of this study highlight the importance of both intraspecific and spatial variability for allometric scaling. In this light, we should consider the statement by Niklas (1995, p. 226) that ‘‘tree allometry is a plastic developmental feature rather than fixed character.’’ Certainly natural selection operates on trees, but the results may not be optimal in any Panglossian sense (Gould and Lewontin, 1979). Trees are subject to the laws of physics, but to our knowledge trees also lack the capacity to perform the calculations needed to use those laws infallibly to their advantage. As such, variability is to be expected around central tendencies shaped by life-history strategy, resource allocation, and the competitive environment. Appendix A Table A1.

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