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Logo of annbotAboutAuthor GuidelinesEditorial BoardAnnals of Botany
Ann Bot. 2016 April; 117(4): 551–563.
Published online 2016 March 14. doi:  10.1093/aob/mcw003
PMCID: PMC4840475

Allometric exponents as a tool to study the influence of climate on the trade-off between primary and secondary growth in major north-eastern American tree species


Background and Aims Trees invest in both primary (e.g. height) and secondary (e.g. diameter) growth. The trade-off between these investments varies between species and changes with the tree growing environment. To better establish this trade-off, readily available allometric exponents relating height to diameter at breast height (γh,dbh) and stem volume to diameter at breast height (αv,dbh) were simultaneously studied.

Methods Allometric exponents αv,dbh and γh,dbh were obtained from 8893 individual tree stem analyses from two broadleaved species (Betula papyrifera, Populus tremuloides) and four conifers (Picea glauca, Picea mariana, Pinus banksiana, Abies balsamea) in the temperate and boreal forests of the province of Quebec, Canada. αv,dbh and γh,dbh were related to tree age, stand density index (SDI), and mean temperature (TGS) and total precipitation (PGS) of the growing season.

Key Results αv,dbh and γh,dbh were found to be invariant with PGS and positively related to SDI and TGS for all species except Pinus banksiana . The parameter values associated with SDI and TGS were of higher value for conifers than for broadleaved species.

Conclusions This suggests that conifers and broadleaved species have different growth patterns. This could be explained by their different mode of development, the conifer species having a stronger apical dominance than broadleaved species. Such results could be further considered in allocation studies to quantify future carbon stocks in managed forests.

Keywords: tree growth strategy, temperature, competition, broadleaved species, conifers, mode of development, Betula papyrifera, Picea glauca, Picea mariana, Populus tremuloides, Pinus banksiana, Abies balsamea


Tree size is optimized to maintain functional requirements (Niklas, 1995; Pretzsch, 2010) such as hydraulic (e.g. sap conduction) and mechanical safety (e.g. resistance to buckling) as well as resource acquirement (e.g. leaf or root production). It has been established that these functional requirements are related to tree metabolism (Niklas, 1994). This premise led to the elaboration of the metabolic scaling theory (MST), which provides a predictive framework that allows a better understanding of plant ecology (West et al., 1999, 2009; Allen and Gillooly, 2009). However, numerous studies have revealed a divergence between empirical results and predictions made by the MST (Duursma et al., 2010; Franceschini and Schneider, 2014; Smith et al., 2014).

Such linkage between tree functioning and metabolism was established using the properties of allometric relationships, which relate the change in scale between two dimensions X and Y of a given individual:


The allometric exponent αX,Y can be interpreted in terms of the relative growth rates of Y over X (Pretzsch et al., 2013):


The allometric exponent can thus be interpreted that an increase of 1 % in X will induce an increase by αX,Y % in Y. In practice, the allometric exponents may be computed from the values of X and Y at year i and i−1 and using logarithmic transformation and are expressed as:


Several studies have focused on understanding how allometric exponents vary with climatic variables. Specifically, in tropical rain forest ecosystems, the height to diameter at breast height (dbh) exponent (γh,dbh) is positively correlated with light competition (Muller-Landau et al., 2006; Antin et al., 2013). In Mediterranean ecosystems, drought was found to reduce the growth investment in height compared with the growth investment in diameter (Lines et al., 2012). Such a pattern was explained by the necessity in case of drought to reduce the root to leaf distance while keeping a sufficient conductive area and maintain the water continuum through the tree (Ryan and Yoder, 1997; Koch et al., 2004; Cramer, 2012). However, little information is available on the influence of climatic factors on tree allometry for northern boreal and temperate ecosystems. To our knowledge, no study has investigated the change in relative investment in height, dbh and volume with climate change in northern ecosystems even if it is expected to have strong effect on tree species growth (Messaoud and Chen, 2011; Gómez-Aparicio et al., 2011; Bontemps et al., 2012).

Such relationships between tree allometry and climatic variables are the direct representation of the optimal partitioning theory, which states that trees prioritize growth allocation to the compartment that favours the acquisition of the limiting resource (Thornley, 1972; McCarthy and Enquist, 2007). However, this theory remains to be better established to reconcile allocation strategies and growth as defined in most allometric studies (McCarthy and Enquist, 2007). For a given tree, more than half of the carbon is located in the stem (Návar, 2009; Petersson et al., 2012). It is thus of great interest to explore in detail stem growth components.

Stem growth can be quantified by its volume increment and is the result of both primary and secondary growth. Specifically, primary growth is the activity of the primary meristems resulting in vertical and horizontal shoot elongation. Secondary growth is the activity of the secondary meristems resulting in wood production. In the present paper, we use stem height increment to quantify stem primary growth and dbh increment as an indicator of stem secondary growth. These two types of growth could thus represent tree investment in different functional requirements: light interception through exploration of the environment (primary growth: Barthelemy and Caraglio, 2007) and both storage and mechanical support functions (secondary growth: Speck and Rowe, 2003).

Allometric exponents can thus be used to gain insight into growth partitioning between primary and secondary growth. From eqn (2), the allometric exponent relating height to dbh (γh,dbh) represents the differential increase in relative height growth (i.e. stem primary growth) with respect to relative diameter growth (i.e. stem secondary growth) while the allometric exponent relating stem volume to dbh (αv,dbh) represents the relative stem volume growth (i.e. both primary and secondary growth) with respect to relative dbh growth (i.e. stem secondary growth) (Pretzsch et al., 2013). Therefore, a larger αv,dbh implies that relative stem volume increment will be more important than relative dbh increment. In this case, a high relative stem volume increment may be related to (1) higher investment in stem primary growth compared with secondary growth (relative height increment would be higher than relative dbh increment) or (2) changes in stem tapering (Goudiaby et al., 2012; Schneider et al., 2013; Ung et al., 2013).

In addition, many studies have used allometric equations to estimate tree volume or biomass using often dbh or tree height (e.g. Jenkins et al., 2003; Zianis and Mencuccini, 2004). Such studies use only one dendrometric measurement, which may be not sufficient to estimate volume or biomass confidently. Note that recent large-scale studies have successfully used both dbh and tree height simultaneously (Chave et al., 2005; Vieilledent et al., 2011). However, these studies did not consider changes in stem primary and secondary growth, which could induce changes in αv,dbh while γh,dbh remains constant. This emphasizes the need to simultaneously consider αv,dbh and γh,dbh in volume and biomass estimation.

Growth strategies vary widely between angiosperms (broadleaved species for our study) and gymnosperms (conifers for our study), which reflect differences in their allometric exponents. These variations have not yet been adequately explained (Lines et al., 2012). These taxonomic groups are expected to have different trade-offs in primary and secondary growth as gymnosperms have a strong apical dominance (monopodial branching system) during their entire life while the apical dominance of angiosperms decreases with tree age (sympodial branching system) (Hallé et al., 1978; Barthelemy and Caraglio, 2007; Millet, 2012).

The main objective of this study was to establish the trade-off between stem primary and secondary growth in trees using allometric exponents αv,dbh and γh,dbh. Our specific objectives were (1) to investigate how stand density and climatic variables influence the height and stem volume to dbh allometric exponents (αv,dbh and γh,dbh) and (2) to identify differences in these relationships between broadleaved species and conifers. Our hypotheses were that (1) site-specific variations of both allometric exponents will be strongly and positively influenced by stand density (Pretzsch and Dieler, 2012), temperature and precipitation (Lines et al., 2012), and (2) the conifer stronger apical dominance (Barthelemy and Caraglio, 2007) will induce higher primary growth of the stem, compared with its secondary growth.


Study area

We took advantage of a large-scale stem analysis database across north-eastern America (Fig. 1). The data were collected between 2000 and 2006 and are the property of the Forest Inventory Branch of the Quebec Ministry of Forest, Wildlife and Parks (, MRNF, 2009). A total of 8893 stem analyses were available for the following species: paper birch (Betula papyrifera), white spruce (Picea glauca), black spruce (Picea mariana), trembling aspen (Populus tremuloides), jack pine (Pinus banksiana) and balsam fir (Abies balsamea).

Fig. 1.
Site location map.

The stem analyses were acquired from 1308 inventory plots located in the most important site types of each ecological region in Quebec covering a land base of 761 000 km2 (Fig. 1). The plot location was based on the provincial ecological regions, and the ecological types found in each region. A total of 48 ecological regions have been defined according to their bioclimatic domain, forest species composition and forest dynamics (Ministère des Ressources Naturelles, 2013). For each ecological region, the three to four ecological types which have the greatest area were selected, and a minimum of five plots were randomly located on each type.

In each 400-m2 plot, the dbh of all living trees with a dbh larger than 9·1 cm was measured. From the inventory data, stand density (number of stems per hectare with a dbh larger than 9.1 cm) for each plot is obtained, which represents the competition level at time of felling. Stand density index (SDI) representing the ‘standardized stem density for a quadratic mean diameter of 25 cm’ (Dieler and Pretzsch, 2013) was then calculated to homogenize competition pressure between each plot:


where SDI is the computed stand density index, SD the actual stand density (stems ha−1) at the moment of data collection, Qd the actual quadratic diameter of the stand (cm) and δSD,Qd an allometric coefficient relating stand density to the quadratic diameter fixed to −1·605 as established in previous studies (Pretzsch and Biber, 2005; Dieler and Pretzsch, 2013).

Sampling and allometric exponent calculation

In each plot, between five and ten dominant and co-dominant trees were randomly selected and felled. A complete description of the sampling design is available in Schneider et al. (2013). The characteristics of the sampled trees are given in Table 1. The selected trees had to be as straight and symmetrical as possible and without forks so as to facilitate determination of the main stem. On each tree, discs were obtained at 0·15, 0·6, 1·00, 1·30 and 3·00 m and every 2 m upward until the top of the tree. Ring widths were measured using the Windendro software (Industries Régent, 2005) on four perpendicular radii on each disc below 1·3 m (including the disc sampled at 1·3 m) and on two opposite radii for discs higher than 3 m (including the disc sampled at 3 m). The COFECHA software (Holmes, 1983) was then used to cross-date the ring width chronologies.

Table 1.
Dataset statistics (s.d. in parentheses)

Retrospective height growth was evaluated using the method of Carmean (1972) as corrected by Newberry (1991). This method is adapted in cases of stem analyses for which the diameter of each cross-section is available (Dyer and Bailey, 1987; Subedi and Sharma, 2010). This interpolation is based on two major assumptions: (1) each stem section is cut in the middle of a height growth year and (2) height growth is constant between two successive cross-sections. Newberry (1991) noted that this method led to biased estimates for height growth computed for the uppermost section. Precisely, the last shoot growth is not located between two cross-sections, but only one at the base, and thus needs correction. The general equation to determine retrospective heights is:


For the upper section, eqn (4) is modified as:


where Hij is the estimated total tree height for year i of section point j, hj the height of section point j, rj the number of rings of section point j and i the number of rings ranging from 1 to rj. At the top of the tree, hj+1 is total tree height and rj+1 equals rj.

Annual volume increment was obtained by estimating the volume of each section bounded by two successive parallel discs (stem log) using Smalian’s formula (Loetsch et al., 1973):


where V is the volume of the stem log, A1 the area of the bottom cross-section, A2 the area of the top cross-section and L the length of the cross-section. This formula was found to have the lowest bias when both cross-sectional areas of a log are available, as is the case in this study (Forslund, 1982; Filho et al., 2000). For each year, the diameter of the stem is available through the ring width data for every height where a disc was cut out. The volume between two cross-sections was computed considering that the shape of a given log is a second-degree paraboloid (Loetsch et al., 1973; Schreuder, 1993). The volume of each log is then summed to obtain stem volume.

The allometric exponents αv,dbh and γh,dbh for each year i were finally computed using the following equations:



Climatic data

Climatic data from the different provincial weather stations were interpolated for each plot using the BIOSIM software (Régnière and Bolstad, 1994; Régnière, 1996). From these interpolations, we obtained 30-year averages (period 1971–2000) for mean temperature during the growing season (TGS) and total precipitation during the growing season (PGS). The growing season is defined as the period delimited by the first three consecutive days without frost during spring until the first three consecutive days with frost during autumn.

Statistical analysis

Models for αv,dbh and γh,dbh as a function of tree age were estimated by considering an age-dependent logistic growth function (Franceschini & Schneider, 2014) whose form is:


where AEijk is the allometric exponent (αv,dbh or γh,dbh) of the growth year i of tree j in site k, TAijk is the tree age at the growth year i of tree j in site k, εijk the residuals of the model for the growth year i of tree j in site k following a normal distribution with mean 0 and variance σ2, (a1, a2, a3) the parameters of the logistic function and fAE(TAijk) is a function of tree age which equals 0 for all species except jack pine. Specifically, jack pine allometric exponents were found to have a local maximum with tree age: αv,dbh and γh,dbh first increase prior to the maximum and decrease thereafter (Franceschini and Schneider, 2014). Therefore, the correction applied was respectively:



The models were fitted with mixed-effects using the nlme function of the ‘nlme’ package (Pinheiro et al., 2007) of the R software. Site and individuals were considered as nested random levels in the models. Random effects on each estimated parameter of the logistic functions were tested and the model with the lowest Akaike’s information criterion (AIC) was finally selected. The temporal correlation was accounted for by a first-order autocorrelation function. In all fitted models, a random effect associated with the parameter a1 was always found to be significant and represented the value of allometric exponents when trees are mature.

For each species, a1 was expressed as a function of SDI and climatic variables characterizing the site conditions by introducing these variables in the non-linear mixed-effects model defined in eqns (9), (10) and (11). The parameter a1 was therefore a linear combination of SDI and climatic variables. In eqn (10), we replaced a1 by a1k, which is expressed as follows:


where SDIk is stand density index of site k as defined by eqn (4), TGSk the 30-year average temperature of the growing season of site k and PGSk the 30-year average precipitation sum during the growing season of site k.

The variation of the asymptote for various climatic conditions and stand densities was then explored using the 5th and the 95th percentiles of each variable used to explain a1 (i.e. SDI, TGS and PGS, Table 2). The parameter estimates of eqn (13) were then used to inspect the variations of the asymptote (i.e. allometric exponents during the mature stage) with SDI, temperature and precipitation.

Table 2.
Mean 5th and 95th percentiles for stand density index (SDI), temperature of the growing season (TGS) and precipitation of the growing season (PGS)


The αv,dbh asymptote was found to be proportional to SDI for all species except trembling aspen (Table 3, Fig. 2). A positive effect of TGS was found for all species except jack pine and balsam fir, which were insensitive to TGS. The parameters associated with SDI and TGS (a11 and a12, respectively, in Table 3) were in general higher for conifers than for broadleaved species. PGS was found to have a significant positive effect on white spruce while this effect was significantly negative for paper birch. The exponent αv,dbh was insensitive to PGS in all other species. In all, PGS had a more limited effect on the αv,dbh asymptote than SDI and TGS as only two of the six species parameters were found to be significant (Table 3, Fig. 2).

Fig. 2.Fig. 2.
(A–R) Variation of αv,dbh with tree age with variations of stand density index (SDI, first column), temperature of the growing season (TGS, second column) and precipitation of the growing season (PGS, third column) from the 5th (black) ...
Table 3.
Species by species fixed effect estimates and statistics for αv,dbh models using eqns (8) and (9)

The γh,dbh asymptote was positively related to SDI for all species except jack pine (Table 4). The γh,dbh asymptote was proportional to TGS for trembling aspen, balsam fir and both spruces while it was inversely proportional to TGS for jack pine. In addition, the SDI and TGS parameter estimates (a11 and a12, respectively, in Table 4) for γh,dbh were larger for the conifers than for broadleaved species (Fig. 3). The γh,dbh asymptote was found to be negatively related to PGS for trembling aspen only.

Fig. 3.Fig. 3.
(A–R) Variation of γh,dbh with tree age with variations of stand density index (SDI, first column), temperature of the growing season (TGS, second column) and precipitation of the growing season (PGS, third column) from the 5th (black) ...
Table 4.
Species by species fixed effect estimates and statistics for γh,dbh models using eqn (8 and 9).

When the relationship between γh,dbh and αv,dbh was plotted (Fig. 4), a general positive relationship was observed (slope of 0·639, P < 10−4). However, note that this relationship was different for conifers and broadleaved species (Fig. 4). Specifically, the slope of the relationship between γh,dbh and αv,dbh was 0·609 for broadleaved species and 0·702 for conifers.

Fig. 4.
γh,dbh as a function of αv,dbh for rings of age superior to 80 years for broadleaved species (black) and conifers (grey). The slope and R2 are 0·702 (P < 10−16) and 85·0 %, respectively, ...


The balance between stem primary and secondary growth was quantified using allometric exponents. Stem volume growth and the trade-off occurring between its growth components (i.e. stem primary growth and secondary growth) could thus be explored as a function of the tree growing environment.

As per the equation for γh,dbh and αv,dbh (eqn 2), the present study provides information regarding the relative species growth investment in dbh, height and stem volume. Specifically, if γh,dbh and αv,dbh increase concomitantly with SDI or a climatic variable, this would signify that for a given relative dbh increment, the relative stem volume increment is imputable to relative height increment: stem volume growth will be explained mainly by an investment in primary growth rather than secondary growth. By contrast, if γh,dbh remains constant and αv,dbh increases, this means: (1) that the relative stem volume increment may be equally imputable to the relative dbh and height increments, i.e. the stem volume growth is the result of both stem primary and secondary growth; or (2) the relative stem volume increment may be attributable to changes in stem form or taper. It has been shown that stem taper changes with competition status (Mäkelä, 2002), stand density (Garber and Maguire, 2003) and soil nutrient availability (Jokela et al., 1989). The present data have already been used to calibrate stem taper equations, whereby taper was found to change with stand density and/or stand basal area, depending on species (Schneider et al., 2013). Changes in stem form with climatic variables, however, remain to be confirmed, although shifts in radial growth distributions have been observed in several species (Courbet and Houllier, 2002; Goudiaby et al., 2012).

Note that past height and volume measurements are in fact interpolated using stem analysis data. Both Newberry’s corrected height interpolation of Carmean (Carmean, 1972; Newberry, 1991) and Smalian’s formula of volume computations (Loetsch et al., 1973) were successfully used numerous studies examining tree volume (Forslund, 1982; Filho et al., 2000) and height growth curves (Dyer and Bailey, 1987; Subedi and Sharma, 2010). Nevertheless, we admit that the assumption behind this method may lead to an uncertainty. However, this uncertainty is integrated in the allometric exponents and therefore will be taken into account in the model residuals without interfering with the relationship between allometric exponents and the variables included in the model. Moreover, stem analysis data are commonly used in carbon estimation studies (Whittaker, 1961; Mäkelä, 2002; Beets et al., 2014). Finally, height–age relationships based on past height interpolations obtained from stem analyses have long been used in forestry (Monserud, 1984; Gamache and Payette, 2004).

Our models indicate that the allometric exponents vary with stand density, as shown by the positive effect of SDI on αv,dbh and γh,dbh (Watt and Kirschbaum, 2011; Lines et al., 2012; Pretzsch and Dieler, 2012). In dense stands, Reineke’s rule states that dominant trees have smaller dbh for the same height (Reineke, 1933; Pretzsch and Biber, 2005). By contrast, dominant tree height is generally hypothesized to be insensitive to the competition level of a forest stand (Lanner, 1985; Mäkinen and Isomäki, 2004). This therefore implies that in stands with high SDI, dominant trees will favour their stem primary growth to optimize their light acquisition compared with secondary growth, leading to higher γh,dbh.

In addition, the dominant tree investment in stem primary growth decreases from the juvenile to the mature phase as the competition for light is less intense (Antin et al., 2013). As trees develop their crown through their branching system and the reiteration process (Barthelemy and Caraglio, 2007), they also have to invest more in the stem to be able to mechanically support their crown (Rowe and Speck, 2005). This means that tree stem volume investment is of higher intensity in the upper part of the stem than at breast height as trees age (Goudiaby et al., 2012). As a general rule, when stands become older their stand density decreases as a consequence of the self-thinning law (Pretzsch and Biber, 2005). High SDI therefore implies that for a given investment in secondary growth, the investment in stem primary growth will be more intensive, explaining the positive relationship between αv,dbh and SDI.

Note that we used a single value of stand density while the model constructed was primarily a variation of allometric exponents as a function of tree age. One can argue that this may lead to erroneous interpretation as stand density is not constant over time. However, when examining the model structure, it can be noted that SDI is integrated in the parameter representing the curve asymptote (parameter a1 in eqn 10). Thus, the asymptote corresponds to the value of allometric exponents at the time of establishment of the experiment. As a consequence, considering a single value of SDI is consistent in this context. Moreover, SDI is used to rank the sample plots in terms of stand density, as SDI characterizes a number of stems for a given mean dbh (in our case, 25 cm). The underlying hypothesis is that a dense stand at the time of felling was still a dense stand after the standardization. Furthermore, the trees felled in this study were not harvested in managed stands, and thus important within-stand changes in density were not present within the dataset (Schneider et al., 2013).

When temperatures are higher, the stem volume growth for most species corresponds to a higher investment in stem primary growth, as indicated by the positive TGS parameter estimates for αv,dbh and γh,dbh models, in accordance with previous studies (Cortini et al., 2010; Ung et al., 2013). Way and Oren (2010) hypothesized that the increase in volume growth with temperature was associated with a higher net carbon uptake (e.g. photosynthesis larger than respiration). They thus concluded that with increasing temperatures, trees shift their allometric patterns to adapt to the new climatic conditions.

Jack pine, however, is the exception to this general pattern, as it presents a negative relationship between γh,dbh and TGS, in contradiction to previous results (Zhang et al., 2002). However, jack pines are likely to grow on sandy soils with poor water retention (Burns et al., 1990). The reduction of jack pine investment in stem primary growth could be explained by a confounding effect of temperature and water availability. Specifically, tree height growth may be limited as a consequence of water stress in order to maintain a sufficient water potential and conductive area (Ryan and Yoder, 1997; Koch et al., 2004; Cramer, 2012). Moreover, the water residency time in sandy soils is low and therefore high levels of precipitation do not necessarily imply high water availability (Cuenca et al., 1997; Teepe et al., 2003). Additional soil data for the jack pine stands would be needed to corroborate our interpretation.

The effect of precipitation on the allometric exponents was more difficult to identify. In our analysis, temperatures ranged from 11·8 to 14·6 °C (minimum and maximum values in Table 2), representing a variation of approx. 20 %, while precipitation ranged from 393 to 590 mm, i.e. a variation of approx. 33 % (minimum and maximum values in Table 2). Despite the range of variation of PGS was larger than for TGS, we were able to detect an effect of TGS on αv,dbh and γh,dbh while PGS only had a marginal effect on these exponents. This indicated that temperatures are a more important driver of growth than hydric conditions in Quebec (Fortin and Langevin, 2010). In addition, Way and Oren (2010) showed that in cold temperate and boreal ecosystems, tree growth could be limited by temperature and a slight warming could have a great effect. Wang et al (2006) found that temperature is the most important factor influencing the height–dbh relationship in regions of China where water is not limiting. Conversely, in drier ecosystems, the effect of precipitation was found to be more important (Martínez and López-Portillo, 2003).

Some studies have found that the relationship between growth and climatic variables may differ according to stand density in both broadleaved species (Europe: Gea-Izquierdo et al., 2009; North-America: Keyser and Brown, 2014) and conifers (North-America: Yeh and Wensel, 2000; Europe: Guillemot et al., 2015). Therefore, one could expect that an interaction between climatic variables and SDI introduced in eqn (13) would lead to better models. This was tested (data not shown) but finally not retained in our analysis for two reasons. (1) Such integration led to strong co-linearities between the variables and interaction terms and therefore made parameter interpretation not possible (Quinn and Keough, 2002). (2) Models with interactions had generally higher AICs (data not shown), and were thus statistically not as good.

Stand density and climatic variables (to a lower extent) were found to have greater influence on the conifer allometric exponents than those of the broadleaved species. Indeed, when considering both intervals of αv,dbh and γh,dbh from Figs 2 and and33 and the value of the parameters from Tables 3 and and4,4, αv,dbh and γh,dbh presented larger variations for conifers than for broadleaved species for SDI and TGS. One exception to this is the relationship between both αv,dbh and γh,dbh with SDI for black spruce, the parameter being smaller than those for paper birch (a11 for αv,dbh being 0·000215 for black spruce compared with 0·000219 for paper birch and a11 for γh,dbh being 0·000235 for black spruce and 0·000236 for paper birch, Tables 3 and and4).4). Such a difference between conifers and broadleaved species was previously found for γh,dbh for Norway spruce and European beech with varying SDI (Pretzsch and Dieler, 2012). In addition, the only species presenting a significant relationship between allometric exponents and precipitation was a conifer (e.g. black spruce).

These differences could be related to the different primary and secondary growth trade-off between conifers and broadleaved species. Conifers have a strong apical dominance, with limited horizontal crown diameter expansion (Millet, 2012). For these species, an increase in stem volume might be related to a higher investment in stem primary growth. This explains that an increase in αv,dbh for conifers is likely to be associated with an increase in γh,dbh. By contrast, broadleaved species are characterized by a poor apical dominance and a large crown diameter. In addition, some of the new branches are the result of intense reiteration that is more common in broadleaved species than in conifers (Barthelemy and Caraglio, 2007; Millet, 2012). For broadleaved species, an increase in stem volume might therefore be associated with a stronger increase in dbh compared with stem height growth as the investment in branch expansion may be important. In other words, the investment in stem secondary growth may be relatively higher than in stem primary growth for broadleaved species. Such an interpretation is consistent with a previous study that observed a difference in biomass allocation between the stem and branches in tropical conditions: trees living in harsh environments were smaller with a higher allocation to branches (Peters et al., 2014). For our allometric exponents, this implies that the slope of the relationship between αv,dbh and γh,dbh would be steeper for broadleaved species than for conifers (Fig. 4). Supporting our interpretation, a previous study considering the allometry relating dbh to crown dimensions found that conifers had a smaller crown diameter, which is less climate-dependent when compared with broadleaved species (Lines et al., 2012). Consistent with our results, it was evidenced that dry matter production of gymnosperms was more sensitive to changes in temperatures than angiosperms, as a consequence of a better water viscosity and conduction (Roderick and Berry, 2001). All these considerations highlight that under boreal conditions, conifers exhibited a higher plasticity to stand density and temperatures. This may be related to the better adaptation of conifers to a northern context when compared with broadleaved species (Bond, 1989). Previous results on changes in allometry with species and climate across the USA have concluded that in harsh environments (i.e. arid or cold), conifers are expected to outcompete broadleaved species (Hulshof et al., 2015).

The MST predicts that allometric exponents αv,dbh and γh,dbh should be constant and equal 8/3 and 2/3, respectively (West et al., 2009). Our study does not support the theoretical results, as with numerous previous studies (e.g. Niklas, 2004; Price et al., 2012). However, rather aiming to validate the MST, the present study aimed to provide empirical results in order to provide some supplementary insight that may improve this theoretical framework. The integration of temperature in the MST was previously investigated (Gillooly et al., 2001). However, our results suggest that the integration of supplementary climatic variables in the MST should also consider the bioclimatic context of organisms: in drier ecosystems, precipitation rather than temperature may be important (Muller-Landau et al., 2006; Lines et al., 2012) while in northern contexts, temperature may be critical.


Our study demonstrated that competition and climatic variables strongly influence the allometric exponents relating dbh to both stem volume and tree height and the simultaneous study of αv,dbh and γh,dbh was beneficial. This allowed us to identify the different trade-offs between stem primary and secondary growth in order to integrate both intrinsic (different modes of development) and extrinsic (competition intensity, temperatures) constraints. In this regard the difference between broadleaved species and conifers is a good example of different growth investment to balance these constraints.

To confirm the results presented here, further investigation of growth distribution along the stem in relation to climate would be needed. For example, a study of the climatic factors influencing the stem taper of the studied species would be valuable (Morris and Forslund, 1992; Schneider et al., 2013). This would help to understand how precisely trees will balance their growth strategies under a warmer climate. At a larger scale, more investigations considering total tree volume, i.e. stem and also branches, leaves and roots, would be of great interest. This would allow for conclusions to be made on how trees may adapt their carbon allocation patterns. A better establishment of future carbon sequestration might also derive from such analyses.


We thank Ministère des Forêts, de la Faune et des Parcs of the province of Quebec (MFFP) for access to the data and Mélanie Desrochers (CEF) for producing the site location map. We also thank Jean-Pierre Saucier and anonymous reviewers for their helpful comments and suggestions on an earlier version of the manuscript. This study was supported by the Fonds de recherche du Québec – Nature et technologies, the Ministère des Forêts, de la Faune et des Parcs of the province of Quebec (MFFP) and the Natural Sciences and Engineering Research Council of Canada.


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