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Biomass distribution, allocation and growth efficiency in European beech trees of different ages in pure even-aged stands in northeast France

Biomass distribution, allocation and growth efficiency in European beech trees of different ages... Determination of the biomass and biomass increment of trees in managed stands is a pre-requisite for estimating the carbon stocks and fluxes, in order to adapt the forests to new climatic requirements, which impose to maximize the CO retained by forests. Tree biomass and biomass increment equations were formerly developed in two young experimental beech stands in the Hesse forest (NE France). To extend such a study to beech stands of different age classes, it was necessary to build biomass and biomass increment equations that could be used for any age, called generalized biomass equations. For that, trees were sampled in plots covering a large age range in Hesse forest, and in each plot several trees were chosen to represent the different social classes. Compatible biomass and biomass increment equations for the different tree compartments and their combination in above and belowground tree parts were developed and fitted, allowing the analysis of the variations of the biomass distribution and allocation with tree age. Stem growth efficiency (stem growth per unit of leaf area) appeared dependent on tree age and tree social status. The biomass and biomass increment equations established for beech allow the estimation of the biomass and carbon stocks and u fl xes (NPP) for the even-aged beech stands of the Hesse forest, whatever their age. These equations could also be used to analyze the effects of silvicultural treatments on the biomass and carbon stocks and fluxes of beech stands, using the available stand growth and yield models of beech. Key words: leaf area; biomass allocation; biomass distribution; biomass equations; growth efficiency Editor: Martin Lukac & Ottorini 2001; Le Goff 2001, unpublished data). The 1. Introduction biomass and biomass increment equations developed at Determination of the biomass and biomass increment that time at tree level (Ottorini & Le Goff 1999), allowed of trees in managed stands is a pre-requisite for estimat- the comparison of the net primary productivity (NPP) ing the carbon stocks and fluxes, in relation to forests estimated from the yearly CO fluxes measured (Granier management, which must adapt to evolving climatic et al. 2000) with the current stand biomass increment conditions, in particular atmospheric CO rising up. In estimated for the appropriate years, using stand inven- this way, forests are expected to increase their CO uptake tories (Granier et al. 2000; Lebaube et al. 2000). Con- and then enlarge the carbon stocks. sidering that the ecophysiological studies, especially the In a preliminary study, specific biomass equations analysis of the links between tree growth and environ- linking the biomass and the biomass increment of above mental factors, conducted in this forest could be extended and belowground tree compartments to tree diameter to younger or older stands, it was considered of interest to were developed for each of two experimental beech plots (Hesse-1 and Hesse-2), with mean-range ages of 30 and develop generalized biomass equations that could apply 20 years, respectively (Le Goff & Ottorini 1998; Le Goff to all the age range of the classical beech rotation (0–120 *Corresponding author. Noël Le Goff, e-mail: noel.le.goff@free.fr © 2022 Authors. This is an open access article under the CC BY 4.0 license. N. Le Goff, J. M. Ottorini / Cent. Eur. For. J. 68 (2022) 117–138 years), avoiding the need to build age-specific biomass characteristics (age, leaf area, canopy position) will be equations. examined more particularly in this study for beech. Such models were successfully developed earlier by introducing different tree characteristics in the biomass equations, and in particular tree height (ht) often com- 2. Material and methods 1 2 bined with tree diameter (d) in the form of d ht, or more α β 2.1. Study site generally d ht (Wutzler et al. 2008; Genet et al. 2011a, b; Shaiek et al. 2011; McElligott & Bragg 2013; Sileshi The study was conducted in the state forest of Hesse, 2014; Zheng et al. 2015). The biomass and biomass located in the East of France (48°40' N, 7°05' E; alti- increment equations primarily established in Hesse for- tude: between 270 and 330 m). It is a high forest, natu- est were fitted independently for each tree compartment rally regenerated, and composed mainly of oak (Quercus and for the aboveground and belowground compart- petraea and Q. robur, 40%) and European beech (Fagus ments, each one taken as a whole. Thus, the constraint sylvatica L., 37%). The climate is continental with oceanic of additivity for the tree compartments composing either inu fl ences: the mean annual temperature averages 9.2 °C the aerial or the belowground tree parts was not consid- and total annual precipitation averages 820 mm. The oak- ered at that time, although it would have been desirable beech forest of Hesse is situated mainly on loamy or sandy (Repola 2008, 2009; Genet et al. 2011a; Parresol 2011; soils moderately deep (24%) and on clay and loamy mod- Zheng et al. 2015). erately deep soils (74%) (see Le Goff & Ottorini (2001) The main objective of this study was then to develop for more details). generalized and compatible biomass and biomass incre- ment equations for beech in the Hesse forest, for the above and belowground tree compartments. Moreover, 2.2. Tree selection the study aimed at analyzing the contribution of the dif- In order to represent the range of ages, trees were sampled ferent above and belowground tree compartments to in different plots of the forest over several years (Table tree biomass (biomass distribution) and to tree biomass 1). The following samples allowed covering an age range increment (biomass allocation) . from 8 to 172 years. In each sample, trees were selected Prediction models for leaf biomass (and leaf area) will so as to represent the different tree social classes in the also be considered, and used to analyze the stem growth stand, that is, dominant, co-dominant, intermediate and efficiency (GE) of beech trees, GE being defined as stem suppressed trees (Table 1). growth per unit of leaf area. This concept of growth effi- Among the 61 trees sampled, a sub-sample of 40 trees ciency is widely used to identify the silviculturally impor- was selected in almost each tree sample (except sample tant patterns of tree and stand productivity (Maguire et #8) for root biomass analysis, so as the range of ages and al. 1998; Seymour & Kenefic 2002; DeRose & Seymour the different social classes would be represented (Table 1). 2009; Hofmeyer et al. 2010; Konôpka et al. 2010, 2021), and the variations of GE with the growth related tree Table 1. Description of the beech samples analyzed for biomass in Hesse forest (48°40’ N, 7°05’ E), from 1996 to 2003. Sampled trees per social class (2) Total Sample# Forest plot Sample year Stand age (1) 1 2 3 4 sampled trees (2) 1 (Hesse-1) 217 1996 24 – 45 3 (3) 3 (3) 3 (3) 2 (2) 11 (11) 2 (Hesse-1) 217 1997 20 – 33 3 (1) 3 (1) 3 (1) 3 (2) 12 (5) 3 222 2000 52 – 73 2 (2) 2 (2) 2 (2) 0 (0) 6 (6) 4 (Hesse-2) 215 2001 8 – 35 4 (3) 5 (3) 4 (4) 4 (4) 17 (14) 5 214 2002 161 – 162 0 (0) 1 (0) 1 (1) 0 (0) 2 (1) 6 220 2002 165 – 172 2 (1) 0 (0) 0 (0) 0 (0) 2 (1) 7 220 2002 35 2 (0) 0 (0) 0 (0) 0 (0) 2 (2) 8 215 2003 23 – 53 8 (0) 1 (0) 0 (0) 0 (0) 9 (0) Total 8 – 172 24 (10) 15 (9) 13 (11) 9 (8) 61 (40) (1) Stand age is given as the range of ages of the trees in each sample (2) Sampled trees are sorted by social class : dominant (1), co-dominant (2), intermediate (3), suppressed (4) following “Kraft classification” (Oliver & Larson 1996); in parenthesis, the number of trees of the sub-sample analyzed for root bio mass is given. Table 2. Median values (k) of the current annual relative volume increments of the root increment samples of sampled trees per social class. Social class Tree sample # Years Dominant Co-dominant Intermediate Suppressed 1 & 2 1996–1997 0.084 0.067 0.051 0.043 3 1999 0.110 0.057 0.224 — 4 2001 0.139 0.044 0.044 0.044 5 2002 0.030 — 0.040 — In this paper, tree diameter is the diameter of the tree at breast height (1.3 m). The definitions of biomass allocation and distribution agree with those used by Reich (2002). 118 N. Le Goff, J. M. Ottorini / Cent. Eur. For. J. 68 (2022) 117–138 ments were made (Le Goff & Ottorini 2018). An addi- 2.3. Data collection tional sample of trees (sample # 8) was taken in the same 2.3.1 Bole measurements plot as sample # 4 (see Table 1) in order to extend the Several bole measurements were taken on sampled trees: range of already observed tree diameters with trees of girth at breast height and at the upper end of the butt log, larger diameter and to better t fi the diameter distribution height to crown base and horizontal crown projection of the stand. The same measurement process as for large area before tree felling, current and most recent annual 4 trees was applied. Additional measurements were also height increments and bole girth at crown base after taken on the stem and branches, in order to evaluate the tree felling. For each sample tree, sections of less than biomass characteristics for year 2001 (as for sample # 1 m long were identified and located on the bole and arm 4), in addition to those of year of tree felling (2003) (Le forks (Ningre 1997). The green weight of each section Goff & Ottorini 2018). was measured, as well as that of a disc sample, 10–15 cm thick, taken off at the base of each section. 2.3.4 Root measurements Ring radius measurements were performed on each stem disc collected, in four perpendicular directions (8 The extraction and treatment of the root systems of the directions at 45° for irregular discs) and for the last 6 40 sub-sampled trees is described in detail in Le Goff & years, allowing the calculation of the radial increment Ottorini (2018). The measurement process used for tree of the last 5 years for each disc. A ring count on the disk samples #1 and #2 (Le Goff & Ottorini 2001) was applied taken at stump level was also performed to obtain tree to the trees sampled later. Roots were sorted into 3 size age. classes depending on the cross-sectional diameter (d) The green weights of a sub-sample of the stem discs of the roots: coarse roots (d ≥ 5 mm), small roots (2 ≤ were measured, with and without bark. Moreover, the d < 5 cm), fine roots ( d < 2 mm). On coarse and small dry weights of the sampled and sub-sampled stem disks roots, root samples were taken (about 10 cm long and were obtained by leaving the wood samples in a drying of regular shape) to estimate the current annual volume oven at 105 °C until the weight was stabilized; for the and biomass increments of the root system; the number of sub-samples, wood and bark were weighted separately. increment samples per tree varied from 2 to more than 30, depending on tree dimensions. The length, the diameter 2.3.2 Branch measurements at both ends along two perpendicular directions and the annual increments every 45° of each root sample were For each sample tree, the branches of second order were measured. Then, the mean annual radial increment and identified, except the very small ones that were grouped. the annual volume increment of each root sample were As for the bole, sections of length less than 1 m were iden- calculated. The diameters of broken root ends were also tified and located on each branch of length larger than measured at the point of breakage for estimating the 1 m. The green weight of each branch, or branch section, missing biomass of broken roots (see Le Goff & Ottorini was measured, as well as that of a disc sample, 10 to 20 cm 2001, 2018). Finally, the root systems were oven-dried to long, taken at the base of each branch section. Dead a constant weight at 105 °C, and the dry weight of each branches, epicormics and beechnuts were harvested root category – coarse, small and fine – was recorded and grouped separately. For each branch and group of separately for each root system and for each unbroken branches and epicormics, the twigs and their leaves were root end. The same drying process was used to obtain harvested and their green weight measured as well as that the dry weights of the root samples. of a sample. Then, the following measures were obtained: green weights of twigs and leaves measured separately for each sample, area of leaves by using a scanner and ImageJ 2.4. Data processing and analysis (http://rsb.info.nih.gov/ij/) software, green weights of The processing of the data obtained from the different wood and bark for a sub-sample of branch discs, ring measurements made on stems, branches, leaves and root widths in 4 perpendicular directions for the last 6 years systems and on samples taken in each compartment, on each branch disc, dry weights of branch discs (sepa- allowed to calculate the volumes, biomasses and incre- rately for wood and bark for the sub-samples), of twigs ments of the different tree compartments. The calcula- and leaves samples (separately) and of beechnuts. tions procedures are detailed in Annex 1 at the end of the paper and values obtained for the different tree character- 2.3.3 Large trees istics considered are presented in the “Results” section of the paper (Tables 4 and 5). For large trees (samples #3 & #5, see Table 1), several adaptations to the protocol of stem and branch measure- Crown base is here defined as the point of the stem where is inserted the first main branch constituting the crown. In this case, only the leaf biomass of trees for year 2001 could not be reconstructed. 119 N. Le Goff, J. M. Ottorini / Cent. Eur. For. J. 68 (2022) 117–138 In the second followed procedure, Eqs. [1] or [2] 2.4.1 Biomass models were fitted as non-linear models (Ritz & Streibig 2008), The following model already retained by Genet et al. using the R project for statistical computing (2009), (2011a), and recommended recently by McElligot et al. with parameters dependent more specifically on tree age (2013) for its good extrapolation properties, was selected (Genet et al. 2011). The t fi ted equation was the following: to represent the variations of the biomass (W) of the dif- dAge 2 e+fAge W = a + (a bAge + cexp )(D Ht) [5] ferent tree compartments (taken alone or grouped) with Eq. [5] was fitted to each above (stem and branches) and measured tree attributes, that is breast height diameter (D) and total height (Ht): belowground (coarse, small and n fi e roots) tree compart - 2 γ ment and for total above and total belowground bio- W = α + β(D Ht) [1] masses with the statistical package nls of R (2009), and In this equation, the parameter α is generally non sig- the residuals were examined as for the first procedure. nificant (Genet et al. 2011b). Then, the model described A multivariate procedure was applied in order to take by Eq. [1] could be reduced to the following equation: 2 γ account of the statistical dependence among the biomass W = β(D Ht) (with α = 0) [2] equations of the different tree compartments. In this way, Moreover, in Eq. [2], the parameters β and γ may vary multivariate models are able to ensure a better additiv- with other tree attributes such as age or competitive sta- ity of tree compartments, compared to the independ- tus, or depend on tree stand belonging. Two procedures ently estimated equations, without the need to address were used for fitting Eq. [2] and then compared: first, a constraint of additivity in the models (Repola 2009). the fitting of Eq. [2] was done after a “both sides” loga- The multivariate models were fitted separately for above rithmic transformation allowing the use of linear regres- and belowground tree compartments as the number of sion; second, Eq. [2] was t fi ted directly using a non-linear observations diverged due to the sub-sampling procedure regression procedure. applied for belowground biomass. The multivariate pro- In the first procedure, the log-transformation of both cedure consisted in t fi ting the biomass equations by using sides of Eq. [2] gave: dummy variables (Zeng et al. 2011) to render the param- LogW = Logβ + γLog (D Ht) or: eters of the equations specific of each tree compartment LogW = λ + γLog(D Ht) (with λ = Logβ) [3] (Repola 2008, 2009). In case of non-linear fitting, the estimated values of the parameters obtained by separate Eq. [3] was fitted using the software Data Desk 6.3 (Velleman 2011) on a Mac OS 10 system, to total above fittings were used as starting values in the simultaneous ground biomass for each age class, after trees were sorted fitting process. into 4 age classes (Table 3). An analysis of the variation of The residuals of the simultaneous fitting of biomass each parameter (λ, γ) with age (Age) and relative crown equations were examined with particular attention for a length (RCL) was then performed, λ and γ being linearly possible remaining “stand” or “tree status” (social class) related to RCL and to the inverse of Age, allowing to intro- effect, in relation with the sampling scheme. In such case, duce covariates in the model (see Wutzler et al. 2008). a mixed model procedure, using the lme or nlme package of R, was applied to take account of the above random Table 3. Distribution of tree samples into 4 age classes, with effects in the biomass equations (Bolker 2008; Wutzler et corresponding mean age. al. 2008) and an analysis of the residuals was performed Age class Tree samples # Mean age [years] to verify that no such remaining effect was detectable. 1 4 21.7 2 1, 2, 7, 8 31.6 Uncertainty around fixed model parameters was 3 3 58.8 evaluated by considering the percent relative standard 4 5, 6 165.0 error (PRSE) defined as PRSE = 100(SE/|θ|), where θ The following equation, derived from Eq. [3] and is the estimated value of a given parameter and SE its including Age and RCL variables, was then fitted to bio- corresponding standard error: point estimates of θ are mass data: generally considered unreliable if PRSE > 25% (Sileshi LogW = (a +a 1⁄Age + a RCL) + (b + b 1⁄Age + * * * 2014). 0 1 2 0 1 b RCL) Log(D Ht) [4] * * To evaluate the quality of the fitted biomass models, Eq. [4] was fitted with Data Desk 6.3 to each above the observed values were plotted and regressed against (stem and branches) and belowground (coarse, small and the predicted values (Pineiro et al. 2008; Sileshi 2014), fine roots) tree compartment and to total above and total and the regression lines were compared graphically with belowground biomasses – with possible adaptations to the 1:1 lines (for a good model, the coefficients of the regression lines would be close to 0 for the constant and Eq. [4] – and the residuals of this equation were examined to detect any bias or remaining tree or stand effect. 1 for the slope). In this paper, as recommended by Sileshi (2014), it will not be referred to “allometric models” to design the biomass equations used, as they don’t follow the typical power- law function. The relative crown length (RCL) of a tree was defined as the ratio of crown length (distance from crown base to stem apex) to total tree height ( Ht). 120 N. Le Goff, J. M. Ottorini / Cent. Eur. For. J. 68 (2022) 117–138 2.4.2 Biomass increment models 3. results Two alternative models were proposed by Hofmeyer et 3.1. Tree sample characteristics al. (2010) in order to represent the relationship between 3.1.1 Aboveground tree sample annual stem volume increment and tree leaf area. The fol- lowing exponential model (Eq.[6]) proved better adapted The main characteristics of the tree sample which are than the allometric model as it was in accordance with the listed in Table 4 let appear the wide range of observed non-monotonically variation of stem growth efficiency values for the aerial part of trees, due mainly to the large with tree leaf area, as observed in our case. Then, this range of the tree ages and of the competitive status of model was retained here to explore the variations of the trees (crown ratio – the ratio of crown length to total biomass increment (∆W) of the different tree compart- tree height (RCL) – varying between 0.2 and 0.9); this ments with tree leaf area (LA). is particularly the case for biomass values which vary in ∆W= a(1 – exp(– LA⁄b) ) [6] the proportion of more than 1 to 10000. The possible dependence of ∆W on other tree char- 3.1.2 Above and belowground tree sample acteristics measured was explored by examining the residuals of Eq. [6] (for additive effects) and the ratios The belowground attributes, together with the above- of the observed and estimated biomass increments (for ground ones, were only measured on a sub-sample of 40 multiplicative effects). trees. However, the range of observed values for above As for biomass equations, multivariate non-linear and belowground attributes of the sub-sample remains models were t fi ted separately for above and below ground large, as the range of tree ages is the same as for the com- tree compartments, and separate t fi tings were performed plete sample (Table 3). Thus, the total root biomass of for each compartment to obtain starting values of the sampled trees varies in the proportion of 1 to 5000, while model parameters when fitting the multivariate models. the total aboveground biomass still vary in the proportion Mixed models were fitted with nlme (R) to test possible of 1 to 10000. random effects due to “forest plot”, “year of sampling” The biomass data collected for the beech tree sample or “tree social status”. Weightings (specic fi of each com - of Hesse forest were published earlier in a data paper (Le partment) and correlations were also considered when Goff 2019). fitting simultaneously the biomass increment models for above and below ground tree compartments: in this scope, an indicator variable was introduced in the data 3.2. Above and belowground biomass set to identify each tree compartment . 3.2.1 Biomass distribution (sample trees) As for biomass equations also, percent relative stand- ard errors (PRSE) were considered to judge of the uncer- The variations of the tree biomass distribution among tainty around fixed model parameters, and observed a b o v e a n d b e l o w g r o u n d t r e e c o m p a r t m e n t s w e r e against predicted biomass increment values were plotted observed by splitting sample trees in different social and regressed to assess the quality of the models. and age classes. Social classes refer to the classical Kraft Table 4. Descriptive attributes of the 61 destructively sampled beech trees in Hesse forest (NE France) analyzed for above- ground biomass and representing different age and social status classes. Attributes Nb. of trees (1) Mean (SE) Range Age [years] 61 40.3 (35.5) 8 – 172 Diameter [cm] 61 10.5 (11.4) 1.1 – 60.5 Height [m] 61 12.2 (8.3) 2.2 – 39.3 Crown length [m] 61 5.9 (4.4) 1.0 – 24.2 Crown ratio 61 0.50 (0.16) 0.22 – 0.89 Crown projection area [m ] 39 9.77 (20) 0.85 – 101.53 Stem area [m ] 61 5.09 (11.64) 0.08 – 66.56 Stem volume [m ] 61 0.2802 (0.9373) 0.0002 – 5.8775 Leaf area [m ] 59 46.74 (102.03) 1.11 – 709.63 2 −2 LAI [m m ] 39 3.62 (1.59) 1.30 – 7.98 Leaf mass [kg] 59 2.057 (4.493) 0.008 – 31.523 Branch mass [kg] 61 26.620 (79.096) 0.026 – 493.856 Stem mass [kg] 61 162.434 (545.336) 0.126 – 3442.037 3 −1 Stem volume increment [m an ] 61 0.011 (0.022) 0.000 – 0.112 −1 Stem mass increment [kg an ] 61 6.027 (12.179) 0.003 – 61.197 −1 Branch mass increment [kg an ] 61 1.759 (3.916) 0.001 – 21.916 (1) Crown projection area could not be measured on all trees and then this variable, as well as leaf area index (LAI), were only available for 39 trees. Leaf area and biomass could not be obtained for 2 trees and were then available for 59 trees only. Growth efficiency, defined as stem volume increment per unit of leaf area, presents a peaking pattern when plotted against tree leaf area (Hofmeyer et al. 2010; Seymour & Kenefic 2002). Repola, personal communication. 121 N. Le Goff, J. M. Ottorini / Cent. Eur. For. J. 68 (2022) 117–138 Table 5. Descriptive attributes of the sub-sample of 40 destructively sampled beech trees in Hesse forest (NE France) analyzed for root and aerial biomass and representing different age and social status classes. Attributes Number of trees (1) Mean (SE) Range Age 40 38.4 (33.1) 8 - 172 Diameter [cm] 40 9.8 (11.9) 1.1 – 63.0 Height [m] 40 12.0 (8.2) 2.2 – 39.3 Crown length [m] 40 5.7 (4.8) 1.0 – 23.0 Crown ratio 40 0.48 (0.15) 0.22 – 0.89 Leaf mass [kg] 38 2.054 (5.309) 0.008 – 31.523 Branch mass [kg] 40 26.831 (84.902) 0.026 – 493.856 Stem mass [kg] 40 154.435 (555.231) 0.126 – 3442.037 Total root mass [kg] 40 27.420 (77.703) 0.081 – 451.969 – coarse roots 25.297 (73.968) 0.059 – 435.160 – small roots 1.262 (2.766) 0.010 – 12.528 – fine roots 0.860 (1.616) 0.009 – 6.229 −1 Stem mass increment [kg an ] 40 6.514 (14.097) 0.003 – 61.197 −1 Branch mass increment [kg an ] 40 1.857 (4.734) 0.001 – 21.916 −1 Total root biomass increment [kg an ] 38 1.706 (3.749) 0.003 – 14.975 – coarse roots 38 1.614 (3.567) 0.003 – 14.000 – small roots 38 0.093 (0.194) 0.000 – 0.975 (1) Leaf and root biomass increments could not be obtained for the 2 trees of sample # 6 (see Table 1). classification (Oliver & Larson 1996) which differenci- 3.2.2 Biomass equations ates dominants, co-dominants, intermediate and sup- Aboveground biomass equations were established for pressed trees. The sample trees were sorted into 4 age the following tree compartments: stem (wood + bark), classes (numbered 1, 2, 3, 4) with mean ages 22, 32, 59 branches (wood + bark) + twigs called all together and 165 respectively. “branches”, total aboveground (stem + “branches”). The distribution of the aboveground biomass among The non-linear fitting of Eq. [5] gave better results tree compartments showed the same pattern with age, than the linear t fi ting of the log-transformed Eq. [3] with independently of tree social class (Fig. 1): the propor- which biased estimations were observed (even after cor- tion of aboveground tree biomass corresponding to stem rection for inverse log transformation). The simultane- wood – between 60 and 80% – increased with age, while, ous estimation of the parameters retained after a sepa- at the same time, it decreased for leaves and seemed to rate fitting of the equations for each tree compartment, peak at intermediate ages for branches. produced the following results (Table 6). As shown in Fig. 2, the proportion of tree biomass The observation of the residuals of Eq. [5] did not present in roots tended to decrease with age, from nearly reveal any bias in the biomass estimation of each com- 20% to 10% or less. The biomass of the root system partment, nor any relation with tree variables not already appeared comparable to that of the branch compartment, entered in the equation. Moreover, the plotting of residu- but seemed generally slightly larger for a given age class, als for trees belonging to the different forest plots or social except for dominant trees in the two highest age classes. classes sampled did not reveal any marked dependence. Fig. 1. Distribution (in %), by age and social classes, of the aboveground tree biomass among the tree compartments: leaves, twigs, branches (bark and wood) and stem (bark and wood). 122 N. Le Goff, J. M. Ottorini / Cent. Eur. For. J. 68 (2022) 117–138 Fig. 2. Distribution (in % and kg), by age and social classes, of the above and belowground tree biomasses among the main tree compartments: leaves, branches (including twigs), stem and roots (bark added to wood for stem and branches). Table 6. Estimated values of the parameters of Eq. [5], with their standard errors (in parenthesis), for each aboveground tree compartment (stem and branches) and for the total aboveground biomass (all parameters are significant at the 0.05 level or more, except the parameter “c” for branches which was nevertheless retained in Eq. [5] as it was significant when fitting separately the branch biomass equation). Aboveground tree compartments Parameters of Eq. [5] Stem Branches Total aboveground 3.169 a0 (1.375) 0.02353 0.01536 (0.00221) (0.00221) −0.00008522 -0.00006495 (0.00001426) (0.00000803) 0.00007442 0.03506 (0.00004970) (0.00979) −0.01436 −0.02547 (0.00117) (0.00745) 0.9828 1.530 0.9804 (0.0125) (0.072) (0.0295) 0.0005855 0.0009841 (0.0001105) (0.0002093) This was confirmed by the limited effects observed when ity coefc fi ients equal to 0.0689 (SE = 0.0004) and 0.1288 adding random effects in Eq. [5] – fitted in this case with (SE = 0.0032) respectively. Stem and branch wood bio- nlme (R): among all possible random effects associated masses can then be derived by subtracting stem and with each parameter of Eq. [5], a significant one asso - branch bark biomasses from total stem and total branch ciated with “forest plot” was only observable for the biomasses respectively. parameter “f ” of stem biomass equation, and it was then Biomass equations were established for the follow- decided to ignore random effects when fitting Eq. [5]. ing belowground tree compartments: coarse roots, small The estimated biomass of the different aerial tree roots, fine roots and whole roots (= coarse + small + fine compartments compared favorably with the observed roots). Eq. [5] could not be fitted to belowground data, biomass values. Moreover, the sum of the estimated stem maybe due to an excessive number of parameters. The 2 c and branch biomasses compared relatively well with the reduced model W = (a + bAge) (D Ht) , with only 3 total aboveground biomass estimated as a whole (Figs parameters, was successfully fitted to the data from each 3A–D in Le Goff & Ottorini 2018). compartment, but biased estimations were observed for Stem and branch bark biomasses appeared propor- small and fine roots . The following alternative model tional to stem and branch biomasses, with proportional- gave better results: Small and fine roots data of tree # 35 were dropped from the belowground data file, as they appeared abnormally low. 123 N. Le Goff, J. M. Ottorini / Cent. Eur. For. J. 68 (2022) 117–138 2 c LogW = a + b(D Ht) [7] ground biomass estimated as a whole (Figs 4A–D in Le 2 e b(D Ht) a Goff & Ottorini 2018). that is equivalent to W= αexp (where α = exp ) [8] The model described by Eq. [5] for aerial tree com- The simultaneous estimation of the parameters of partments was tested for foliage biomass (W ). Several Eq. [7] for each root compartment, with starting values parameters in Eq. [5] were not significant and the fol - 2 e+fAge obtained after a separate fitting of each equation, pro - lowing reduced model W = a(D Ht) was then fitted duced the following results (Table 7). to foliage biomass data after a log-transformation of The observation of the residuals of Eq. [7] did not both sides of the equation. An additional variable (RCL reveal any bias in the biomass estimation of each below- = relative crown length) was introduced in the model after ground tree compartment, nor any relation with tree observation of the residuals of the preceding equation. variables not already entered in the equation, only a The n fi al model expressed by Eq. [9] was t fi ted using non- weak dependence with the social status of trees. Random linear least-square regression (nlme, R) to take account effects linked to social status and attached to the param- of the yearly random effects further detected and which eter a, were then added in Eq. [7] fitted in this case with were supported by the parameter a: nlme (R). The comparison of the estimations obtained (a + bRCL) 2 e W = exp (D Ht) [9] with nls or nlme – with or without consideration of a cor- The estimated values of the parameters of Eq. [9], relation effect between tree compartments – did not show which correspond to x fi ed effects, and the random effects a significantly better fitting when adding random effects associated with the parameter a are listed in Table 8. in Eq. [7]; then, it was decided to keep the simpler model The estimated foliage biomasses of sampled trees with only fixed effects considered (Table 7). were in relatively good accordance with the observed val- The estimation of the biomass of the different below- ues (Fig. 5, Le Goff & Ottorini 2018), and no bias could ground tree compartments was then obtained by using be detected. Moreover, the examination of the residuals Eq. [8] and multiplying the estimated values obtained by did not reveal any additional effect of the sampling years 1/2(RSE ) the correction factor e (Flewelling 1981), where nor of tree sampling characteristics (forest plot or tree RSE is the residual standard error of Eq. [7] (RSE = social class belonging). 0.3534). Tree leaf area (LA) appeared proportional to foli- The estimated biomass of the different belowground age biomass (W ), and then a linear relation was fitted tree compartments compared favorably with the corre- using lme (R), as the slope coefficient (s) in the relation sponding observed biomass values, except for the larger LA = s * W presented random effects linked to the year tree of the sample (tree # 35) for which the biomass of of tree sampling (Table 9). The estimated leaf area values coarse roots and of the whole root system seemed overes- were in good accordance with the observed ones (Fig. 6 in timated . Moreover, the sum of the estimated biomasses Le Goff & Ottorini 2018), and no other significant effect of each root category t fi ted relatively well the total below - could be detected. Table 7. Estimated values of the parameters of Eq. [7], with their standard errors (in parenthesis), for each root category (coarse, small and fine roots) and for the whole roots compartment ( all parameters significant at the 0.05 level or more). Belowground tree compartments Parameters of Eq. [7] Coarse roots Small roots Fine roots Whole roots a −15.827 −8.472 −6.661 −12.868 (5.002) (1.673) (1.104) (3.843) b 12.096 3.743 2.332 9.638 (4.808) (1.475) (0.913) (3.650) e 0.05204 0.10131 0.12639 0.05948 (0.01541) (0.02411) (0.02690) (0.01614) Table 8. Estimated values and standard errors of the parameters of Eq. [9] linking foliage biomass (W , kg) to tree diameter (D, cm), height (Ht, m) and relative crown length (RCL), with fixed and random effects distinguished for the parameter “a”. Fixed effects Random effects (Year) Parameters of Eq. [9] Estimate Std error 1996 1997 1999 2000 2001 2002 2003 a −7.870 0.534 0.475 0.535 −0.416 0.066 0.089 −0.687 −0.063 b 3.781 0.397 e 0.813 0.057 Table 9. Estimated value of the slope coefficient s linking leaf area (LA) to foliage biomass (W ), with fixed and random effects distinguished. Fixed effects Random effects (year) Parameter Estimate Std error 1996 1997 1999 2000 2001 2002 2003 s 20.62 1.87 −4.02 −4.08 6.34 2.11 −0.82 1.85 −1.39 In fact, the measured root biomasses of tree # 35 were more probably underestimated due to the difficulty to estimate the biomass of the missing parts of the root system after soil extraction. 124 N. Le Goff, J. M. Ottorini / Cent. Eur. For. J. 68 (2022) 117–138 2 −1 The mean specic fi leaf area (SLA, cm g ) of the sam- the main above and belowground compartments to tree biomass is represented, while in Fig. 4 the contributions pled trees was obtained by multiplying the slope coeffi - 2 −1 of the different root compartments (coarse, small and n fi e cient s in the preceding relation (s = LA/W , m kg ) by 2 −1 roots) to total belowground biomass are represented. 10, leading to the following value: SLA = 206.2 cm g . Tree stem appears as the main tree compartment, representing more than 60% of the tree biomass, except 3.2.3 Biomass distribution factors maybe in the young ages where branch biomass seems to The biomass equations fitted were used to analyze the exceed that of the stem for the smallest trees. Roots con- biomass distribution in above and belowground com- tribute to tree biomass at a relatively constant rate across partments in relation to tree dimensions (diameter and ages, the mean root-shoot ratio being equal to 0.23 for height) and age. As height (Ht) is correlated with diam- the whole sub-sample of trees, with slightly higher values eter (D) at a given age, a height-diameter equation with (0.32) for the youngest trees of the sample aged about 20. age-dependent parameters was fitted to sampled trees Coarse roots contribute to about 90% of total below- data. The following power model was retained after fit - ground biomass for the largest trees, independently of age ting separate equations to data from different age classes class. This contribution tends to decrease with decreasing and analyzing the variation of equation parameters with size of trees when trees are young, for the benefit of small age: and fine roots compartments. (c Age ht) Ht = (a + b Age) D [10] ht ht ht In this equation, the parameter a was dependent ht 3.3. Biomass increment on forest plot. Then, Eq. [10] was fitted with nlme (R), fixed and random effects appearing in Table 10. Plotting 3.3.1 Aboveground compartments residuals against fitted values did not reveal any bias. Biomass distribution in trees was then represented in The following model, derived from the model of Eq. [6], relation to diameter at breast height (D) and age, replac- was retained to represent the variations of the biomass ing tree height (Ht) in biomass equations by its estima- increment of aboveground tree compartments (∆W ) ag tion obtained from Eq. [10]. In Fig. 3, the contributions of with tree leaf area (LA), age (Age) and foliar density Table 10. Estimated values of the parameters of Eq. [10] linking tree height (Ht) to diameter at breast height (D) and age (Age), with fixed and random effects distinguished. Fixed effects Random effects (forest plot) Parameters of Eq. [10] Estimate Std error P214 P215 P217 P220 P222 5.3402 0.6915 0.5316 −1.5525 0.5495 −0.5049 0.9762 ht ht 0.0041 0.0157 0.1748 0.0776 ht 0.1987 0.1214 ht Fig. 3 Distribution of the biomasses of the main tree compartments – stem, branches and roots – in relation to tree diameter (D) and Age. The root-shoot ratio of the sampled trees was calculated as the ratio of total belowground biomass on total aboveground biomass of trees (Reich 2002). 125 N. Le Goff, J. M. Ottorini / Cent. Eur. For. J. 68 (2022) 117–138 Fig. 4. Distribution of the biomasses of the different root compartments – coarse, small and fine roots – in relation to tree diam- eter (D) and Age. d and e are common parameters of above ground com- (DSF) : ag ag c partments; k and k are the multiplicative factors of a ∆W = a (1 – exp(–LA⁄b ) ag)exp((d – e s b ag ag ag ag ag ag for stem and branch biomass increments respectively. LogDSF)⁄Age) [11] To estimate the parameters of Eq. [12], in which Eq. [11] was simultaneously fitted to each above- ∆W stands for the biomass increment of either above- ag ground tree compartment (stem and branches) and to ground tree compartment (stem, branches or total above- total aboveground. As the biomass increment of the ground), a weighted non-linear mixed-effects regression aboveground tree compartments (stem and branches) was performed (nlme, R) with random effects due to for- appeared proportional to total aboveground biomass est plot belonging supported by the parameter a . The ag increment, only the parameter a in the above equation introduction of correlations among the parameters, in varied with tree compartments, and Eq. [11] was re- relation with the inter-dependence of tree compartments, written and fitted as follows: was not considered, as it did not change much the esti- ∆W = a (X + k X + k X )(1 – exp(–LA⁄b ) ag) mated values of the parameters. ag ag t s s b b ag exp((d – e LogDSF)⁄Age) [12] The estimated values of the parameters of Eq. [12], ag ag with their standard errors, are listed in Table 11. All In Eq. [12], X , X and X are dummy variables tak- parameters were significant at the 0.001 level. Random t s b ing the value “1” for total aboveground, stem or branch effects associated with forest plot belonging (P214 to compartments respectively (“0”, otherwise); a , b , c , P222) are also listed. ag ag ag Table 11. Estimated values of the parameters of Eq. [12], with fixed and random effects distinguished for the multiplicative parameter which takes the values a , a k and a k for total aboveground, stem and branch biomass increments respectively. ag ag s ag b Fixed effects Random effects (forest plot) Parameters of Eq. [12] Estimate Std error P214 P215 P217 P220 P222 68.322 13.464 −34.928 42.618 3.471 −20.936 9.775 ag 0.7587 0.0467 0.0416 −0.1594 0.0699 0.0982 −0.0504 0.2413 0.0441 −0.0391 0.1580 −0.0713 −0.0978 0.0503 344.71 15.238 ag ag 1.5826 0.0380 88.577 7.347 ag ag 28.290 3.442 Table 12. Estimated values of the parameters of Eq. [13] with their standard errors; the multiplicative parameter a in Eq. [11] takes here the values a , a k and a k for total belowground, coarse roots and small roots biomass increments respectively. bg bg cr bg sr Parameters of Eq. [13] Characteristic a k k b c d e bg cr sr bg bg bg bg Estimate 7.2673 0.9507 0.0493 236.958 1.9492 117.565 34.570 Std. Error 0.5340 0.0170 0.0124 7.120 0.0425 14.201 7.974 12 1.5 Foliar density is here defined as the ratio LA/BS where LA is tree leaf area and BS is stem surface area (a similar ratio where leaf biomass replaced leaf area was used in a preceding study: Le Goff & Ottorini 1996). 126 N. Le Goff, J. M. Ottorini / Cent. Eur. For. J. 68 (2022) 117–138 The observation of the residuals of Eq. [12] did not 3.4. Biomass allocation reveal any bias in the biomass increment estimations, and In order to analyze the variations of the distribution no other significant effect on the biomass increment of of biomass increment in trees with age, leaf area (LA) the different tree compartments could be detected, espe- and density of foliage (DSF) – from which depends tree cially in relation with the social status of trees or the year growth – LA and DSF were related to tree age (Age). The of tree sampling. The observed and estimated values of following relations could be established, using non-linear the biomass increments of the aboveground tree com- and linear regressions for LA and DSF, respectively: partments of the sampled trees in Hesse forest compared LA=l Age 2 [14] relatively well. Moreover, the sum of the estimated bio- mass increments of each aboveground tree compartment with l = 0.1160 and l = 1.5568 1 2 t fi ted relatively well the aboveground biomass increment Log(DSF) = ν + θLog(Age) [15] estimated as a whole (Figs. 9A–D in Le Goff & Ottorini with ν = 5.308 and θ = −1.0119 (R = 0.57, df = 57, 2018). s = 0.518) The distribution of the biomass increment in trees 3.3.2 Belowground compartments was then represented in relation to tree age, replacing The model described by Eq. [11] allowed the representa- leaf area (LA) and density of foliage (DSF) in biomass tion of the variations of the biomass increments of the increment equations by their estimations obtained from belowground tree compartments (coarse roots, small Eq. [14] and Eq. [15] respectively . In Fig. 5, the con- roots and total root system), which appeared also pro- tributions of the main above and belowground compart- portional. Then, Eq. [12] was adapted for belowground ments to tree biomass increment are represented: bio- tree compartments and fitted in the following form: mass increment appears preferentially allocated to the stem (more than 60%), then to branches (about 20%) ∆W = a (X + k X + k X )(1 – exp(–LA⁄b ) bg) bg bg t cr cr sr sr bg and roots (less than 20%). With regard to the root com- exp((d – e LogDSF)⁄Age) [13] bg bg partment, coarse roots appear to contribute to 95% of In Eq. [13], X , X and X are dummy variables tak- t c s total belowground biomass increment while small roots ing the value “1” for total belowground, coarse roots and contribute to 5% only, independently of tree age . small roots compartments respectively (“0”, otherwise); a , b , c , d and e are common parameters of below bg bg bg bg bg ground compartments; k and k are the multiplicative cr sr factors of a for the biomass increments of coarse roots bg and small roots compartments respectively. A non-linear regression model was fitted to Eq. [13] using nls (R). Weights and correlations were introduced in the model as before, but seemed to generate biased esti- mations and then were not retained in the t fi ting process. Furthermore, no significant random effect – in relation with tree location (forest plot) or tree social class belong- ing – could be detected. Additionally, no signic fi ant effect of the year of tree sampling could be detected. The estimated values of the parameters of Eq. [13], Fig. 5. Distribution of the biomass increments among the with their standard errors, are listed in Table 12. All main tree compartments, in relation to tree age. parameters were significant at the 0.001 level. The observed and estimated values of the biomass increments of the belowground tree compartments of the 3.5. Stem volume increment and growth sampled trees compared relatively well. Moreover, the efficiency sum of the estimated biomass increments of each below- The model developed to represent the variations of the ground tree compartment equaled the belowground bio- annual biomass increment of aboveground tree compart- mass increment estimated as a whole (Figs. 10A–D in Le ments (Eq. [11]) was retained to represent the variations Goff & Ottorini 2018). of bole (or stem) annual volume increment (BI), that is: BI=a (1 – exp(–LA⁄b ) )exp((d – e LogDSF) s s s s /Age) [16] DSF values obtained from Eq. (14) were multiplied by the correction factor e^(1/2 s^2 )(Flewelling & Pienaar 1981). Fine roots biomass increment was not evaluated in this study, as the main part of it is due to fine root turnover whose quantification would have necessitated specific studies (Le Goff & Ottorini 2001). 127 N. Le Goff, J. M. Ottorini / Cent. Eur. For. J. 68 (2022) 117–138 To estimate the parameters of Eq. [16], a non-linear as to represent the same range of social status and ages mixed-effects regression was performed (nlme, R) with as the main tree sample, allowed to obtain biomass equa- random effects due to forest plot belonging supported tions for the belowground parts of trees defined in rela- by the parameters b and d . The estimated values of the tion to root diameter (coarse, small and fine roots), and s s parameters of Eq. [16], with their standard errors, are for total belowground biomass. listed in Table 13. Random effects associated with forest The excavation of the root systems of the sampled plot belonging (P214 to P222) are also listed for b and beech trees caused the loss of some parts of the root d parameters. systems, and then equations were established so as to No other significant effect on BI could be detected, estimate the missing parts of each root system by root including the social status of trees and the year of tree category, as was done in a preceding study (Le Goff & sampling, and the fitted values of BI appeared in good Ottorini 2001); in addition, for establishing these equa- agreement with the observed ones (Fig. 12, Le Goff & tions in the present study, the distinction was made Ottorini 2018). between horizontal and vertical roots for the largest Growth efficiency (GE) of trees, defined as stem trees. It seems, however, that for the largest tree of the annual volume increment per unit of leaf area, was esti- sample (tree # 35), the belowground biomass was under- mated by dividing the BI model (Eq. [16]) predictions by estimated, due probably to an incomplete inventory of their corresponding observed leaf areas, as was done by broken roots during excavation, which resulted in an Hofmayer et al. (2010) and DeRose & Seymour (2009). underestimation of the biomass of missing root parts The estimated values of GE fitted relatively well the for that tree. observed ones (Fig. 6A). Due to the large dimensions of the oldest trees in the The simulated GE values, calculated by replacing LA sample, the biomass of the aboveground tree compart- and DSF values by their estimations obtained from Eq. ments could not be measured directly for large trees, but [13] and [14] respectively, were in good accordance with via volume and wood density evaluations. In addition, all the trend revealed by plotting observed GE values in rela- branches were not measured for these trees, and a strati- tion to age (Fig. 6B). The decrease in GE observed for e fi d sample of branches was used and biomass equations very young and very old trees appears closely reproduced were established to estimate the biomass of non-sampled by the model. branches. Table 13. Estimated values of the parameters of Eq. [16] linking bole volume increment BI to leaf area (LA), density of foliage (DSF) and age (Age), with fixed and random effects distinguished for the parameters b and d . s s Parameters Fixed effects Random effects (forest plot) Estimate Std error P214 P215 P217 P220 P222 [Eq. 16] s 65.8972 5.5281 361.8440 65.2292 170.811 32.418 −55.867 −18.408 −128.954 1.5018 0.05293 114.4202 18.9182 28.235 5.359 −9.235 −3.043 −21.316 35.3697 7.6299 Fig. 6. Observed stem volume growth efficiency (GE) for the tree sample of Hesse forest versus estimated values obtained from Eq. [16], using either observed (A) or estimated (B) LA and DSF values (LA and DSF estimates obtained from Eq. [14] and Eq. [15] respectively). 4. Discussion 4.1. Fitting biomass and biomass increment models The sampling of more than 60 trees of different social status, and representing the range of ages for a total beech Linear and non-linear models were examined to fit bio - stand rotation, allowed to establish generalized biomass mass and biomass increment data. When linear or non- equations for the main aboveground tree compartments linear models could equally be used, notably after log- (stem, branches and leaves) and for total aboveground transformation, the non-linear ones presented a better t fi . biomass. Moreover, a subsample of 40 trees, chosen so 128 N. Le Goff, J. M. Ottorini / Cent. Eur. For. J. 68 (2022) 117–138 When fitting the relations, a particular attention was A comparison of estimated stem biomasses with our model and with the “dh3” model established by Wutzler brought to the unexplained variation and to the quality et al. (2008) showed a close correspondence when attrib- of the fitting in order to obtain an eventually better fit uting the appropriate values to the covariates site index by adding covariates in the model (as done by Wutzler (si), altitude (alt) and age included in the model of Wut- et al. 2008). Variables not introduced in the models but zler (see Appendix A3, Wutzler et al. 2008): diverging characterizing the status of sampled trees – tree social estimates appear only at the extreme ages. status, year of tree sampling, forest plot belonging – were T h e p a r a m e t e r β o f t h e a b o v e g e n e r i c m o d e l retained for the analysis of residuals and eventually added decreased linearly with increasing tree age for the stem in the models as random effects (as done also by Wutzler compartment while it decreased exponentially for the et al. (2008) to differentiate between the data sources). In branch compartment. As γ is constant for branches, this this last case, mixed models were fitted using the pack - means that branch biomass is comparatively lower for age nlme of R. It appeared that such random effects were trees with same diameter and height but older, probably significant for yearly varying biomass variables (foliar in relation with a smaller crown due to higher crowding biomass, biomass increment of aboveground tree com- conditions. This is not true for the stem as the increase partments): in this case, it could be interesting to try to of β with age more than compensates for the decrease of identify these effects, probably related to the yearling γ with increasing age: the stem biomass is comparatively varying climate and particularly its consequences on higher for trees with same diameter and height but which the water availability for trees as it is a limiting factor of are older, as the stem of more crowded trees is more cylin- the growth of beech (Le Goff & Ottorini 1999; Granier drical and has then a higher volume (and biomass) for a et al. 2008). given diameter and height. Additive models should have been t fi ted for above and b(D Ht) An exponential model – W = αexp – appeared belowground data to ensure that the total tree biomass better suited for belowground biomass data. In this case, and biomass increment equals respectively the sums of the parameters of the model did not seem to depend on the biomasses and biomass increments of the different tree age, as it was the case in the model fitted for above- compartments in which they were divided. To simplify ground biomass data. This result confirms preceding the fitting process, multivariate models were used which findings (Le Goff & Ottorini 2001). allowed to obtaining a relatively good agreement for the While tree diameter and height explain a large part biomass and biomass increments of the above and below- of tree biomass variations, tree age appeared also as an ground tree parts estimated as a whole or as the sum of important variable to consider, at least for aboveground their constituting compartments. This is in line with the tree compartments, as already shown by Wutzler et al. results obtained by Repola (2008, 2009). (2008), Genet et al. (2011a,b) or Shaiek et al. (2011). In fact, it can take into account the competitive conditions supported by trees which influence the dimensions of 4.2. Biomass models tree crowns and then the branch biomass itself, but also 2 γ The generic model W = α + β(D Ht) – already used by the distribution of the increments on the stem and then Wutzler et al. (2008) and then by Genet et al. (2011a) stem form (stem tapering) and biomass (Repola 2009). – appeared well suited here to represent the biomass Tree age in biomass equations may also reflect a possi - variations of aboveground tree compartments with tree ble effect of wood density, which tends to increase with diameter (D) and height (Ht). The constant α (a in our age for beech (Bouriaud et al. 2004). However, no age case, Eq. [5]) was significant only for the branch com - effect could be detected in belowground biomass equa- partment, as it was also the case for Genet et al. (2011a, tions, agreeing with previously published results (Bond- b). Moreover, as for Genet et al. (2011b), the parameters Lamberty et al. 2002; Le Goff & Ottorini 2001; Genet β and γ of the biomass model appeared dependent on tree et al. 2011a, b): this may be due to a weaker connection age (Age) and could be expressed with the same func- between the root system dimensions and tree growing tions whose parameters vary with tree compartment (Eq. conditions, as tree crowding. [5] and Table 4). However, in our case, the parameter Tree foliage biomass could be expressed with the β was decreasing with age, independently of the tree same model as aboveground tree compartments, and compartment considered, while it increased for stem then appeared dependent on tree diameter and height. compartment in Genet et al. (2011a, b); furthermore, the However, foliage biomass was also dependent on tree parameter γ slightly increased with age, from about 1 to crown dimensions, increasing with the relative crown 1.1 or 1.15 (stem and overall aerial part respectively) or length of the tree (RCL), as already observed for birch in remained constant, close to 1.5 (branches) in our case, Finland (Repola 2008). For a given diameter and height, while it appeared independent of age regardless of the foliage biomass increases with crown dimensions with compartment considered for Genet et al. (2011a, b). In the “dh3” stem biomass model of Wutzler (2008), si is equal to 36 and alt is equal to 300 for the site of Hesse (Table 1, Wutzler et al. 2008), while age can be varied. (Le Goff & Ottorini 2001). 129 N. Le Goff, J. M. Ottorini / Cent. Eur. For. J. 68 (2022) 117–138 which branch biomass increases, the tree being then able ent with those found by other authors in Germany (Bolte et al. 2004) and Central Europe (Konôpka et al. 2010) to support more foliage. A year-to-year variation of foli- and with those extracted by Genet et al. (2010) from a age biomass could also be detected. It has been widely literature review. The decrease of the root/shoot ratio documented that the quantity of foliage may vary signi- observed with increasing age may be the consequence of ficatively from year to year for a given tree or stand, in an ontogenetic drift with plant size and age (Reich 2002). particular in relation with climatic conditions (Bréda & The fraction of tree biomass included in the root system Granier, 1996; Bréda 1999; Le Dantec et al. 2000). In the appeared then relatively independent of the tree status, as case of Hesse forest – from which the tree sample of this already observed by Bolte et al. (2004) for beech, unlike study came from – year-to-year variations of the stand what happened for branches. LAI could be observed, apart from those due to thinning Coarse roots contributed between 80 and 90% to total operations (Granier et al. 2008). The close proportional root system biomass, the proportion being relatively con- relation observed between tree leaf area and biomass of stant and close to 90% for mature trees (tree age ≥ 60 sampled beech trees allowed to estimate a mean specific years). For younger trees, coarse root biomass contribu- 2 −1 leaf area (SLA) value of 206.2 cm g for these trees: Bar- tion tended to decrease with decreasing tree size (Fig. telink (1997) observed also such a relationship for beech 4), together with a higher contribution of small and fine 2 −1 leaf area, leading to a mean SLA value of 172 cm g for a roots, as already found (Le Goff & Ottorini 2001). The smaller sample of trees ranging in age from 8 to 59 years, coarse root biomass data obtained in this study for trees of a SLA value comparable to that found in our study. various ages appear consistent with the data obtained by Pellinen (1986) for trees of various dimensions and aged between 100 and 115 years (Fig. 8), but differ from those 4.3. Biomass distribution in trees obtained by Bolte et al. (2004) which appeared well below those of Pellinen. This could be related to the lower root/ Tree stem represents the main part of tree biomass shoot ratio observed for beech trees in the case of Bolte et (between 60 and 80%), except in young ages where the al. study – coarse roots biomass representing the major branches may contribute more than the stem to tree bio- part of the root system biomass – and explained by dif- mass in the smallest trees. When trees are ageing, the ferences in the environmental conditions of the different branch contribution to tree biomass tends to decrease to sites (Bolte et al. 2004). less than 20%, and relatively more for smaller trees (Fig. 3). Regarding diameter as an indicator of tree status in stands at a given age, this means that dominance, or tree competitive status, affects the amount of branch biomass (Bartelink 1997): with increasing inter-tree competi- tion, a lower fraction of tree biomass is represented in branches, except maybe for suppressed trees in young stands (Fig. 1). Stem and branch biomass data in our study appear consistent with those obtained by Bartelink (1997), when related to tree diameter (Fig. 7). The root system contributed less than 20% to tree bio- mass, this proportion appearing relatively independent of tree age and status, except maybe for the smallest trees of young age classes (Fig. 3). For very young trees, the root/ Fig. 8. Coarse root biomass (W )data in relation to tree di- shoot ratio amounted to 0.32 while the mean value for ameter (D), for the trees sampled in Hesse forest (this study) the whole tree sample was 0.23: these values are consist- compared with those obtained by Pellinen (1986) in Germany. Fig. 7. Stem (A) and branch (B) biomass data in relation with tree diameter at breast height (D), as observed from the Hesse sample (this study) and from the relation established by Bartelink (1997) which explains 90% of the variation in his sample (Hesse sample here restricted to fit the age range of Bartelink’s study). 130 N. Le Goff, J. M. Ottorini / Cent. Eur. For. J. 68 (2022) 117–138 Relating leaf area and density of foliage to tree age 4.4. Biomass increment models allowed to representing the evolution with age of the The sigmoid model described by Eq. [11] was success- allocation of biomass increment to the main tree com- fully fitted for above and belowground components. ponents (Fig. 5). It appeared that the stem contributed Moreover, the increment of the different components to more than 60% of tree biomass increment – nearly of the above and belowground biomasses appeared pro- 70% in young ages – whereas branches contributed to portional to total aboveground and total belowground a relatively constant fraction close to 20% and roots to biomasses respectively, the increment models differing less than 20% (only 10% in young ages). These propor- only by a multiplicative parameter (or allocation coeffi - tions compare relatively well with those obtained on ash cient) in each case. Then, 76% of aboveground biomass (Fraxinus excelsior L.) in a study conducted in a nearby increment appeared allocated to the stem, compared to region on a sample of trees aged 25 (Le Goff et al. 2004), 24% to branches (comparable to the results obtained for whereas some variations seemed to occur between ash beech by Pajtik et al. 2013, only in young ages), while trees of different competitive status, which was not the 95% of belowground biomass increment was allocated case here with beech. to coarse roots compared to 5% to small roots. The bio- mass increment of aboveground components appeared dependent on forest plot, in relation probably with vary- 4.5. Stem volume increment and growth ing environmental conditions, which was not the case efficiency of trees for belowground compartments. However, no effect of The sigmoid model fitted to biomass increment data varying climatic conditions over sampled years could be was successfully fitted to bole volume increment data detected, in relation maybe with the sampling scheme (Eq. [16]), not surprisingly as stem biomass increment of the study where forest plots were not sampled every appeared proportional to stem volume increment. Thus, sampled year, which may have led to confused stand and the mean stem wood density of the beech sample, which climatic effects. appears to be the slope of the linear relation t fi ted between The biomass increment models fitted – Eq. [11] and stem biomass and volume increments, was equal to 0.549 Eq. [13] – show that biomass increment depends not only (Fig. 10). This density value is in the range of the observed on tree leaf area – as in the basic model used by Hofmeyer values for different beech samples in France and other et al. (2010) to describe bole volume increment – but also countries in Europe (Nepveu 1981), and is close to the on foliage density and age. Biomass increment increases mean value (0.556) obtained from biomass equations by with tree leaf area, but at a slowing rate as trees are age- Genet et al. (2011b). ing (Fig. 9), while foliar density (DSF), which decreases exponentially with age (Eq. [15]), shows a positive effect on tree biomass increment when it decreases. While the 3-variable model fitted explains more variation than the model with only leaf area as independent variable, there remains a large unexplained variation that could eventu- ally be reduced with a larger sample of trees. Fig. 10. Annual stem biomass increment (∆W ) in relation with stem volume increment (BI): observed data and linear 3 2 relation fitted ∆W = r BI, with r = 0.549 kg/dm (R = 0.99). s s s As for biomass increment, a “forest plot” effect was detected for stem volume increment, probably also in rela- tion with environmental conditions (soil and climate). Stem wood growth efficiency (GE), defined here as annual stem volume increment per unit of leaf area, appeared to increase rapidly with age until trees reached Fig. 9. Observed aboveground annual biomass increment data the age of 20–30 years (Fig. 6), and then increased more (∆W ) in relation with tree leaf area (LA) and projected values ag,t slowly until it began to decrease after the age of about 100 obtained from Eq. [12] for trees of ages covering the sample age years. This result was obtained after taking account of range (in Eq. [12], the density of foliage was estimated from the the variations of tree leaf area (LA) and density of foliage relation established with tree age, that is Eq. [15]). Wood density, or wood specific gravity ( ρ ), is here defined as the ratio of dry weight on green volume. 131 N. Le Goff, J. M. Ottorini / Cent. Eur. For. J. 68 (2022) 117–138 (DSF) with tree age (Eq. [14] and Eq. [15] respectively). decrease of the density of foliage with age, as observed in The decline of GE with age, after culminating at relatively the sample, contributes to counterbalance the negative young ages, has been already reported for coniferous effect of increasing age on the growth efficiency of trees. species, at tree level, (Kaufmann & Ryan 1986; Cannell Moreover, there is a relationship between the density of 1989; Ryan et al. 1997; Day et al. 2001). But other stud- foliage and the crown ratio that shows a minimum for ies failed to reveal such a decrease of GE with age when trees moderately crowded (crown ratio of about 0.45): leaf area effects were not taken into account (Seymour thus, those trees exhibit a better growth efficiency com- et al. 2002; Harper 2008). The pattern of variation of GE pared to trees less or more crowded, which contrasts with with age could be either attributable to variations of pro- the results obtained with ash (Le Goff et al. 1996). ductivity per unit of leaf area or to variations of biomass Then, the most growth efficient beech trees appear allocation, as trees get older. However, no important to be middle-aged (around 50 years old), dominant with variation of biomass allocation with tree age could be relatively large crowns (leaf area around 200 m ) and observed (Fig. 5), only a small advantage for the stem moderately crowded (crown ratio around 0.45). Such at an early age. Then, the pattern of variation of GE with trees exhibit a mean annual stem volume increment of age could be attributable to an ontogenetic effect (Day about 100 dm . et al. 2001, Seymour et al. 2002), the decrease of GE at higher ages ree fl cting probably a less efc fi ient physiologi - cal functioning of trees as they get older (Ryan et al. 1997; 5. Conclusion Konôpka et al. 2010). The biomass and biomass increment models established As shown by Fig. 11, growth efc fi iency ( GE) depends for beech in this study allow the estimation of the biomass not only on age, but also on leaf area (LA) and density of and carbon stocks and fluxes for the even-aged beech foliage (DSF). Thus, the asymptotic model for BI (Eq. stands of Hesse forest, whatever the age of the stand. [16]) predicts also a declining GE with increasing tree Thus, it should help to extend the studies on the ecophysi- leaf area (cf Maguire et al. 1998; Seymour et al. 2002), ological functioning of beech stands presently conducted but only above a value of about 300 m for leaf area, only in Hesse forest (Granier et al. 2008) to younger and older observed in the oldest trees of the sample. GE decreases stands, and in particular the comparison of the net pri- also, for a given LA, with increasing values of the density of foliage, which is the ratio of leaf area on transformed mary productivity (NPP) of stands estimated from the bole area: such a decrease, already observed with ash (Le CO fluxes with the stand biomass increment (Granier Goff et al. 1996), a less shade tolerant species than beech, et al. 2000). Moreover, it could help to test the ability of may be related to a less favorable ratio of assimilatory to bio-geochemical models, like BIOME-BGC, to assess the gross and net primary production of beech stands, as was respiratory processes associated with the increase of foli- age area per unit of bole surface area. But, conversely, the done by Chiesi et al. (2014) for beech forests in Italy. Fig. 11. Growth efficiency (GE) of beech, in relation with leaf area (LA) and density of foliage (DSF), for trees of increasing ages (from 20 to 160 years) (the curves represented were restricted to the range of leaf areas and densities of foliage observed, accord- ing to age in the tree sample). 132 N. Le Goff, J. M. Ottorini / Cent. Eur. For. J. 68 (2022) 117–138 The biomass equations established could also be used Bond-Lamberty, B., Wang, C., Gower, S. T., 2002: Aboveground and belowground biomass and sap- to analyze the effects of different silvicultural treatments wood area allometric equations for six boreal tree on the biomass and carbon stocks and fluxes of beech species of northern Manitoba. Canadian Journal of stands, using the available stand growth and yield models Forest Research, 32:1441–1450. built in France, that is “Fagacées” (Dhôte & Le Mogue- Bouriaud, O., Bréda, N., Le Moguedec, G., Nepveu, G., dec 2005) or “SimCAP” (Ottorini & Le Goff 2006). 2004: Modelling variability of wood density in beech The generalized biomass and biomass increment as affected by ring age, radial growth and climate. equations established for Hesse forest should however Trees, Structure and Function, 18:264–276. be used with care for beech stands of other regions dif- Bréda, N., 1999: L’indice foliaire des couverts fores- fering by site conditions, although the models developed tiers: mesure, variabilité et rôle fonctionnel. Revue for biomass are very similar to the ones developed at a Forestière Française, 51:135–150. larger scale by Wutzler et al. (2008) and Genet et al. Bréda, N., Granier, A., 1996: Intra- and inter-annual (2011). More cond fi ent data are still necessary to obtain, variations of transpiration, leaf area index and radial in particular for the root biomass compartments, so as to growth of a sessile oak stand (Quercus petraea). develop more precise biomass and biomass increment Annals of Forest Science, 53:521–536. equations. Cannell, M.G.R, 1989: Physiological basis of wood pro- duction: a review. Scandinavian Journal of Forest Research, 4:459–490. Acknowledgments Chiesi, M., Maselli, F., Chirici, G., Corona, P., Lombardi, Our thanks go the INRA technicians of the LERFoB research F., Tognetti, R., Marchetti, M., 2014: Assessing most unit at INRA-Nancy, who proceeded to the tree measurements: relevant factors to simulate current annual incre- R. Canta, F. Bordat, G. Maréchal and S. Daviller. Special thanks ments of beech forests in Italy. iForest, 7:115–122. are addressed to R. Canta who supervised the e fi ld and laboratory Day, M., Greenwood, M., White, A., 2001: Age-related measurements and developed a specific apparatus to allow the changes in foliar morphology and physiology in red biomass measurements on the large root systems. The support of spruce and their inu fl ence on declining photosynthe - the ONF section of Sarrebourg (57), greatly appreciated, made sis rates and productivity with tree age. Tree Physiol- possible the felling of the tree samples used in this study. We would like also to thank warmly A. Granier (EEF, INRA-Nancy) ogy, 21:1195–1204. for his interest in the biomass studies that we conducted in the DeRose, R. J., Seymour, R. S., 2009: The effect of site Hesse forest over several years, in parallel with the ecophysiologi- quality on growth efficiency of upper crown class cal studies that he conducted himself, and for his comments on Picea rubens and Abies balsamea in Maine, USA. a first draft of the manuscript. Our thanks are also addressed Canadian Journal of Forest Research, 39:777–784. to F. Ningre (Silva, INRA-Nancy) who warmly encouraged and Dhôte, J.-F., Le Moguedec, G., 2005: Présentation du helped us in publishing the results of this study. This work was modèle Fagacées. Nancy: LERFoB, UMR 1092 supported by grants from ONF (French National Forest Service) INRA-ENGREF (Document interne). and from the GIP “ECOFOR” (a French public benefit corpora- Flewelling, J. W., Pienaar, L. V., 1981: Multiplicative tion on FORest ECOsystems). The UMR Silva, regrouping the regression with lognormal errors. Forest Science, previous LERFoB and EEF research units, is supported by the 27:281–289. French National research Agency (ANR) through the Laboratory Genet, A., Wernsdörfer, H., Jonard, M., Pretzsch, H., of Excellence ARBRE (ANR-11-LABX-0002-01). Rauch, M., Ponette, Q. et al., 2011a: Ontogeny partly explains the apparent heterogeneity of published bio- mass equations for Fagus sylvatica in central Europe. references Forest Ecology and Management, 261:1188–1202. Bartelink, H. H., 1997: Allometric relationships for Genet, A., Wernsdörfer, H., Mothe, F., Bock, J., Ponette, biomass and leaf area of beech (Fagus sylvatica L). Q., Jonard, M. et al., 2011b: Des modèles robustes et Annals of Forest Science, 54:39–50. génériques de biomasse. Exemple du Hêtre. Revue Bolker, B. M., 2008: Ecological Models and Data in R. Forestière Française, 63:179–190. Princeton University Press, 41 William Street, Princ- Genet, H., Bréda, N., Dufrêne, E., 2010: Age-related eton, New Jersey 08540, USA. variation in carbon allocation at tree and stand scales Bolte, A., Rahmann, T., Kuhr, M., Pogoda, P., Murach, in beech (Fagus sylvatica L.) and sessile oak (Quer- D., Gadow, K. V., 2004: Relationships between tree cus petraea (Matt.) Liebl.) using a chronosequence dimension and coarse root biomass in mixed stands approach. Tree Physiology, 30:177–192. of European beech (Fagus sylvatica L.) and Nor- Granier, A., Ceschia, E., Damesin, C., Dufrêne, E., way spruce (Picea abies [L.] Karst.). Plant and Soil, Epron, D., Gross, P. et al., 2000: The carbon bal- 264:1–11. ance of a young beech forest. Functional Ecology, 14:312–325. 133 N. Le Goff, J. M. Ottorini / Cent. Eur. For. J. 68 (2022) 117–138 Granier, A., Bréda, N., Longdoz, B., Gross, P., Ngao, J., Le Goff, N., Ottorini, J.-M., 2018: Mathematical and 2008: Ten years of u fl xes and stand growth in a young ecological traits of above and below ground biomass beech forest at Hesse, North-eastern France. Annals production of beech (Fagus sylvatica L.) trees grow- of Forest Science, 64:704p1–704p13. ing in pure even-aged stands in north-east France. Harper, G., 2008: Quantifying branch, crown and bole BioRxiv, Available online: https://www.biorxiv.org/ development in Populus tremuloïdes Michx. from content/early/2018/04/13/300210.full.pdfhtml north-eastern British Columbia. Forest Ecology and Le Goff, N., 2019: Above and belowground biomass data Management, 255:2286–2296. for a set of beech trees of different age and crown Hofmeyer, P. V., Seymour, R. S., Kenefic, L. S., 2010: classes sampled in Hesse state forest (NE France) Production ecology of Thuya occidentalis. Canadian with a view to analyzing the distribution and the Journal of Forest Research, 40:1155–1164. allocation of biomass in the tree. Available online: Kaufmann, M. R., Ryan, M. G., 1986: Physiographic, https://data.inra.fr/dataset.xhtml?persistentId=do stand, and environmental effects on individual tree i:10.15454/8CLEGO growth and growth efficiency in subalpine forests. Maguire, D. A., Brissette, J. C., Gu, L., 1998: Crown Tree Physiology, 2:47–59. structure and growth efc fi iency of red spruce in even- Konôpka, B., Pajtik, J., Moravcik, M., Lukac, M., 2010: aged, mixed-species stands in Maine. Canadian Jour- Biomass partitioning and growth efficiency in four nal of Forest Research, 28:1233–1240. naturally regenerated forest tree species. Basic and McElligott, K. M., Bragg, D. C., 2013: Deriving biomass Applied Ecology, 11:234–243. models for Small-diameter Loblolly Pine on the Cros- Konôpka, B., Pajtik, J., Seben, V., Surovy, P. et al., 2021: sett Experimental Forest. Journal of the Arkansas Woody and foliage biomass, foliage traits and growth Academy of Science, 67:94–101. efc fi iency in young trees of four broadleaved tree spe - Nepveu, G., 1981 : Propriétés du bois de Hêtre. In: Le cies in a temperate forest. Plants, 10:2155. Hêtre, Monographie INRA, Paris, 1981, p. 377–387. Lebaube, S., Le Goff, N., Ottorini, J.-M., Granier, A., Ningre, F., 1997: Une définition raisonnée de la fourche 2000: Carbon balance and tree growth in a Fagus du jeune hêtre. Revue forestière française, 1:32–40. sylvatica stand. Annals of Forest Science, 57:49–61. Oliver, C.D., Larson, B.C., 1996: Forest stand dynamics. Le Dantec, V., Dufrene, E., Saugier, B., 2000: Interan- John Wiley and Sons, Inc., New York, USA. nual and spatial variation in maximum leaf area index Ottorini, J.-M., Le Goff, N., 1999: Aspects quantitatifs et of temperate deciduous stands. Forest Ecology and qualitatifs de la biomasse. Rapport scientifique final Management, 134:71–81. (3ième année), Convention de recherche ONF-INRA Le Goff, N., Ottorini, J.-M., 1996: Leaf development and “Etude de la croissance du hêtre sur le Plateau lor- stem growth of ash (Fraxinus excelsior L.) as affected rain”, Juillet 1999, 18 p. by tree competitive status. Journal of Applied Eco- Ottorini, J.-M., Le Goff, N., 2006 : SimCAP, Simulation et logy, 33:793–802. intégration des connaissances: données expérimen- Le Goff, N., Ottorini, J.-M., 1998: Biomasses aériennes tales et simulées de la croissance du Frêne et du Hêtre. et racinaires et accroissements annuels en biomasse Conseil Scientifique LERFoB 2006, 14 mars 2006 , dans le dispositif écophysiologique de la forêt de ENGREF, Nancy (document “PowerPoint”), 21 p. Hesse. Rapport scientifique annuel, Contrat ONF- Parresol, B. R., 2001: Additivity of nonlinear biomass INRA “Croissance du Hêtre sur le Plateau lorrain”, equations. Canadian Journal of Forest Research, 29 p. 31:865–878. Le Goff, N., Ottorini, J.-M., 1999: Effets des éclaircies sur Pajtik, J., Konôpka, B., Marusak, R., 2013: Aboveground la croissance du hêtre. Interaction avec les facteurs net primary productivity in young stands of beech and climatiques. Revue Forestière Française, LI-2:355– spruce. Lesnicky casopis-Forestry Journal, 59:154– Le Goff, N., Ottorini, J.-M., 2001: Root biomass and Pellinen, P., 1986: Biomasseuntersuchungen im Kalk- biomass increment in a beech (Fagus sylvatica L.) buchenwald, Dissertation Universität Göttingen, stand in North-East France. Annals of Forest Sci- Germany, 134 p. ence, 58:1–13. Pineiro, G., Perelman, S., Guerschman, J. P., Paruelo, J. Le Goff, N., Granier A., Ottorini J.-M., Peiffer M., 2004: M., 2008: How to evaluate models : Observed vs. Pre- Biomass increment and carbon balance of ash (Frax- dicted or Predicted vs. Observed? Ecological Model- inus Excelsior L.) trees in an experimental stand in ling, 216:316–322. northeastern France. Annals of Forest Science, 61:1–12. 134 N. Le Goff, J. M. Ottorini / Cent. Eur. For. J. 68 (2022) 117–138 R Development Core Team, 2009: R: A Language and Shaiek, O., Loustau, D., Trichet, P., Meredieu, C., Bach- Environment for Statistical Computing. R Founda- tobji, B., Garchi, et al., 2011: Generalized biomass tion for Statistical Computing, Vienna, Austria. ISBN equations for the main aboveground biomass com- 3-900051-070. ponents of maritime pine across contrasting environ- Reich, P. B., 2002: Root-shoot relations: optimality in ments. Annals of Forest Science, 68:443–452. acclimation and adaptation or the “Emperor’s New Sileshi, G. W., 2014: A critical review of forest biomass Clothes”? In: Plant Roots, The Hidden Half, 3rd Ed., estimation models, common mistakes and correc- Marcel Dekker, Inc., New York. tive measures. Forest Ecology and Management, Repola, J., 2008: Biomass equations for Birch in Finland. 329:237–254. Silva Fennica, 43:605–623. Velleman, P. F., 2011: Data Desk 6.3, Data Description Repola, J., 2009: Biomass equations for Scots pine and Inc., P.O. Box 4555, Ithaca, NY 14852, USA. Norway spruce in Finland. Silva Fennica, 43:625– Wutzler, T., Wirth, C., Schumacher, J., 2008: Generic 647. biomass functions for Common beech (Fagus syl- Ritz, C., Streibig, J. C., 2008: Nonlinear Regression with vatica L.) in Central Europe – predictions and com- R. Springer ScienceBusiness Media, LLC, 233 Spring ponents of uncertainty. Canadian Journal of Forest Street, New York, NY 10013, USA. Research, 38:1661–1675. Ryan, M. G., Binkley, D., Fownes, J. H., 1997: Age-related Zeng, W. S., Zhang, H. R., Tang, S. Z., 2011: Using the decline in forest productivity: Patterns and processes. dummy variable model approach to construct com- Advances in Ecological Research, 27:213–256. patible single-tree biomass equations at different Seymour, R. S., Kenefic, L. S., 2002: Influence of age scales – a case study for Masson pine (Pinus masso- on growth efficiency of Tsuga canadensis and Picea niana) in southern China. Canadian Journal of Forest rubens trees in mixed-species, multiaged northern Research, 41:1547–1554. conifer stands. Canadian Journal of Forest Research, Zheng, C., Mason, E. G., Jia, L., Wei, S., Sun, C., Duan, 32:2032–2042. J., 2015: A single-tree additive biomass model of Quercus variabilis Blume forests in North China. Trees, 29:705–716. 135 N. Le Goff, J. M. Ottorini / Cent. Eur. For. J. 68 (2022) 117–138 Appendix Annex 1. Data processing This annex describes how the measurements taken on sampled trees (see text) were used in calculating the charac- teristics of each tree compartment (stem, branches, leaves and roots). Stem When stem analysis was performed, the stem volume was obtained as the sum of the volumes of the different sec- tions making the stem. Each section was considered as a truncated cone, except the last one on stem ends that was considered as a cone. In this case, the current volume increment of stem sections was calculated as the product of the stem volume sections by the relative current area increment of the increment samples taken on each stem section. When stem analysis was not performed (sample # 1), the stem volume was obtained by converting dry weights of stem sections into volume using the specific gravity (ratio of dry weight to volume) of the sampled stem discs. In this case, bole volume increment was derived from bole biomass increment, using a relation established on the whole set of trees subjected to stem analysis. Stem biomass was calculated as the sum of the dry weights of the bole and of the fork arms sections, the dry weight of each section being generally evaluated as the product of the green weight of the section by the ratio of dry weight to green weight of sample disks taken in each stem section. When samples were not available for each stem section, a special procedure was applied (see Le Goff & Ottorini 2018). The weighting separately of wood and bark for a sub-sample of stem disks allowed to estimate the dry weight of wood and bark of the stem sections and of the whole stem, using a relation describing the variation of the ratio of bark (or wood) to total dry weight along the stem for the sub-sample of stem discs (see Le Goff & Ottorini 2018, for more details). The current biomass increment of stem sections was calculated, as for current volume increment, as the product of stem sections biomass by the relative current area increment of the increment samples taken in each stem section. When increment samples were not available for each stem section, a relation was established relating the relative current area increment of available increment samples to their height (or relative height) in the tree. The stem area of trees was obtained as the sum of the areas of the different sections making the stem as for bole volume when stem analysis was performed. Otherwise, the stem area of trees was derived from bole biomass, using a relation established on the whole set of trees subjected to stem analysis. Branches The basal diameter of branches was calculated as the geometric mean of the 2 diameters measured at right angles at the base of branches. In case of a complete inventory of branches on sampled trees, the dry weight of each branch was calculated as the sum of the dry weights of the branch sections estimated as the product of sections green weights by the mean ratio of dry weight to green weight calculated for the whole set of branch samples. In case of branch sampling, relations were established at tree level linking branch biomass to branch basal diameter and these relations were used to estimate the biomass of non-sampled branches. The total dry weight of branches per tree was then calculated as the sum of individual branch dry weights, of the dry weight of grouped small branches (obtained as for sampled branches), and of the dry weight of stem ends branches and of epicormics for concerned trees (the dry weight of grouped epicormics being obtained as for sampled branches). The weighting separately of wood and bark for a sub-sample of branch disks allowed estimating a mean branch wood biomass ratio for each tree. This ratio was used to estimate the wood biomass of each branch from its total biomass and the bark biomass was obtained as the difference between total and wood biomasses. The current annual biomass increment of branch sections was calculated as for stem sections. For trees with sampled branches, relations were established between branch biomass increment and either branch basal diameter (tree sample # 3) or foliage biomass (tree sample # 5); these relations were used to estimate the biomass increment of non-sampled branches. The current biomass increments of grouped branches (branches on stem ends and groups of small branches) were calculated as the product of branch group’s biomasses by the relative current area increment of the increment samples taken in each group. 136 N. Le Goff, J. M. Ottorini / Cent. Eur. For. J. 68 (2022) 117–138 leaves (biomass) In case of a total branch inventory of leaves with their supporting twigs (tree samples #1 & #2), branch leaf dry weights were obtained by multiplying the “leaf+twigs” green weight by the ratio of sample leaf dry weight to sample “leaf+twigs” green weight. In case of leaves and twigs collected together for all branches, except for a sample of branches for which “leaf+twigs” samples were taken (tree samples # 4, # 7) allowing to calculate their leaf dry weight as before, the leaf dry weight of grouped branches was obtained by multiplying their total “leaf+twigs” green weight by the mean ratio of leaf dry weight to green weight of “leaf+twigs” samples. In case of “leaf+twigs” collected only for a sample of branches (tree samples # 3 & # 5), after estimating the leaf dry weight of sampled branches from a “leaf+twigs” sample as before, relations were established at tree level linking branch leaf dry weight to basal branch diameter (quadratic or power model) or to dry weight of branches (power model). These relations were then used to estimate the leaf dry weight of non-sampled branches. For each stem end den fi ed (tree samples # 3 & #5), the total leaf dry weight was calculated from total “leaf+twigs” green weight, leaf dry weight and “leaf+twigs” green weight of a “leaf+twigs” sample, as for sampled branches, and the leaf dry weights of all stem ends were summed. For each set of epicormics recognized, the total leaf dry weight was calculated from total “leaf+twigs” green weight, leaf dry weight and “leaf+twigs” green weight of a “leaf+twigs” epicormics sample. The total tree leaf dry weight was then calculated as the sum of the leaf dry weights of branches, stem ends (if any) and epicormics (if any). leaves (area) In case of “leaf+twigs” samples taken on each inventoried branch (tree samples # 1 & # 2), total leaf branch area was obtained by multiplying the leaf sample area by the ratio of branch leaf dry weight (measured or estimated) to leaf sample dry weight. In case of “leaf+twigs” collected together for all branches, except for a sample of branches for which “leaf+twigs” samples were taken (tree samples # 4, # 7) allowing to calculate their leaf area as before, the leaf area of grouped branches was obtained by multiplying the total calculated leaf dry weight by the mean ratio of leaf area to leaf dry weight – that is specific leaf area (SLA) – of the samples taken in each crown stratum. In case of “leaf+twigs” collected only for a sample of branches (tree samples # 3 & #5), after estimating the leaf area of sampled branches as before, relations were established at tree level (tree sample # 5) or for the whole sample of trees (tree sample # 3), linking directly total branch leaf area to basal branch diameter (see Le Goff & Ottorini 2018). For each stem end defined (tree samples # 3 & # 5), total leaf area was obtained by multiplying the leaf sample area by the ratio of stem end leaf dry weight to leaf sample dry weight. For each set of epicormics recognized, total leaf area was obtained by multiplying the leaf sample area by the ratio of epicormics leaf dry weight to leaf sample dry weight. The total tree leaf area was obtained as the sum of leaf area of branches, stem ends (if any) and epicormics (if any). Twigs The same process as for leaves was followed to obtain the dry weight of branch twigs, replacing leaf weight by twigs weight in the calculations performed or in the relations to be established to estimate the total dry weight of twigs from basal branch diameter. roots Biomass equations were established for broken roots on a sample of intact root ends (see Le Goff & Ottorini 2001, 2018) in order to estimate total missing root biomass, with distinction made between horizontal and vertical roots for larger trees (samples # 3 and # 5), and in order to estimate the missing root biomass for each root fraction of each category of roots. The total tree root biomass was obtained as the sum of the dry weights calculated for each root category, for measured roots, sampled root ends, root increment samples and missing root ends. The missing root biomass estimated represented between 0 and 10% of the total root biomass of trees (sample # 4), between 2 and 7% (sample # 5) and between 5 and 20% (sample # 3). In this case, 2 or 3 branches were sampled in each of the two crown strata defined, depending on the tree sample. 137 N. Le Goff, J. M. Ottorini / Cent. Eur. For. J. 68 (2022) 117–138 The calculation of the current annual biomass increment of the root systems was based on the current annual relative volume increments of the root increment samples taken, with the following steps (see Le Goff & Ottorini 2018 for details): calculation of inside bark current annual relative volume increments of the root increment samples; calculation of the median (k) of the current annual relative volume increments of the root increment samples of trees for each social class (Table 2), the median values (k) being used as estimates of the relative annual volume increments of the whole root systems of trees in each social class (Le Goff & Ottorini 2001); calculation of the current annual biomass increments of large and small roots by multiplying their biomass by the appropriate “k” value, considering that the wood density of all parts of the root system was constant (see Le Goff & Ottorini 2001). −1 −1 In this study, the fine root turnover was not considered; it was estimated around 0.6 t ha an at stand scale for the experimental stand “Hesse-1” at the age of 20 with a stand density of about 3500 stems per ha, which corresponds −1 to about 0.17 kg an at tree scale (Le Goff & Ottorini 2001). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Forestry Journal de Gruyter

Biomass distribution, allocation and growth efficiency in European beech trees of different ages in pure even-aged stands in northeast France

Forestry Journal , Volume 68 (3): 22 – Sep 1, 2022

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References (34)

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de Gruyter
Copyright
© 2022 Noël Le Goff et al., published by Sciendo
ISSN
0323-1046
eISSN
2454-0358
DOI
10.2478/forj-2022-0008
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Abstract

Determination of the biomass and biomass increment of trees in managed stands is a pre-requisite for estimating the carbon stocks and fluxes, in order to adapt the forests to new climatic requirements, which impose to maximize the CO retained by forests. Tree biomass and biomass increment equations were formerly developed in two young experimental beech stands in the Hesse forest (NE France). To extend such a study to beech stands of different age classes, it was necessary to build biomass and biomass increment equations that could be used for any age, called generalized biomass equations. For that, trees were sampled in plots covering a large age range in Hesse forest, and in each plot several trees were chosen to represent the different social classes. Compatible biomass and biomass increment equations for the different tree compartments and their combination in above and belowground tree parts were developed and fitted, allowing the analysis of the variations of the biomass distribution and allocation with tree age. Stem growth efficiency (stem growth per unit of leaf area) appeared dependent on tree age and tree social status. The biomass and biomass increment equations established for beech allow the estimation of the biomass and carbon stocks and u fl xes (NPP) for the even-aged beech stands of the Hesse forest, whatever their age. These equations could also be used to analyze the effects of silvicultural treatments on the biomass and carbon stocks and fluxes of beech stands, using the available stand growth and yield models of beech. Key words: leaf area; biomass allocation; biomass distribution; biomass equations; growth efficiency Editor: Martin Lukac & Ottorini 2001; Le Goff 2001, unpublished data). The 1. Introduction biomass and biomass increment equations developed at Determination of the biomass and biomass increment that time at tree level (Ottorini & Le Goff 1999), allowed of trees in managed stands is a pre-requisite for estimat- the comparison of the net primary productivity (NPP) ing the carbon stocks and fluxes, in relation to forests estimated from the yearly CO fluxes measured (Granier management, which must adapt to evolving climatic et al. 2000) with the current stand biomass increment conditions, in particular atmospheric CO rising up. In estimated for the appropriate years, using stand inven- this way, forests are expected to increase their CO uptake tories (Granier et al. 2000; Lebaube et al. 2000). Con- and then enlarge the carbon stocks. sidering that the ecophysiological studies, especially the In a preliminary study, specific biomass equations analysis of the links between tree growth and environ- linking the biomass and the biomass increment of above mental factors, conducted in this forest could be extended and belowground tree compartments to tree diameter to younger or older stands, it was considered of interest to were developed for each of two experimental beech plots (Hesse-1 and Hesse-2), with mean-range ages of 30 and develop generalized biomass equations that could apply 20 years, respectively (Le Goff & Ottorini 1998; Le Goff to all the age range of the classical beech rotation (0–120 *Corresponding author. Noël Le Goff, e-mail: noel.le.goff@free.fr © 2022 Authors. This is an open access article under the CC BY 4.0 license. N. Le Goff, J. M. Ottorini / Cent. Eur. For. J. 68 (2022) 117–138 years), avoiding the need to build age-specific biomass characteristics (age, leaf area, canopy position) will be equations. examined more particularly in this study for beech. Such models were successfully developed earlier by introducing different tree characteristics in the biomass equations, and in particular tree height (ht) often com- 2. Material and methods 1 2 bined with tree diameter (d) in the form of d ht, or more α β 2.1. Study site generally d ht (Wutzler et al. 2008; Genet et al. 2011a, b; Shaiek et al. 2011; McElligott & Bragg 2013; Sileshi The study was conducted in the state forest of Hesse, 2014; Zheng et al. 2015). The biomass and biomass located in the East of France (48°40' N, 7°05' E; alti- increment equations primarily established in Hesse for- tude: between 270 and 330 m). It is a high forest, natu- est were fitted independently for each tree compartment rally regenerated, and composed mainly of oak (Quercus and for the aboveground and belowground compart- petraea and Q. robur, 40%) and European beech (Fagus ments, each one taken as a whole. Thus, the constraint sylvatica L., 37%). The climate is continental with oceanic of additivity for the tree compartments composing either inu fl ences: the mean annual temperature averages 9.2 °C the aerial or the belowground tree parts was not consid- and total annual precipitation averages 820 mm. The oak- ered at that time, although it would have been desirable beech forest of Hesse is situated mainly on loamy or sandy (Repola 2008, 2009; Genet et al. 2011a; Parresol 2011; soils moderately deep (24%) and on clay and loamy mod- Zheng et al. 2015). erately deep soils (74%) (see Le Goff & Ottorini (2001) The main objective of this study was then to develop for more details). generalized and compatible biomass and biomass incre- ment equations for beech in the Hesse forest, for the above and belowground tree compartments. Moreover, 2.2. Tree selection the study aimed at analyzing the contribution of the dif- In order to represent the range of ages, trees were sampled ferent above and belowground tree compartments to in different plots of the forest over several years (Table tree biomass (biomass distribution) and to tree biomass 1). The following samples allowed covering an age range increment (biomass allocation) . from 8 to 172 years. In each sample, trees were selected Prediction models for leaf biomass (and leaf area) will so as to represent the different tree social classes in the also be considered, and used to analyze the stem growth stand, that is, dominant, co-dominant, intermediate and efficiency (GE) of beech trees, GE being defined as stem suppressed trees (Table 1). growth per unit of leaf area. This concept of growth effi- Among the 61 trees sampled, a sub-sample of 40 trees ciency is widely used to identify the silviculturally impor- was selected in almost each tree sample (except sample tant patterns of tree and stand productivity (Maguire et #8) for root biomass analysis, so as the range of ages and al. 1998; Seymour & Kenefic 2002; DeRose & Seymour the different social classes would be represented (Table 1). 2009; Hofmeyer et al. 2010; Konôpka et al. 2010, 2021), and the variations of GE with the growth related tree Table 1. Description of the beech samples analyzed for biomass in Hesse forest (48°40’ N, 7°05’ E), from 1996 to 2003. Sampled trees per social class (2) Total Sample# Forest plot Sample year Stand age (1) 1 2 3 4 sampled trees (2) 1 (Hesse-1) 217 1996 24 – 45 3 (3) 3 (3) 3 (3) 2 (2) 11 (11) 2 (Hesse-1) 217 1997 20 – 33 3 (1) 3 (1) 3 (1) 3 (2) 12 (5) 3 222 2000 52 – 73 2 (2) 2 (2) 2 (2) 0 (0) 6 (6) 4 (Hesse-2) 215 2001 8 – 35 4 (3) 5 (3) 4 (4) 4 (4) 17 (14) 5 214 2002 161 – 162 0 (0) 1 (0) 1 (1) 0 (0) 2 (1) 6 220 2002 165 – 172 2 (1) 0 (0) 0 (0) 0 (0) 2 (1) 7 220 2002 35 2 (0) 0 (0) 0 (0) 0 (0) 2 (2) 8 215 2003 23 – 53 8 (0) 1 (0) 0 (0) 0 (0) 9 (0) Total 8 – 172 24 (10) 15 (9) 13 (11) 9 (8) 61 (40) (1) Stand age is given as the range of ages of the trees in each sample (2) Sampled trees are sorted by social class : dominant (1), co-dominant (2), intermediate (3), suppressed (4) following “Kraft classification” (Oliver & Larson 1996); in parenthesis, the number of trees of the sub-sample analyzed for root bio mass is given. Table 2. Median values (k) of the current annual relative volume increments of the root increment samples of sampled trees per social class. Social class Tree sample # Years Dominant Co-dominant Intermediate Suppressed 1 & 2 1996–1997 0.084 0.067 0.051 0.043 3 1999 0.110 0.057 0.224 — 4 2001 0.139 0.044 0.044 0.044 5 2002 0.030 — 0.040 — In this paper, tree diameter is the diameter of the tree at breast height (1.3 m). The definitions of biomass allocation and distribution agree with those used by Reich (2002). 118 N. Le Goff, J. M. Ottorini / Cent. Eur. For. J. 68 (2022) 117–138 ments were made (Le Goff & Ottorini 2018). An addi- 2.3. Data collection tional sample of trees (sample # 8) was taken in the same 2.3.1 Bole measurements plot as sample # 4 (see Table 1) in order to extend the Several bole measurements were taken on sampled trees: range of already observed tree diameters with trees of girth at breast height and at the upper end of the butt log, larger diameter and to better t fi the diameter distribution height to crown base and horizontal crown projection of the stand. The same measurement process as for large area before tree felling, current and most recent annual 4 trees was applied. Additional measurements were also height increments and bole girth at crown base after taken on the stem and branches, in order to evaluate the tree felling. For each sample tree, sections of less than biomass characteristics for year 2001 (as for sample # 1 m long were identified and located on the bole and arm 4), in addition to those of year of tree felling (2003) (Le forks (Ningre 1997). The green weight of each section Goff & Ottorini 2018). was measured, as well as that of a disc sample, 10–15 cm thick, taken off at the base of each section. 2.3.4 Root measurements Ring radius measurements were performed on each stem disc collected, in four perpendicular directions (8 The extraction and treatment of the root systems of the directions at 45° for irregular discs) and for the last 6 40 sub-sampled trees is described in detail in Le Goff & years, allowing the calculation of the radial increment Ottorini (2018). The measurement process used for tree of the last 5 years for each disc. A ring count on the disk samples #1 and #2 (Le Goff & Ottorini 2001) was applied taken at stump level was also performed to obtain tree to the trees sampled later. Roots were sorted into 3 size age. classes depending on the cross-sectional diameter (d) The green weights of a sub-sample of the stem discs of the roots: coarse roots (d ≥ 5 mm), small roots (2 ≤ were measured, with and without bark. Moreover, the d < 5 cm), fine roots ( d < 2 mm). On coarse and small dry weights of the sampled and sub-sampled stem disks roots, root samples were taken (about 10 cm long and were obtained by leaving the wood samples in a drying of regular shape) to estimate the current annual volume oven at 105 °C until the weight was stabilized; for the and biomass increments of the root system; the number of sub-samples, wood and bark were weighted separately. increment samples per tree varied from 2 to more than 30, depending on tree dimensions. The length, the diameter 2.3.2 Branch measurements at both ends along two perpendicular directions and the annual increments every 45° of each root sample were For each sample tree, the branches of second order were measured. Then, the mean annual radial increment and identified, except the very small ones that were grouped. the annual volume increment of each root sample were As for the bole, sections of length less than 1 m were iden- calculated. The diameters of broken root ends were also tified and located on each branch of length larger than measured at the point of breakage for estimating the 1 m. The green weight of each branch, or branch section, missing biomass of broken roots (see Le Goff & Ottorini was measured, as well as that of a disc sample, 10 to 20 cm 2001, 2018). Finally, the root systems were oven-dried to long, taken at the base of each branch section. Dead a constant weight at 105 °C, and the dry weight of each branches, epicormics and beechnuts were harvested root category – coarse, small and fine – was recorded and grouped separately. For each branch and group of separately for each root system and for each unbroken branches and epicormics, the twigs and their leaves were root end. The same drying process was used to obtain harvested and their green weight measured as well as that the dry weights of the root samples. of a sample. Then, the following measures were obtained: green weights of twigs and leaves measured separately for each sample, area of leaves by using a scanner and ImageJ 2.4. Data processing and analysis (http://rsb.info.nih.gov/ij/) software, green weights of The processing of the data obtained from the different wood and bark for a sub-sample of branch discs, ring measurements made on stems, branches, leaves and root widths in 4 perpendicular directions for the last 6 years systems and on samples taken in each compartment, on each branch disc, dry weights of branch discs (sepa- allowed to calculate the volumes, biomasses and incre- rately for wood and bark for the sub-samples), of twigs ments of the different tree compartments. The calcula- and leaves samples (separately) and of beechnuts. tions procedures are detailed in Annex 1 at the end of the paper and values obtained for the different tree character- 2.3.3 Large trees istics considered are presented in the “Results” section of the paper (Tables 4 and 5). For large trees (samples #3 & #5, see Table 1), several adaptations to the protocol of stem and branch measure- Crown base is here defined as the point of the stem where is inserted the first main branch constituting the crown. In this case, only the leaf biomass of trees for year 2001 could not be reconstructed. 119 N. Le Goff, J. M. Ottorini / Cent. Eur. For. J. 68 (2022) 117–138 In the second followed procedure, Eqs. [1] or [2] 2.4.1 Biomass models were fitted as non-linear models (Ritz & Streibig 2008), The following model already retained by Genet et al. using the R project for statistical computing (2009), (2011a), and recommended recently by McElligot et al. with parameters dependent more specifically on tree age (2013) for its good extrapolation properties, was selected (Genet et al. 2011). The t fi ted equation was the following: to represent the variations of the biomass (W) of the dif- dAge 2 e+fAge W = a + (a bAge + cexp )(D Ht) [5] ferent tree compartments (taken alone or grouped) with Eq. [5] was fitted to each above (stem and branches) and measured tree attributes, that is breast height diameter (D) and total height (Ht): belowground (coarse, small and n fi e roots) tree compart - 2 γ ment and for total above and total belowground bio- W = α + β(D Ht) [1] masses with the statistical package nls of R (2009), and In this equation, the parameter α is generally non sig- the residuals were examined as for the first procedure. nificant (Genet et al. 2011b). Then, the model described A multivariate procedure was applied in order to take by Eq. [1] could be reduced to the following equation: 2 γ account of the statistical dependence among the biomass W = β(D Ht) (with α = 0) [2] equations of the different tree compartments. In this way, Moreover, in Eq. [2], the parameters β and γ may vary multivariate models are able to ensure a better additiv- with other tree attributes such as age or competitive sta- ity of tree compartments, compared to the independ- tus, or depend on tree stand belonging. Two procedures ently estimated equations, without the need to address were used for fitting Eq. [2] and then compared: first, a constraint of additivity in the models (Repola 2009). the fitting of Eq. [2] was done after a “both sides” loga- The multivariate models were fitted separately for above rithmic transformation allowing the use of linear regres- and belowground tree compartments as the number of sion; second, Eq. [2] was t fi ted directly using a non-linear observations diverged due to the sub-sampling procedure regression procedure. applied for belowground biomass. The multivariate pro- In the first procedure, the log-transformation of both cedure consisted in t fi ting the biomass equations by using sides of Eq. [2] gave: dummy variables (Zeng et al. 2011) to render the param- LogW = Logβ + γLog (D Ht) or: eters of the equations specific of each tree compartment LogW = λ + γLog(D Ht) (with λ = Logβ) [3] (Repola 2008, 2009). In case of non-linear fitting, the estimated values of the parameters obtained by separate Eq. [3] was fitted using the software Data Desk 6.3 (Velleman 2011) on a Mac OS 10 system, to total above fittings were used as starting values in the simultaneous ground biomass for each age class, after trees were sorted fitting process. into 4 age classes (Table 3). An analysis of the variation of The residuals of the simultaneous fitting of biomass each parameter (λ, γ) with age (Age) and relative crown equations were examined with particular attention for a length (RCL) was then performed, λ and γ being linearly possible remaining “stand” or “tree status” (social class) related to RCL and to the inverse of Age, allowing to intro- effect, in relation with the sampling scheme. In such case, duce covariates in the model (see Wutzler et al. 2008). a mixed model procedure, using the lme or nlme package of R, was applied to take account of the above random Table 3. Distribution of tree samples into 4 age classes, with effects in the biomass equations (Bolker 2008; Wutzler et corresponding mean age. al. 2008) and an analysis of the residuals was performed Age class Tree samples # Mean age [years] to verify that no such remaining effect was detectable. 1 4 21.7 2 1, 2, 7, 8 31.6 Uncertainty around fixed model parameters was 3 3 58.8 evaluated by considering the percent relative standard 4 5, 6 165.0 error (PRSE) defined as PRSE = 100(SE/|θ|), where θ The following equation, derived from Eq. [3] and is the estimated value of a given parameter and SE its including Age and RCL variables, was then fitted to bio- corresponding standard error: point estimates of θ are mass data: generally considered unreliable if PRSE > 25% (Sileshi LogW = (a +a 1⁄Age + a RCL) + (b + b 1⁄Age + * * * 2014). 0 1 2 0 1 b RCL) Log(D Ht) [4] * * To evaluate the quality of the fitted biomass models, Eq. [4] was fitted with Data Desk 6.3 to each above the observed values were plotted and regressed against (stem and branches) and belowground (coarse, small and the predicted values (Pineiro et al. 2008; Sileshi 2014), fine roots) tree compartment and to total above and total and the regression lines were compared graphically with belowground biomasses – with possible adaptations to the 1:1 lines (for a good model, the coefficients of the regression lines would be close to 0 for the constant and Eq. [4] – and the residuals of this equation were examined to detect any bias or remaining tree or stand effect. 1 for the slope). In this paper, as recommended by Sileshi (2014), it will not be referred to “allometric models” to design the biomass equations used, as they don’t follow the typical power- law function. The relative crown length (RCL) of a tree was defined as the ratio of crown length (distance from crown base to stem apex) to total tree height ( Ht). 120 N. Le Goff, J. M. Ottorini / Cent. Eur. For. J. 68 (2022) 117–138 2.4.2 Biomass increment models 3. results Two alternative models were proposed by Hofmeyer et 3.1. Tree sample characteristics al. (2010) in order to represent the relationship between 3.1.1 Aboveground tree sample annual stem volume increment and tree leaf area. The fol- lowing exponential model (Eq.[6]) proved better adapted The main characteristics of the tree sample which are than the allometric model as it was in accordance with the listed in Table 4 let appear the wide range of observed non-monotonically variation of stem growth efficiency values for the aerial part of trees, due mainly to the large with tree leaf area, as observed in our case. Then, this range of the tree ages and of the competitive status of model was retained here to explore the variations of the trees (crown ratio – the ratio of crown length to total biomass increment (∆W) of the different tree compart- tree height (RCL) – varying between 0.2 and 0.9); this ments with tree leaf area (LA). is particularly the case for biomass values which vary in ∆W= a(1 – exp(– LA⁄b) ) [6] the proportion of more than 1 to 10000. The possible dependence of ∆W on other tree char- 3.1.2 Above and belowground tree sample acteristics measured was explored by examining the residuals of Eq. [6] (for additive effects) and the ratios The belowground attributes, together with the above- of the observed and estimated biomass increments (for ground ones, were only measured on a sub-sample of 40 multiplicative effects). trees. However, the range of observed values for above As for biomass equations, multivariate non-linear and belowground attributes of the sub-sample remains models were t fi ted separately for above and below ground large, as the range of tree ages is the same as for the com- tree compartments, and separate t fi tings were performed plete sample (Table 3). Thus, the total root biomass of for each compartment to obtain starting values of the sampled trees varies in the proportion of 1 to 5000, while model parameters when fitting the multivariate models. the total aboveground biomass still vary in the proportion Mixed models were fitted with nlme (R) to test possible of 1 to 10000. random effects due to “forest plot”, “year of sampling” The biomass data collected for the beech tree sample or “tree social status”. Weightings (specic fi of each com - of Hesse forest were published earlier in a data paper (Le partment) and correlations were also considered when Goff 2019). fitting simultaneously the biomass increment models for above and below ground tree compartments: in this scope, an indicator variable was introduced in the data 3.2. Above and belowground biomass set to identify each tree compartment . 3.2.1 Biomass distribution (sample trees) As for biomass equations also, percent relative stand- ard errors (PRSE) were considered to judge of the uncer- The variations of the tree biomass distribution among tainty around fixed model parameters, and observed a b o v e a n d b e l o w g r o u n d t r e e c o m p a r t m e n t s w e r e against predicted biomass increment values were plotted observed by splitting sample trees in different social and regressed to assess the quality of the models. and age classes. Social classes refer to the classical Kraft Table 4. Descriptive attributes of the 61 destructively sampled beech trees in Hesse forest (NE France) analyzed for above- ground biomass and representing different age and social status classes. Attributes Nb. of trees (1) Mean (SE) Range Age [years] 61 40.3 (35.5) 8 – 172 Diameter [cm] 61 10.5 (11.4) 1.1 – 60.5 Height [m] 61 12.2 (8.3) 2.2 – 39.3 Crown length [m] 61 5.9 (4.4) 1.0 – 24.2 Crown ratio 61 0.50 (0.16) 0.22 – 0.89 Crown projection area [m ] 39 9.77 (20) 0.85 – 101.53 Stem area [m ] 61 5.09 (11.64) 0.08 – 66.56 Stem volume [m ] 61 0.2802 (0.9373) 0.0002 – 5.8775 Leaf area [m ] 59 46.74 (102.03) 1.11 – 709.63 2 −2 LAI [m m ] 39 3.62 (1.59) 1.30 – 7.98 Leaf mass [kg] 59 2.057 (4.493) 0.008 – 31.523 Branch mass [kg] 61 26.620 (79.096) 0.026 – 493.856 Stem mass [kg] 61 162.434 (545.336) 0.126 – 3442.037 3 −1 Stem volume increment [m an ] 61 0.011 (0.022) 0.000 – 0.112 −1 Stem mass increment [kg an ] 61 6.027 (12.179) 0.003 – 61.197 −1 Branch mass increment [kg an ] 61 1.759 (3.916) 0.001 – 21.916 (1) Crown projection area could not be measured on all trees and then this variable, as well as leaf area index (LAI), were only available for 39 trees. Leaf area and biomass could not be obtained for 2 trees and were then available for 59 trees only. Growth efficiency, defined as stem volume increment per unit of leaf area, presents a peaking pattern when plotted against tree leaf area (Hofmeyer et al. 2010; Seymour & Kenefic 2002). Repola, personal communication. 121 N. Le Goff, J. M. Ottorini / Cent. Eur. For. J. 68 (2022) 117–138 Table 5. Descriptive attributes of the sub-sample of 40 destructively sampled beech trees in Hesse forest (NE France) analyzed for root and aerial biomass and representing different age and social status classes. Attributes Number of trees (1) Mean (SE) Range Age 40 38.4 (33.1) 8 - 172 Diameter [cm] 40 9.8 (11.9) 1.1 – 63.0 Height [m] 40 12.0 (8.2) 2.2 – 39.3 Crown length [m] 40 5.7 (4.8) 1.0 – 23.0 Crown ratio 40 0.48 (0.15) 0.22 – 0.89 Leaf mass [kg] 38 2.054 (5.309) 0.008 – 31.523 Branch mass [kg] 40 26.831 (84.902) 0.026 – 493.856 Stem mass [kg] 40 154.435 (555.231) 0.126 – 3442.037 Total root mass [kg] 40 27.420 (77.703) 0.081 – 451.969 – coarse roots 25.297 (73.968) 0.059 – 435.160 – small roots 1.262 (2.766) 0.010 – 12.528 – fine roots 0.860 (1.616) 0.009 – 6.229 −1 Stem mass increment [kg an ] 40 6.514 (14.097) 0.003 – 61.197 −1 Branch mass increment [kg an ] 40 1.857 (4.734) 0.001 – 21.916 −1 Total root biomass increment [kg an ] 38 1.706 (3.749) 0.003 – 14.975 – coarse roots 38 1.614 (3.567) 0.003 – 14.000 – small roots 38 0.093 (0.194) 0.000 – 0.975 (1) Leaf and root biomass increments could not be obtained for the 2 trees of sample # 6 (see Table 1). classification (Oliver & Larson 1996) which differenci- 3.2.2 Biomass equations ates dominants, co-dominants, intermediate and sup- Aboveground biomass equations were established for pressed trees. The sample trees were sorted into 4 age the following tree compartments: stem (wood + bark), classes (numbered 1, 2, 3, 4) with mean ages 22, 32, 59 branches (wood + bark) + twigs called all together and 165 respectively. “branches”, total aboveground (stem + “branches”). The distribution of the aboveground biomass among The non-linear fitting of Eq. [5] gave better results tree compartments showed the same pattern with age, than the linear t fi ting of the log-transformed Eq. [3] with independently of tree social class (Fig. 1): the propor- which biased estimations were observed (even after cor- tion of aboveground tree biomass corresponding to stem rection for inverse log transformation). The simultane- wood – between 60 and 80% – increased with age, while, ous estimation of the parameters retained after a sepa- at the same time, it decreased for leaves and seemed to rate fitting of the equations for each tree compartment, peak at intermediate ages for branches. produced the following results (Table 6). As shown in Fig. 2, the proportion of tree biomass The observation of the residuals of Eq. [5] did not present in roots tended to decrease with age, from nearly reveal any bias in the biomass estimation of each com- 20% to 10% or less. The biomass of the root system partment, nor any relation with tree variables not already appeared comparable to that of the branch compartment, entered in the equation. Moreover, the plotting of residu- but seemed generally slightly larger for a given age class, als for trees belonging to the different forest plots or social except for dominant trees in the two highest age classes. classes sampled did not reveal any marked dependence. Fig. 1. Distribution (in %), by age and social classes, of the aboveground tree biomass among the tree compartments: leaves, twigs, branches (bark and wood) and stem (bark and wood). 122 N. Le Goff, J. M. Ottorini / Cent. Eur. For. J. 68 (2022) 117–138 Fig. 2. Distribution (in % and kg), by age and social classes, of the above and belowground tree biomasses among the main tree compartments: leaves, branches (including twigs), stem and roots (bark added to wood for stem and branches). Table 6. Estimated values of the parameters of Eq. [5], with their standard errors (in parenthesis), for each aboveground tree compartment (stem and branches) and for the total aboveground biomass (all parameters are significant at the 0.05 level or more, except the parameter “c” for branches which was nevertheless retained in Eq. [5] as it was significant when fitting separately the branch biomass equation). Aboveground tree compartments Parameters of Eq. [5] Stem Branches Total aboveground 3.169 a0 (1.375) 0.02353 0.01536 (0.00221) (0.00221) −0.00008522 -0.00006495 (0.00001426) (0.00000803) 0.00007442 0.03506 (0.00004970) (0.00979) −0.01436 −0.02547 (0.00117) (0.00745) 0.9828 1.530 0.9804 (0.0125) (0.072) (0.0295) 0.0005855 0.0009841 (0.0001105) (0.0002093) This was confirmed by the limited effects observed when ity coefc fi ients equal to 0.0689 (SE = 0.0004) and 0.1288 adding random effects in Eq. [5] – fitted in this case with (SE = 0.0032) respectively. Stem and branch wood bio- nlme (R): among all possible random effects associated masses can then be derived by subtracting stem and with each parameter of Eq. [5], a significant one asso - branch bark biomasses from total stem and total branch ciated with “forest plot” was only observable for the biomasses respectively. parameter “f ” of stem biomass equation, and it was then Biomass equations were established for the follow- decided to ignore random effects when fitting Eq. [5]. ing belowground tree compartments: coarse roots, small The estimated biomass of the different aerial tree roots, fine roots and whole roots (= coarse + small + fine compartments compared favorably with the observed roots). Eq. [5] could not be fitted to belowground data, biomass values. Moreover, the sum of the estimated stem maybe due to an excessive number of parameters. The 2 c and branch biomasses compared relatively well with the reduced model W = (a + bAge) (D Ht) , with only 3 total aboveground biomass estimated as a whole (Figs parameters, was successfully fitted to the data from each 3A–D in Le Goff & Ottorini 2018). compartment, but biased estimations were observed for Stem and branch bark biomasses appeared propor- small and fine roots . The following alternative model tional to stem and branch biomasses, with proportional- gave better results: Small and fine roots data of tree # 35 were dropped from the belowground data file, as they appeared abnormally low. 123 N. Le Goff, J. M. Ottorini / Cent. Eur. For. J. 68 (2022) 117–138 2 c LogW = a + b(D Ht) [7] ground biomass estimated as a whole (Figs 4A–D in Le 2 e b(D Ht) a Goff & Ottorini 2018). that is equivalent to W= αexp (where α = exp ) [8] The model described by Eq. [5] for aerial tree com- The simultaneous estimation of the parameters of partments was tested for foliage biomass (W ). Several Eq. [7] for each root compartment, with starting values parameters in Eq. [5] were not significant and the fol - 2 e+fAge obtained after a separate fitting of each equation, pro - lowing reduced model W = a(D Ht) was then fitted duced the following results (Table 7). to foliage biomass data after a log-transformation of The observation of the residuals of Eq. [7] did not both sides of the equation. An additional variable (RCL reveal any bias in the biomass estimation of each below- = relative crown length) was introduced in the model after ground tree compartment, nor any relation with tree observation of the residuals of the preceding equation. variables not already entered in the equation, only a The n fi al model expressed by Eq. [9] was t fi ted using non- weak dependence with the social status of trees. Random linear least-square regression (nlme, R) to take account effects linked to social status and attached to the param- of the yearly random effects further detected and which eter a, were then added in Eq. [7] fitted in this case with were supported by the parameter a: nlme (R). The comparison of the estimations obtained (a + bRCL) 2 e W = exp (D Ht) [9] with nls or nlme – with or without consideration of a cor- The estimated values of the parameters of Eq. [9], relation effect between tree compartments – did not show which correspond to x fi ed effects, and the random effects a significantly better fitting when adding random effects associated with the parameter a are listed in Table 8. in Eq. [7]; then, it was decided to keep the simpler model The estimated foliage biomasses of sampled trees with only fixed effects considered (Table 7). were in relatively good accordance with the observed val- The estimation of the biomass of the different below- ues (Fig. 5, Le Goff & Ottorini 2018), and no bias could ground tree compartments was then obtained by using be detected. Moreover, the examination of the residuals Eq. [8] and multiplying the estimated values obtained by did not reveal any additional effect of the sampling years 1/2(RSE ) the correction factor e (Flewelling 1981), where nor of tree sampling characteristics (forest plot or tree RSE is the residual standard error of Eq. [7] (RSE = social class belonging). 0.3534). Tree leaf area (LA) appeared proportional to foli- The estimated biomass of the different belowground age biomass (W ), and then a linear relation was fitted tree compartments compared favorably with the corre- using lme (R), as the slope coefficient (s) in the relation sponding observed biomass values, except for the larger LA = s * W presented random effects linked to the year tree of the sample (tree # 35) for which the biomass of of tree sampling (Table 9). The estimated leaf area values coarse roots and of the whole root system seemed overes- were in good accordance with the observed ones (Fig. 6 in timated . Moreover, the sum of the estimated biomasses Le Goff & Ottorini 2018), and no other significant effect of each root category t fi ted relatively well the total below - could be detected. Table 7. Estimated values of the parameters of Eq. [7], with their standard errors (in parenthesis), for each root category (coarse, small and fine roots) and for the whole roots compartment ( all parameters significant at the 0.05 level or more). Belowground tree compartments Parameters of Eq. [7] Coarse roots Small roots Fine roots Whole roots a −15.827 −8.472 −6.661 −12.868 (5.002) (1.673) (1.104) (3.843) b 12.096 3.743 2.332 9.638 (4.808) (1.475) (0.913) (3.650) e 0.05204 0.10131 0.12639 0.05948 (0.01541) (0.02411) (0.02690) (0.01614) Table 8. Estimated values and standard errors of the parameters of Eq. [9] linking foliage biomass (W , kg) to tree diameter (D, cm), height (Ht, m) and relative crown length (RCL), with fixed and random effects distinguished for the parameter “a”. Fixed effects Random effects (Year) Parameters of Eq. [9] Estimate Std error 1996 1997 1999 2000 2001 2002 2003 a −7.870 0.534 0.475 0.535 −0.416 0.066 0.089 −0.687 −0.063 b 3.781 0.397 e 0.813 0.057 Table 9. Estimated value of the slope coefficient s linking leaf area (LA) to foliage biomass (W ), with fixed and random effects distinguished. Fixed effects Random effects (year) Parameter Estimate Std error 1996 1997 1999 2000 2001 2002 2003 s 20.62 1.87 −4.02 −4.08 6.34 2.11 −0.82 1.85 −1.39 In fact, the measured root biomasses of tree # 35 were more probably underestimated due to the difficulty to estimate the biomass of the missing parts of the root system after soil extraction. 124 N. Le Goff, J. M. Ottorini / Cent. Eur. For. J. 68 (2022) 117–138 2 −1 The mean specic fi leaf area (SLA, cm g ) of the sam- the main above and belowground compartments to tree biomass is represented, while in Fig. 4 the contributions pled trees was obtained by multiplying the slope coeffi - 2 −1 of the different root compartments (coarse, small and n fi e cient s in the preceding relation (s = LA/W , m kg ) by 2 −1 roots) to total belowground biomass are represented. 10, leading to the following value: SLA = 206.2 cm g . Tree stem appears as the main tree compartment, representing more than 60% of the tree biomass, except 3.2.3 Biomass distribution factors maybe in the young ages where branch biomass seems to The biomass equations fitted were used to analyze the exceed that of the stem for the smallest trees. Roots con- biomass distribution in above and belowground com- tribute to tree biomass at a relatively constant rate across partments in relation to tree dimensions (diameter and ages, the mean root-shoot ratio being equal to 0.23 for height) and age. As height (Ht) is correlated with diam- the whole sub-sample of trees, with slightly higher values eter (D) at a given age, a height-diameter equation with (0.32) for the youngest trees of the sample aged about 20. age-dependent parameters was fitted to sampled trees Coarse roots contribute to about 90% of total below- data. The following power model was retained after fit - ground biomass for the largest trees, independently of age ting separate equations to data from different age classes class. This contribution tends to decrease with decreasing and analyzing the variation of equation parameters with size of trees when trees are young, for the benefit of small age: and fine roots compartments. (c Age ht) Ht = (a + b Age) D [10] ht ht ht In this equation, the parameter a was dependent ht 3.3. Biomass increment on forest plot. Then, Eq. [10] was fitted with nlme (R), fixed and random effects appearing in Table 10. Plotting 3.3.1 Aboveground compartments residuals against fitted values did not reveal any bias. Biomass distribution in trees was then represented in The following model, derived from the model of Eq. [6], relation to diameter at breast height (D) and age, replac- was retained to represent the variations of the biomass ing tree height (Ht) in biomass equations by its estima- increment of aboveground tree compartments (∆W ) ag tion obtained from Eq. [10]. In Fig. 3, the contributions of with tree leaf area (LA), age (Age) and foliar density Table 10. Estimated values of the parameters of Eq. [10] linking tree height (Ht) to diameter at breast height (D) and age (Age), with fixed and random effects distinguished. Fixed effects Random effects (forest plot) Parameters of Eq. [10] Estimate Std error P214 P215 P217 P220 P222 5.3402 0.6915 0.5316 −1.5525 0.5495 −0.5049 0.9762 ht ht 0.0041 0.0157 0.1748 0.0776 ht 0.1987 0.1214 ht Fig. 3 Distribution of the biomasses of the main tree compartments – stem, branches and roots – in relation to tree diameter (D) and Age. The root-shoot ratio of the sampled trees was calculated as the ratio of total belowground biomass on total aboveground biomass of trees (Reich 2002). 125 N. Le Goff, J. M. Ottorini / Cent. Eur. For. J. 68 (2022) 117–138 Fig. 4. Distribution of the biomasses of the different root compartments – coarse, small and fine roots – in relation to tree diam- eter (D) and Age. d and e are common parameters of above ground com- (DSF) : ag ag c partments; k and k are the multiplicative factors of a ∆W = a (1 – exp(–LA⁄b ) ag)exp((d – e s b ag ag ag ag ag ag for stem and branch biomass increments respectively. LogDSF)⁄Age) [11] To estimate the parameters of Eq. [12], in which Eq. [11] was simultaneously fitted to each above- ∆W stands for the biomass increment of either above- ag ground tree compartment (stem and branches) and to ground tree compartment (stem, branches or total above- total aboveground. As the biomass increment of the ground), a weighted non-linear mixed-effects regression aboveground tree compartments (stem and branches) was performed (nlme, R) with random effects due to for- appeared proportional to total aboveground biomass est plot belonging supported by the parameter a . The ag increment, only the parameter a in the above equation introduction of correlations among the parameters, in varied with tree compartments, and Eq. [11] was re- relation with the inter-dependence of tree compartments, written and fitted as follows: was not considered, as it did not change much the esti- ∆W = a (X + k X + k X )(1 – exp(–LA⁄b ) ag) mated values of the parameters. ag ag t s s b b ag exp((d – e LogDSF)⁄Age) [12] The estimated values of the parameters of Eq. [12], ag ag with their standard errors, are listed in Table 11. All In Eq. [12], X , X and X are dummy variables tak- parameters were significant at the 0.001 level. Random t s b ing the value “1” for total aboveground, stem or branch effects associated with forest plot belonging (P214 to compartments respectively (“0”, otherwise); a , b , c , P222) are also listed. ag ag ag Table 11. Estimated values of the parameters of Eq. [12], with fixed and random effects distinguished for the multiplicative parameter which takes the values a , a k and a k for total aboveground, stem and branch biomass increments respectively. ag ag s ag b Fixed effects Random effects (forest plot) Parameters of Eq. [12] Estimate Std error P214 P215 P217 P220 P222 68.322 13.464 −34.928 42.618 3.471 −20.936 9.775 ag 0.7587 0.0467 0.0416 −0.1594 0.0699 0.0982 −0.0504 0.2413 0.0441 −0.0391 0.1580 −0.0713 −0.0978 0.0503 344.71 15.238 ag ag 1.5826 0.0380 88.577 7.347 ag ag 28.290 3.442 Table 12. Estimated values of the parameters of Eq. [13] with their standard errors; the multiplicative parameter a in Eq. [11] takes here the values a , a k and a k for total belowground, coarse roots and small roots biomass increments respectively. bg bg cr bg sr Parameters of Eq. [13] Characteristic a k k b c d e bg cr sr bg bg bg bg Estimate 7.2673 0.9507 0.0493 236.958 1.9492 117.565 34.570 Std. Error 0.5340 0.0170 0.0124 7.120 0.0425 14.201 7.974 12 1.5 Foliar density is here defined as the ratio LA/BS where LA is tree leaf area and BS is stem surface area (a similar ratio where leaf biomass replaced leaf area was used in a preceding study: Le Goff & Ottorini 1996). 126 N. Le Goff, J. M. Ottorini / Cent. Eur. For. J. 68 (2022) 117–138 The observation of the residuals of Eq. [12] did not 3.4. Biomass allocation reveal any bias in the biomass increment estimations, and In order to analyze the variations of the distribution no other significant effect on the biomass increment of of biomass increment in trees with age, leaf area (LA) the different tree compartments could be detected, espe- and density of foliage (DSF) – from which depends tree cially in relation with the social status of trees or the year growth – LA and DSF were related to tree age (Age). The of tree sampling. The observed and estimated values of following relations could be established, using non-linear the biomass increments of the aboveground tree com- and linear regressions for LA and DSF, respectively: partments of the sampled trees in Hesse forest compared LA=l Age 2 [14] relatively well. Moreover, the sum of the estimated bio- mass increments of each aboveground tree compartment with l = 0.1160 and l = 1.5568 1 2 t fi ted relatively well the aboveground biomass increment Log(DSF) = ν + θLog(Age) [15] estimated as a whole (Figs. 9A–D in Le Goff & Ottorini with ν = 5.308 and θ = −1.0119 (R = 0.57, df = 57, 2018). s = 0.518) The distribution of the biomass increment in trees 3.3.2 Belowground compartments was then represented in relation to tree age, replacing The model described by Eq. [11] allowed the representa- leaf area (LA) and density of foliage (DSF) in biomass tion of the variations of the biomass increments of the increment equations by their estimations obtained from belowground tree compartments (coarse roots, small Eq. [14] and Eq. [15] respectively . In Fig. 5, the con- roots and total root system), which appeared also pro- tributions of the main above and belowground compart- portional. Then, Eq. [12] was adapted for belowground ments to tree biomass increment are represented: bio- tree compartments and fitted in the following form: mass increment appears preferentially allocated to the stem (more than 60%), then to branches (about 20%) ∆W = a (X + k X + k X )(1 – exp(–LA⁄b ) bg) bg bg t cr cr sr sr bg and roots (less than 20%). With regard to the root com- exp((d – e LogDSF)⁄Age) [13] bg bg partment, coarse roots appear to contribute to 95% of In Eq. [13], X , X and X are dummy variables tak- t c s total belowground biomass increment while small roots ing the value “1” for total belowground, coarse roots and contribute to 5% only, independently of tree age . small roots compartments respectively (“0”, otherwise); a , b , c , d and e are common parameters of below bg bg bg bg bg ground compartments; k and k are the multiplicative cr sr factors of a for the biomass increments of coarse roots bg and small roots compartments respectively. A non-linear regression model was fitted to Eq. [13] using nls (R). Weights and correlations were introduced in the model as before, but seemed to generate biased esti- mations and then were not retained in the t fi ting process. Furthermore, no significant random effect – in relation with tree location (forest plot) or tree social class belong- ing – could be detected. Additionally, no signic fi ant effect of the year of tree sampling could be detected. The estimated values of the parameters of Eq. [13], Fig. 5. Distribution of the biomass increments among the with their standard errors, are listed in Table 12. All main tree compartments, in relation to tree age. parameters were significant at the 0.001 level. The observed and estimated values of the biomass increments of the belowground tree compartments of the 3.5. Stem volume increment and growth sampled trees compared relatively well. Moreover, the efficiency sum of the estimated biomass increments of each below- The model developed to represent the variations of the ground tree compartment equaled the belowground bio- annual biomass increment of aboveground tree compart- mass increment estimated as a whole (Figs. 10A–D in Le ments (Eq. [11]) was retained to represent the variations Goff & Ottorini 2018). of bole (or stem) annual volume increment (BI), that is: BI=a (1 – exp(–LA⁄b ) )exp((d – e LogDSF) s s s s /Age) [16] DSF values obtained from Eq. (14) were multiplied by the correction factor e^(1/2 s^2 )(Flewelling & Pienaar 1981). Fine roots biomass increment was not evaluated in this study, as the main part of it is due to fine root turnover whose quantification would have necessitated specific studies (Le Goff & Ottorini 2001). 127 N. Le Goff, J. M. Ottorini / Cent. Eur. For. J. 68 (2022) 117–138 To estimate the parameters of Eq. [16], a non-linear as to represent the same range of social status and ages mixed-effects regression was performed (nlme, R) with as the main tree sample, allowed to obtain biomass equa- random effects due to forest plot belonging supported tions for the belowground parts of trees defined in rela- by the parameters b and d . The estimated values of the tion to root diameter (coarse, small and fine roots), and s s parameters of Eq. [16], with their standard errors, are for total belowground biomass. listed in Table 13. Random effects associated with forest The excavation of the root systems of the sampled plot belonging (P214 to P222) are also listed for b and beech trees caused the loss of some parts of the root d parameters. systems, and then equations were established so as to No other significant effect on BI could be detected, estimate the missing parts of each root system by root including the social status of trees and the year of tree category, as was done in a preceding study (Le Goff & sampling, and the fitted values of BI appeared in good Ottorini 2001); in addition, for establishing these equa- agreement with the observed ones (Fig. 12, Le Goff & tions in the present study, the distinction was made Ottorini 2018). between horizontal and vertical roots for the largest Growth efficiency (GE) of trees, defined as stem trees. It seems, however, that for the largest tree of the annual volume increment per unit of leaf area, was esti- sample (tree # 35), the belowground biomass was under- mated by dividing the BI model (Eq. [16]) predictions by estimated, due probably to an incomplete inventory of their corresponding observed leaf areas, as was done by broken roots during excavation, which resulted in an Hofmayer et al. (2010) and DeRose & Seymour (2009). underestimation of the biomass of missing root parts The estimated values of GE fitted relatively well the for that tree. observed ones (Fig. 6A). Due to the large dimensions of the oldest trees in the The simulated GE values, calculated by replacing LA sample, the biomass of the aboveground tree compart- and DSF values by their estimations obtained from Eq. ments could not be measured directly for large trees, but [13] and [14] respectively, were in good accordance with via volume and wood density evaluations. In addition, all the trend revealed by plotting observed GE values in rela- branches were not measured for these trees, and a strati- tion to age (Fig. 6B). The decrease in GE observed for e fi d sample of branches was used and biomass equations very young and very old trees appears closely reproduced were established to estimate the biomass of non-sampled by the model. branches. Table 13. Estimated values of the parameters of Eq. [16] linking bole volume increment BI to leaf area (LA), density of foliage (DSF) and age (Age), with fixed and random effects distinguished for the parameters b and d . s s Parameters Fixed effects Random effects (forest plot) Estimate Std error P214 P215 P217 P220 P222 [Eq. 16] s 65.8972 5.5281 361.8440 65.2292 170.811 32.418 −55.867 −18.408 −128.954 1.5018 0.05293 114.4202 18.9182 28.235 5.359 −9.235 −3.043 −21.316 35.3697 7.6299 Fig. 6. Observed stem volume growth efficiency (GE) for the tree sample of Hesse forest versus estimated values obtained from Eq. [16], using either observed (A) or estimated (B) LA and DSF values (LA and DSF estimates obtained from Eq. [14] and Eq. [15] respectively). 4. Discussion 4.1. Fitting biomass and biomass increment models The sampling of more than 60 trees of different social status, and representing the range of ages for a total beech Linear and non-linear models were examined to fit bio - stand rotation, allowed to establish generalized biomass mass and biomass increment data. When linear or non- equations for the main aboveground tree compartments linear models could equally be used, notably after log- (stem, branches and leaves) and for total aboveground transformation, the non-linear ones presented a better t fi . biomass. Moreover, a subsample of 40 trees, chosen so 128 N. Le Goff, J. M. Ottorini / Cent. Eur. For. J. 68 (2022) 117–138 When fitting the relations, a particular attention was A comparison of estimated stem biomasses with our model and with the “dh3” model established by Wutzler brought to the unexplained variation and to the quality et al. (2008) showed a close correspondence when attrib- of the fitting in order to obtain an eventually better fit uting the appropriate values to the covariates site index by adding covariates in the model (as done by Wutzler (si), altitude (alt) and age included in the model of Wut- et al. 2008). Variables not introduced in the models but zler (see Appendix A3, Wutzler et al. 2008): diverging characterizing the status of sampled trees – tree social estimates appear only at the extreme ages. status, year of tree sampling, forest plot belonging – were T h e p a r a m e t e r β o f t h e a b o v e g e n e r i c m o d e l retained for the analysis of residuals and eventually added decreased linearly with increasing tree age for the stem in the models as random effects (as done also by Wutzler compartment while it decreased exponentially for the et al. (2008) to differentiate between the data sources). In branch compartment. As γ is constant for branches, this this last case, mixed models were fitted using the pack - means that branch biomass is comparatively lower for age nlme of R. It appeared that such random effects were trees with same diameter and height but older, probably significant for yearly varying biomass variables (foliar in relation with a smaller crown due to higher crowding biomass, biomass increment of aboveground tree com- conditions. This is not true for the stem as the increase partments): in this case, it could be interesting to try to of β with age more than compensates for the decrease of identify these effects, probably related to the yearling γ with increasing age: the stem biomass is comparatively varying climate and particularly its consequences on higher for trees with same diameter and height but which the water availability for trees as it is a limiting factor of are older, as the stem of more crowded trees is more cylin- the growth of beech (Le Goff & Ottorini 1999; Granier drical and has then a higher volume (and biomass) for a et al. 2008). given diameter and height. Additive models should have been t fi ted for above and b(D Ht) An exponential model – W = αexp – appeared belowground data to ensure that the total tree biomass better suited for belowground biomass data. In this case, and biomass increment equals respectively the sums of the parameters of the model did not seem to depend on the biomasses and biomass increments of the different tree age, as it was the case in the model fitted for above- compartments in which they were divided. To simplify ground biomass data. This result confirms preceding the fitting process, multivariate models were used which findings (Le Goff & Ottorini 2001). allowed to obtaining a relatively good agreement for the While tree diameter and height explain a large part biomass and biomass increments of the above and below- of tree biomass variations, tree age appeared also as an ground tree parts estimated as a whole or as the sum of important variable to consider, at least for aboveground their constituting compartments. This is in line with the tree compartments, as already shown by Wutzler et al. results obtained by Repola (2008, 2009). (2008), Genet et al. (2011a,b) or Shaiek et al. (2011). In fact, it can take into account the competitive conditions supported by trees which influence the dimensions of 4.2. Biomass models tree crowns and then the branch biomass itself, but also 2 γ The generic model W = α + β(D Ht) – already used by the distribution of the increments on the stem and then Wutzler et al. (2008) and then by Genet et al. (2011a) stem form (stem tapering) and biomass (Repola 2009). – appeared well suited here to represent the biomass Tree age in biomass equations may also reflect a possi - variations of aboveground tree compartments with tree ble effect of wood density, which tends to increase with diameter (D) and height (Ht). The constant α (a in our age for beech (Bouriaud et al. 2004). However, no age case, Eq. [5]) was significant only for the branch com - effect could be detected in belowground biomass equa- partment, as it was also the case for Genet et al. (2011a, tions, agreeing with previously published results (Bond- b). Moreover, as for Genet et al. (2011b), the parameters Lamberty et al. 2002; Le Goff & Ottorini 2001; Genet β and γ of the biomass model appeared dependent on tree et al. 2011a, b): this may be due to a weaker connection age (Age) and could be expressed with the same func- between the root system dimensions and tree growing tions whose parameters vary with tree compartment (Eq. conditions, as tree crowding. [5] and Table 4). However, in our case, the parameter Tree foliage biomass could be expressed with the β was decreasing with age, independently of the tree same model as aboveground tree compartments, and compartment considered, while it increased for stem then appeared dependent on tree diameter and height. compartment in Genet et al. (2011a, b); furthermore, the However, foliage biomass was also dependent on tree parameter γ slightly increased with age, from about 1 to crown dimensions, increasing with the relative crown 1.1 or 1.15 (stem and overall aerial part respectively) or length of the tree (RCL), as already observed for birch in remained constant, close to 1.5 (branches) in our case, Finland (Repola 2008). For a given diameter and height, while it appeared independent of age regardless of the foliage biomass increases with crown dimensions with compartment considered for Genet et al. (2011a, b). In the “dh3” stem biomass model of Wutzler (2008), si is equal to 36 and alt is equal to 300 for the site of Hesse (Table 1, Wutzler et al. 2008), while age can be varied. (Le Goff & Ottorini 2001). 129 N. Le Goff, J. M. Ottorini / Cent. Eur. For. J. 68 (2022) 117–138 which branch biomass increases, the tree being then able ent with those found by other authors in Germany (Bolte et al. 2004) and Central Europe (Konôpka et al. 2010) to support more foliage. A year-to-year variation of foli- and with those extracted by Genet et al. (2010) from a age biomass could also be detected. It has been widely literature review. The decrease of the root/shoot ratio documented that the quantity of foliage may vary signi- observed with increasing age may be the consequence of ficatively from year to year for a given tree or stand, in an ontogenetic drift with plant size and age (Reich 2002). particular in relation with climatic conditions (Bréda & The fraction of tree biomass included in the root system Granier, 1996; Bréda 1999; Le Dantec et al. 2000). In the appeared then relatively independent of the tree status, as case of Hesse forest – from which the tree sample of this already observed by Bolte et al. (2004) for beech, unlike study came from – year-to-year variations of the stand what happened for branches. LAI could be observed, apart from those due to thinning Coarse roots contributed between 80 and 90% to total operations (Granier et al. 2008). The close proportional root system biomass, the proportion being relatively con- relation observed between tree leaf area and biomass of stant and close to 90% for mature trees (tree age ≥ 60 sampled beech trees allowed to estimate a mean specific years). For younger trees, coarse root biomass contribu- 2 −1 leaf area (SLA) value of 206.2 cm g for these trees: Bar- tion tended to decrease with decreasing tree size (Fig. telink (1997) observed also such a relationship for beech 4), together with a higher contribution of small and fine 2 −1 leaf area, leading to a mean SLA value of 172 cm g for a roots, as already found (Le Goff & Ottorini 2001). The smaller sample of trees ranging in age from 8 to 59 years, coarse root biomass data obtained in this study for trees of a SLA value comparable to that found in our study. various ages appear consistent with the data obtained by Pellinen (1986) for trees of various dimensions and aged between 100 and 115 years (Fig. 8), but differ from those 4.3. Biomass distribution in trees obtained by Bolte et al. (2004) which appeared well below those of Pellinen. This could be related to the lower root/ Tree stem represents the main part of tree biomass shoot ratio observed for beech trees in the case of Bolte et (between 60 and 80%), except in young ages where the al. study – coarse roots biomass representing the major branches may contribute more than the stem to tree bio- part of the root system biomass – and explained by dif- mass in the smallest trees. When trees are ageing, the ferences in the environmental conditions of the different branch contribution to tree biomass tends to decrease to sites (Bolte et al. 2004). less than 20%, and relatively more for smaller trees (Fig. 3). Regarding diameter as an indicator of tree status in stands at a given age, this means that dominance, or tree competitive status, affects the amount of branch biomass (Bartelink 1997): with increasing inter-tree competi- tion, a lower fraction of tree biomass is represented in branches, except maybe for suppressed trees in young stands (Fig. 1). Stem and branch biomass data in our study appear consistent with those obtained by Bartelink (1997), when related to tree diameter (Fig. 7). The root system contributed less than 20% to tree bio- mass, this proportion appearing relatively independent of tree age and status, except maybe for the smallest trees of young age classes (Fig. 3). For very young trees, the root/ Fig. 8. Coarse root biomass (W )data in relation to tree di- shoot ratio amounted to 0.32 while the mean value for ameter (D), for the trees sampled in Hesse forest (this study) the whole tree sample was 0.23: these values are consist- compared with those obtained by Pellinen (1986) in Germany. Fig. 7. Stem (A) and branch (B) biomass data in relation with tree diameter at breast height (D), as observed from the Hesse sample (this study) and from the relation established by Bartelink (1997) which explains 90% of the variation in his sample (Hesse sample here restricted to fit the age range of Bartelink’s study). 130 N. Le Goff, J. M. Ottorini / Cent. Eur. For. J. 68 (2022) 117–138 Relating leaf area and density of foliage to tree age 4.4. Biomass increment models allowed to representing the evolution with age of the The sigmoid model described by Eq. [11] was success- allocation of biomass increment to the main tree com- fully fitted for above and belowground components. ponents (Fig. 5). It appeared that the stem contributed Moreover, the increment of the different components to more than 60% of tree biomass increment – nearly of the above and belowground biomasses appeared pro- 70% in young ages – whereas branches contributed to portional to total aboveground and total belowground a relatively constant fraction close to 20% and roots to biomasses respectively, the increment models differing less than 20% (only 10% in young ages). These propor- only by a multiplicative parameter (or allocation coeffi - tions compare relatively well with those obtained on ash cient) in each case. Then, 76% of aboveground biomass (Fraxinus excelsior L.) in a study conducted in a nearby increment appeared allocated to the stem, compared to region on a sample of trees aged 25 (Le Goff et al. 2004), 24% to branches (comparable to the results obtained for whereas some variations seemed to occur between ash beech by Pajtik et al. 2013, only in young ages), while trees of different competitive status, which was not the 95% of belowground biomass increment was allocated case here with beech. to coarse roots compared to 5% to small roots. The bio- mass increment of aboveground components appeared dependent on forest plot, in relation probably with vary- 4.5. Stem volume increment and growth ing environmental conditions, which was not the case efficiency of trees for belowground compartments. However, no effect of The sigmoid model fitted to biomass increment data varying climatic conditions over sampled years could be was successfully fitted to bole volume increment data detected, in relation maybe with the sampling scheme (Eq. [16]), not surprisingly as stem biomass increment of the study where forest plots were not sampled every appeared proportional to stem volume increment. Thus, sampled year, which may have led to confused stand and the mean stem wood density of the beech sample, which climatic effects. appears to be the slope of the linear relation t fi ted between The biomass increment models fitted – Eq. [11] and stem biomass and volume increments, was equal to 0.549 Eq. [13] – show that biomass increment depends not only (Fig. 10). This density value is in the range of the observed on tree leaf area – as in the basic model used by Hofmeyer values for different beech samples in France and other et al. (2010) to describe bole volume increment – but also countries in Europe (Nepveu 1981), and is close to the on foliage density and age. Biomass increment increases mean value (0.556) obtained from biomass equations by with tree leaf area, but at a slowing rate as trees are age- Genet et al. (2011b). ing (Fig. 9), while foliar density (DSF), which decreases exponentially with age (Eq. [15]), shows a positive effect on tree biomass increment when it decreases. While the 3-variable model fitted explains more variation than the model with only leaf area as independent variable, there remains a large unexplained variation that could eventu- ally be reduced with a larger sample of trees. Fig. 10. Annual stem biomass increment (∆W ) in relation with stem volume increment (BI): observed data and linear 3 2 relation fitted ∆W = r BI, with r = 0.549 kg/dm (R = 0.99). s s s As for biomass increment, a “forest plot” effect was detected for stem volume increment, probably also in rela- tion with environmental conditions (soil and climate). Stem wood growth efficiency (GE), defined here as annual stem volume increment per unit of leaf area, appeared to increase rapidly with age until trees reached Fig. 9. Observed aboveground annual biomass increment data the age of 20–30 years (Fig. 6), and then increased more (∆W ) in relation with tree leaf area (LA) and projected values ag,t slowly until it began to decrease after the age of about 100 obtained from Eq. [12] for trees of ages covering the sample age years. This result was obtained after taking account of range (in Eq. [12], the density of foliage was estimated from the the variations of tree leaf area (LA) and density of foliage relation established with tree age, that is Eq. [15]). Wood density, or wood specific gravity ( ρ ), is here defined as the ratio of dry weight on green volume. 131 N. Le Goff, J. M. Ottorini / Cent. Eur. For. J. 68 (2022) 117–138 (DSF) with tree age (Eq. [14] and Eq. [15] respectively). decrease of the density of foliage with age, as observed in The decline of GE with age, after culminating at relatively the sample, contributes to counterbalance the negative young ages, has been already reported for coniferous effect of increasing age on the growth efficiency of trees. species, at tree level, (Kaufmann & Ryan 1986; Cannell Moreover, there is a relationship between the density of 1989; Ryan et al. 1997; Day et al. 2001). But other stud- foliage and the crown ratio that shows a minimum for ies failed to reveal such a decrease of GE with age when trees moderately crowded (crown ratio of about 0.45): leaf area effects were not taken into account (Seymour thus, those trees exhibit a better growth efficiency com- et al. 2002; Harper 2008). The pattern of variation of GE pared to trees less or more crowded, which contrasts with with age could be either attributable to variations of pro- the results obtained with ash (Le Goff et al. 1996). ductivity per unit of leaf area or to variations of biomass Then, the most growth efficient beech trees appear allocation, as trees get older. However, no important to be middle-aged (around 50 years old), dominant with variation of biomass allocation with tree age could be relatively large crowns (leaf area around 200 m ) and observed (Fig. 5), only a small advantage for the stem moderately crowded (crown ratio around 0.45). Such at an early age. Then, the pattern of variation of GE with trees exhibit a mean annual stem volume increment of age could be attributable to an ontogenetic effect (Day about 100 dm . et al. 2001, Seymour et al. 2002), the decrease of GE at higher ages ree fl cting probably a less efc fi ient physiologi - cal functioning of trees as they get older (Ryan et al. 1997; 5. Conclusion Konôpka et al. 2010). The biomass and biomass increment models established As shown by Fig. 11, growth efc fi iency ( GE) depends for beech in this study allow the estimation of the biomass not only on age, but also on leaf area (LA) and density of and carbon stocks and fluxes for the even-aged beech foliage (DSF). Thus, the asymptotic model for BI (Eq. stands of Hesse forest, whatever the age of the stand. [16]) predicts also a declining GE with increasing tree Thus, it should help to extend the studies on the ecophysi- leaf area (cf Maguire et al. 1998; Seymour et al. 2002), ological functioning of beech stands presently conducted but only above a value of about 300 m for leaf area, only in Hesse forest (Granier et al. 2008) to younger and older observed in the oldest trees of the sample. GE decreases stands, and in particular the comparison of the net pri- also, for a given LA, with increasing values of the density of foliage, which is the ratio of leaf area on transformed mary productivity (NPP) of stands estimated from the bole area: such a decrease, already observed with ash (Le CO fluxes with the stand biomass increment (Granier Goff et al. 1996), a less shade tolerant species than beech, et al. 2000). Moreover, it could help to test the ability of may be related to a less favorable ratio of assimilatory to bio-geochemical models, like BIOME-BGC, to assess the gross and net primary production of beech stands, as was respiratory processes associated with the increase of foli- age area per unit of bole surface area. But, conversely, the done by Chiesi et al. (2014) for beech forests in Italy. Fig. 11. Growth efficiency (GE) of beech, in relation with leaf area (LA) and density of foliage (DSF), for trees of increasing ages (from 20 to 160 years) (the curves represented were restricted to the range of leaf areas and densities of foliage observed, accord- ing to age in the tree sample). 132 N. Le Goff, J. M. Ottorini / Cent. Eur. For. J. 68 (2022) 117–138 The biomass equations established could also be used Bond-Lamberty, B., Wang, C., Gower, S. T., 2002: Aboveground and belowground biomass and sap- to analyze the effects of different silvicultural treatments wood area allometric equations for six boreal tree on the biomass and carbon stocks and fluxes of beech species of northern Manitoba. Canadian Journal of stands, using the available stand growth and yield models Forest Research, 32:1441–1450. built in France, that is “Fagacées” (Dhôte & Le Mogue- Bouriaud, O., Bréda, N., Le Moguedec, G., Nepveu, G., dec 2005) or “SimCAP” (Ottorini & Le Goff 2006). 2004: Modelling variability of wood density in beech The generalized biomass and biomass increment as affected by ring age, radial growth and climate. equations established for Hesse forest should however Trees, Structure and Function, 18:264–276. be used with care for beech stands of other regions dif- Bréda, N., 1999: L’indice foliaire des couverts fores- fering by site conditions, although the models developed tiers: mesure, variabilité et rôle fonctionnel. Revue for biomass are very similar to the ones developed at a Forestière Française, 51:135–150. larger scale by Wutzler et al. (2008) and Genet et al. Bréda, N., Granier, A., 1996: Intra- and inter-annual (2011). More cond fi ent data are still necessary to obtain, variations of transpiration, leaf area index and radial in particular for the root biomass compartments, so as to growth of a sessile oak stand (Quercus petraea). develop more precise biomass and biomass increment Annals of Forest Science, 53:521–536. equations. Cannell, M.G.R, 1989: Physiological basis of wood pro- duction: a review. Scandinavian Journal of Forest Research, 4:459–490. Acknowledgments Chiesi, M., Maselli, F., Chirici, G., Corona, P., Lombardi, Our thanks go the INRA technicians of the LERFoB research F., Tognetti, R., Marchetti, M., 2014: Assessing most unit at INRA-Nancy, who proceeded to the tree measurements: relevant factors to simulate current annual incre- R. Canta, F. Bordat, G. Maréchal and S. Daviller. Special thanks ments of beech forests in Italy. iForest, 7:115–122. are addressed to R. Canta who supervised the e fi ld and laboratory Day, M., Greenwood, M., White, A., 2001: Age-related measurements and developed a specific apparatus to allow the changes in foliar morphology and physiology in red biomass measurements on the large root systems. The support of spruce and their inu fl ence on declining photosynthe - the ONF section of Sarrebourg (57), greatly appreciated, made sis rates and productivity with tree age. Tree Physiol- possible the felling of the tree samples used in this study. We would like also to thank warmly A. Granier (EEF, INRA-Nancy) ogy, 21:1195–1204. for his interest in the biomass studies that we conducted in the DeRose, R. J., Seymour, R. S., 2009: The effect of site Hesse forest over several years, in parallel with the ecophysiologi- quality on growth efficiency of upper crown class cal studies that he conducted himself, and for his comments on Picea rubens and Abies balsamea in Maine, USA. a first draft of the manuscript. Our thanks are also addressed Canadian Journal of Forest Research, 39:777–784. to F. Ningre (Silva, INRA-Nancy) who warmly encouraged and Dhôte, J.-F., Le Moguedec, G., 2005: Présentation du helped us in publishing the results of this study. This work was modèle Fagacées. Nancy: LERFoB, UMR 1092 supported by grants from ONF (French National Forest Service) INRA-ENGREF (Document interne). and from the GIP “ECOFOR” (a French public benefit corpora- Flewelling, J. W., Pienaar, L. V., 1981: Multiplicative tion on FORest ECOsystems). The UMR Silva, regrouping the regression with lognormal errors. Forest Science, previous LERFoB and EEF research units, is supported by the 27:281–289. French National research Agency (ANR) through the Laboratory Genet, A., Wernsdörfer, H., Jonard, M., Pretzsch, H., of Excellence ARBRE (ANR-11-LABX-0002-01). Rauch, M., Ponette, Q. et al., 2011a: Ontogeny partly explains the apparent heterogeneity of published bio- mass equations for Fagus sylvatica in central Europe. references Forest Ecology and Management, 261:1188–1202. Bartelink, H. H., 1997: Allometric relationships for Genet, A., Wernsdörfer, H., Mothe, F., Bock, J., Ponette, biomass and leaf area of beech (Fagus sylvatica L). Q., Jonard, M. et al., 2011b: Des modèles robustes et Annals of Forest Science, 54:39–50. génériques de biomasse. Exemple du Hêtre. Revue Bolker, B. M., 2008: Ecological Models and Data in R. Forestière Française, 63:179–190. Princeton University Press, 41 William Street, Princ- Genet, H., Bréda, N., Dufrêne, E., 2010: Age-related eton, New Jersey 08540, USA. variation in carbon allocation at tree and stand scales Bolte, A., Rahmann, T., Kuhr, M., Pogoda, P., Murach, in beech (Fagus sylvatica L.) and sessile oak (Quer- D., Gadow, K. V., 2004: Relationships between tree cus petraea (Matt.) Liebl.) using a chronosequence dimension and coarse root biomass in mixed stands approach. Tree Physiology, 30:177–192. of European beech (Fagus sylvatica L.) and Nor- Granier, A., Ceschia, E., Damesin, C., Dufrêne, E., way spruce (Picea abies [L.] Karst.). Plant and Soil, Epron, D., Gross, P. et al., 2000: The carbon bal- 264:1–11. ance of a young beech forest. Functional Ecology, 14:312–325. 133 N. Le Goff, J. M. Ottorini / Cent. Eur. For. J. 68 (2022) 117–138 Granier, A., Bréda, N., Longdoz, B., Gross, P., Ngao, J., Le Goff, N., Ottorini, J.-M., 2018: Mathematical and 2008: Ten years of u fl xes and stand growth in a young ecological traits of above and below ground biomass beech forest at Hesse, North-eastern France. Annals production of beech (Fagus sylvatica L.) trees grow- of Forest Science, 64:704p1–704p13. ing in pure even-aged stands in north-east France. Harper, G., 2008: Quantifying branch, crown and bole BioRxiv, Available online: https://www.biorxiv.org/ development in Populus tremuloïdes Michx. from content/early/2018/04/13/300210.full.pdfhtml north-eastern British Columbia. Forest Ecology and Le Goff, N., 2019: Above and belowground biomass data Management, 255:2286–2296. for a set of beech trees of different age and crown Hofmeyer, P. V., Seymour, R. S., Kenefic, L. S., 2010: classes sampled in Hesse state forest (NE France) Production ecology of Thuya occidentalis. Canadian with a view to analyzing the distribution and the Journal of Forest Research, 40:1155–1164. allocation of biomass in the tree. Available online: Kaufmann, M. R., Ryan, M. G., 1986: Physiographic, https://data.inra.fr/dataset.xhtml?persistentId=do stand, and environmental effects on individual tree i:10.15454/8CLEGO growth and growth efficiency in subalpine forests. Maguire, D. A., Brissette, J. C., Gu, L., 1998: Crown Tree Physiology, 2:47–59. structure and growth efc fi iency of red spruce in even- Konôpka, B., Pajtik, J., Moravcik, M., Lukac, M., 2010: aged, mixed-species stands in Maine. Canadian Jour- Biomass partitioning and growth efficiency in four nal of Forest Research, 28:1233–1240. naturally regenerated forest tree species. Basic and McElligott, K. M., Bragg, D. C., 2013: Deriving biomass Applied Ecology, 11:234–243. models for Small-diameter Loblolly Pine on the Cros- Konôpka, B., Pajtik, J., Seben, V., Surovy, P. et al., 2021: sett Experimental Forest. Journal of the Arkansas Woody and foliage biomass, foliage traits and growth Academy of Science, 67:94–101. efc fi iency in young trees of four broadleaved tree spe - Nepveu, G., 1981 : Propriétés du bois de Hêtre. In: Le cies in a temperate forest. Plants, 10:2155. Hêtre, Monographie INRA, Paris, 1981, p. 377–387. Lebaube, S., Le Goff, N., Ottorini, J.-M., Granier, A., Ningre, F., 1997: Une définition raisonnée de la fourche 2000: Carbon balance and tree growth in a Fagus du jeune hêtre. Revue forestière française, 1:32–40. sylvatica stand. Annals of Forest Science, 57:49–61. Oliver, C.D., Larson, B.C., 1996: Forest stand dynamics. Le Dantec, V., Dufrene, E., Saugier, B., 2000: Interan- John Wiley and Sons, Inc., New York, USA. nual and spatial variation in maximum leaf area index Ottorini, J.-M., Le Goff, N., 1999: Aspects quantitatifs et of temperate deciduous stands. Forest Ecology and qualitatifs de la biomasse. Rapport scientifique final Management, 134:71–81. (3ième année), Convention de recherche ONF-INRA Le Goff, N., Ottorini, J.-M., 1996: Leaf development and “Etude de la croissance du hêtre sur le Plateau lor- stem growth of ash (Fraxinus excelsior L.) as affected rain”, Juillet 1999, 18 p. by tree competitive status. Journal of Applied Eco- Ottorini, J.-M., Le Goff, N., 2006 : SimCAP, Simulation et logy, 33:793–802. intégration des connaissances: données expérimen- Le Goff, N., Ottorini, J.-M., 1998: Biomasses aériennes tales et simulées de la croissance du Frêne et du Hêtre. et racinaires et accroissements annuels en biomasse Conseil Scientifique LERFoB 2006, 14 mars 2006 , dans le dispositif écophysiologique de la forêt de ENGREF, Nancy (document “PowerPoint”), 21 p. Hesse. Rapport scientifique annuel, Contrat ONF- Parresol, B. R., 2001: Additivity of nonlinear biomass INRA “Croissance du Hêtre sur le Plateau lorrain”, equations. Canadian Journal of Forest Research, 29 p. 31:865–878. Le Goff, N., Ottorini, J.-M., 1999: Effets des éclaircies sur Pajtik, J., Konôpka, B., Marusak, R., 2013: Aboveground la croissance du hêtre. Interaction avec les facteurs net primary productivity in young stands of beech and climatiques. Revue Forestière Française, LI-2:355– spruce. Lesnicky casopis-Forestry Journal, 59:154– Le Goff, N., Ottorini, J.-M., 2001: Root biomass and Pellinen, P., 1986: Biomasseuntersuchungen im Kalk- biomass increment in a beech (Fagus sylvatica L.) buchenwald, Dissertation Universität Göttingen, stand in North-East France. Annals of Forest Sci- Germany, 134 p. ence, 58:1–13. Pineiro, G., Perelman, S., Guerschman, J. P., Paruelo, J. Le Goff, N., Granier A., Ottorini J.-M., Peiffer M., 2004: M., 2008: How to evaluate models : Observed vs. Pre- Biomass increment and carbon balance of ash (Frax- dicted or Predicted vs. Observed? Ecological Model- inus Excelsior L.) trees in an experimental stand in ling, 216:316–322. northeastern France. Annals of Forest Science, 61:1–12. 134 N. Le Goff, J. M. Ottorini / Cent. Eur. For. J. 68 (2022) 117–138 R Development Core Team, 2009: R: A Language and Shaiek, O., Loustau, D., Trichet, P., Meredieu, C., Bach- Environment for Statistical Computing. R Founda- tobji, B., Garchi, et al., 2011: Generalized biomass tion for Statistical Computing, Vienna, Austria. ISBN equations for the main aboveground biomass com- 3-900051-070. ponents of maritime pine across contrasting environ- Reich, P. B., 2002: Root-shoot relations: optimality in ments. Annals of Forest Science, 68:443–452. acclimation and adaptation or the “Emperor’s New Sileshi, G. W., 2014: A critical review of forest biomass Clothes”? In: Plant Roots, The Hidden Half, 3rd Ed., estimation models, common mistakes and correc- Marcel Dekker, Inc., New York. tive measures. Forest Ecology and Management, Repola, J., 2008: Biomass equations for Birch in Finland. 329:237–254. Silva Fennica, 43:605–623. Velleman, P. F., 2011: Data Desk 6.3, Data Description Repola, J., 2009: Biomass equations for Scots pine and Inc., P.O. Box 4555, Ithaca, NY 14852, USA. Norway spruce in Finland. Silva Fennica, 43:625– Wutzler, T., Wirth, C., Schumacher, J., 2008: Generic 647. biomass functions for Common beech (Fagus syl- Ritz, C., Streibig, J. C., 2008: Nonlinear Regression with vatica L.) in Central Europe – predictions and com- R. Springer ScienceBusiness Media, LLC, 233 Spring ponents of uncertainty. Canadian Journal of Forest Street, New York, NY 10013, USA. Research, 38:1661–1675. Ryan, M. G., Binkley, D., Fownes, J. H., 1997: Age-related Zeng, W. S., Zhang, H. R., Tang, S. Z., 2011: Using the decline in forest productivity: Patterns and processes. dummy variable model approach to construct com- Advances in Ecological Research, 27:213–256. patible single-tree biomass equations at different Seymour, R. S., Kenefic, L. S., 2002: Influence of age scales – a case study for Masson pine (Pinus masso- on growth efficiency of Tsuga canadensis and Picea niana) in southern China. Canadian Journal of Forest rubens trees in mixed-species, multiaged northern Research, 41:1547–1554. conifer stands. Canadian Journal of Forest Research, Zheng, C., Mason, E. G., Jia, L., Wei, S., Sun, C., Duan, 32:2032–2042. J., 2015: A single-tree additive biomass model of Quercus variabilis Blume forests in North China. Trees, 29:705–716. 135 N. Le Goff, J. M. Ottorini / Cent. Eur. For. J. 68 (2022) 117–138 Appendix Annex 1. Data processing This annex describes how the measurements taken on sampled trees (see text) were used in calculating the charac- teristics of each tree compartment (stem, branches, leaves and roots). Stem When stem analysis was performed, the stem volume was obtained as the sum of the volumes of the different sec- tions making the stem. Each section was considered as a truncated cone, except the last one on stem ends that was considered as a cone. In this case, the current volume increment of stem sections was calculated as the product of the stem volume sections by the relative current area increment of the increment samples taken on each stem section. When stem analysis was not performed (sample # 1), the stem volume was obtained by converting dry weights of stem sections into volume using the specific gravity (ratio of dry weight to volume) of the sampled stem discs. In this case, bole volume increment was derived from bole biomass increment, using a relation established on the whole set of trees subjected to stem analysis. Stem biomass was calculated as the sum of the dry weights of the bole and of the fork arms sections, the dry weight of each section being generally evaluated as the product of the green weight of the section by the ratio of dry weight to green weight of sample disks taken in each stem section. When samples were not available for each stem section, a special procedure was applied (see Le Goff & Ottorini 2018). The weighting separately of wood and bark for a sub-sample of stem disks allowed to estimate the dry weight of wood and bark of the stem sections and of the whole stem, using a relation describing the variation of the ratio of bark (or wood) to total dry weight along the stem for the sub-sample of stem discs (see Le Goff & Ottorini 2018, for more details). The current biomass increment of stem sections was calculated, as for current volume increment, as the product of stem sections biomass by the relative current area increment of the increment samples taken in each stem section. When increment samples were not available for each stem section, a relation was established relating the relative current area increment of available increment samples to their height (or relative height) in the tree. The stem area of trees was obtained as the sum of the areas of the different sections making the stem as for bole volume when stem analysis was performed. Otherwise, the stem area of trees was derived from bole biomass, using a relation established on the whole set of trees subjected to stem analysis. Branches The basal diameter of branches was calculated as the geometric mean of the 2 diameters measured at right angles at the base of branches. In case of a complete inventory of branches on sampled trees, the dry weight of each branch was calculated as the sum of the dry weights of the branch sections estimated as the product of sections green weights by the mean ratio of dry weight to green weight calculated for the whole set of branch samples. In case of branch sampling, relations were established at tree level linking branch biomass to branch basal diameter and these relations were used to estimate the biomass of non-sampled branches. The total dry weight of branches per tree was then calculated as the sum of individual branch dry weights, of the dry weight of grouped small branches (obtained as for sampled branches), and of the dry weight of stem ends branches and of epicormics for concerned trees (the dry weight of grouped epicormics being obtained as for sampled branches). The weighting separately of wood and bark for a sub-sample of branch disks allowed estimating a mean branch wood biomass ratio for each tree. This ratio was used to estimate the wood biomass of each branch from its total biomass and the bark biomass was obtained as the difference between total and wood biomasses. The current annual biomass increment of branch sections was calculated as for stem sections. For trees with sampled branches, relations were established between branch biomass increment and either branch basal diameter (tree sample # 3) or foliage biomass (tree sample # 5); these relations were used to estimate the biomass increment of non-sampled branches. The current biomass increments of grouped branches (branches on stem ends and groups of small branches) were calculated as the product of branch group’s biomasses by the relative current area increment of the increment samples taken in each group. 136 N. Le Goff, J. M. Ottorini / Cent. Eur. For. J. 68 (2022) 117–138 leaves (biomass) In case of a total branch inventory of leaves with their supporting twigs (tree samples #1 & #2), branch leaf dry weights were obtained by multiplying the “leaf+twigs” green weight by the ratio of sample leaf dry weight to sample “leaf+twigs” green weight. In case of leaves and twigs collected together for all branches, except for a sample of branches for which “leaf+twigs” samples were taken (tree samples # 4, # 7) allowing to calculate their leaf dry weight as before, the leaf dry weight of grouped branches was obtained by multiplying their total “leaf+twigs” green weight by the mean ratio of leaf dry weight to green weight of “leaf+twigs” samples. In case of “leaf+twigs” collected only for a sample of branches (tree samples # 3 & # 5), after estimating the leaf dry weight of sampled branches from a “leaf+twigs” sample as before, relations were established at tree level linking branch leaf dry weight to basal branch diameter (quadratic or power model) or to dry weight of branches (power model). These relations were then used to estimate the leaf dry weight of non-sampled branches. For each stem end den fi ed (tree samples # 3 & #5), the total leaf dry weight was calculated from total “leaf+twigs” green weight, leaf dry weight and “leaf+twigs” green weight of a “leaf+twigs” sample, as for sampled branches, and the leaf dry weights of all stem ends were summed. For each set of epicormics recognized, the total leaf dry weight was calculated from total “leaf+twigs” green weight, leaf dry weight and “leaf+twigs” green weight of a “leaf+twigs” epicormics sample. The total tree leaf dry weight was then calculated as the sum of the leaf dry weights of branches, stem ends (if any) and epicormics (if any). leaves (area) In case of “leaf+twigs” samples taken on each inventoried branch (tree samples # 1 & # 2), total leaf branch area was obtained by multiplying the leaf sample area by the ratio of branch leaf dry weight (measured or estimated) to leaf sample dry weight. In case of “leaf+twigs” collected together for all branches, except for a sample of branches for which “leaf+twigs” samples were taken (tree samples # 4, # 7) allowing to calculate their leaf area as before, the leaf area of grouped branches was obtained by multiplying the total calculated leaf dry weight by the mean ratio of leaf area to leaf dry weight – that is specific leaf area (SLA) – of the samples taken in each crown stratum. In case of “leaf+twigs” collected only for a sample of branches (tree samples # 3 & #5), after estimating the leaf area of sampled branches as before, relations were established at tree level (tree sample # 5) or for the whole sample of trees (tree sample # 3), linking directly total branch leaf area to basal branch diameter (see Le Goff & Ottorini 2018). For each stem end defined (tree samples # 3 & # 5), total leaf area was obtained by multiplying the leaf sample area by the ratio of stem end leaf dry weight to leaf sample dry weight. For each set of epicormics recognized, total leaf area was obtained by multiplying the leaf sample area by the ratio of epicormics leaf dry weight to leaf sample dry weight. The total tree leaf area was obtained as the sum of leaf area of branches, stem ends (if any) and epicormics (if any). Twigs The same process as for leaves was followed to obtain the dry weight of branch twigs, replacing leaf weight by twigs weight in the calculations performed or in the relations to be established to estimate the total dry weight of twigs from basal branch diameter. roots Biomass equations were established for broken roots on a sample of intact root ends (see Le Goff & Ottorini 2001, 2018) in order to estimate total missing root biomass, with distinction made between horizontal and vertical roots for larger trees (samples # 3 and # 5), and in order to estimate the missing root biomass for each root fraction of each category of roots. The total tree root biomass was obtained as the sum of the dry weights calculated for each root category, for measured roots, sampled root ends, root increment samples and missing root ends. The missing root biomass estimated represented between 0 and 10% of the total root biomass of trees (sample # 4), between 2 and 7% (sample # 5) and between 5 and 20% (sample # 3). In this case, 2 or 3 branches were sampled in each of the two crown strata defined, depending on the tree sample. 137 N. Le Goff, J. M. Ottorini / Cent. Eur. For. J. 68 (2022) 117–138 The calculation of the current annual biomass increment of the root systems was based on the current annual relative volume increments of the root increment samples taken, with the following steps (see Le Goff & Ottorini 2018 for details): calculation of inside bark current annual relative volume increments of the root increment samples; calculation of the median (k) of the current annual relative volume increments of the root increment samples of trees for each social class (Table 2), the median values (k) being used as estimates of the relative annual volume increments of the whole root systems of trees in each social class (Le Goff & Ottorini 2001); calculation of the current annual biomass increments of large and small roots by multiplying their biomass by the appropriate “k” value, considering that the wood density of all parts of the root system was constant (see Le Goff & Ottorini 2001). −1 −1 In this study, the fine root turnover was not considered; it was estimated around 0.6 t ha an at stand scale for the experimental stand “Hesse-1” at the age of 20 with a stand density of about 3500 stems per ha, which corresponds −1 to about 0.17 kg an at tree scale (Le Goff & Ottorini 2001).

Journal

Forestry Journalde Gruyter

Published: Sep 1, 2022

Keywords: leaf area; biomass allocation; biomass distribution; biomass equations; growth efficiency

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