ORIGINAL PAPER

Jarosław Socha Æ Piotr Wezyk

Allometric equations for estimating the foliage biomass of Scots pine

Received: 4 July 2005 / Accepted: 28 June 2006 / Published online: 15 August 2006� Springer-Verlag 2006

Abstract The research described in this paper was per-formed in the Niepolomice Forest (Southern Poland) in2001 as part of the Forest Environmental Monitoringand Management System (FOREMMS; 5FP IST) pro-ject. The material for the present study consisted of themeasurement results of the biomass of Scots pine shootswith needles and needles alone carried out on 113 felledsample trees. The purpose of this study was to constructempirical equations for estimating the foliage biomass ofScots pine from easy to measure parameters. To achievethis aim, the dependence of the foliage biomass of Scotspine on stem diameter, height, age, crown length, basalarea increment of the trees was analyzed. Using thebiometric characteristics such as: tree diameter at breastheight (dbh), basal area increment, age, height, andcrown length empirical equations for estimating the fo-liage biomass of Scots pine reasonably precisely havebeen established. The created empirical equation givesaccurate foliage biomass estimates. The explained vari-ability varies between 65 and 85%, it depends on thenumber of variables applied in the equation. The equa-tions presented in this paper were created with a view totheir possible use in ecological studies where biomassquantity may be used, for example, in modeling carboncirculation in the forest ecosystem. From the point ofview of forestry practice, these equations may help toassess biomass production in Scots pine stands.

Keywords Foliage biomass Æ Allometric equations ÆPinus sylvestris L.

Introduction

Carbon dynamics of forest ecosystems depend on foliagebiomass because of the short life span of the foliage(Lehtonen 2005). The quantity of leaf biomass is one ofthe most important factors for determining a tree’s po-tential to utilize solar energy, assimilate carbon throughphotosynthesis (Grace et al. 1987) and contributing tothe development of a stand (De los Santos-Posadas andBorders 2002). The foliage biomass is required formodeling CO2 exchange (Goulden et al. 1996; Hookerand Compton 2003) and the development of processmodels of forest growth (Baldwin et al. 1997; Monserudand Marshall 1999). The structure and quantity of thebiomass of a forest stand is an important indicator ofenvironmental conditions because leaf biomass hasproven to be very sensitive to climatic patterns and sil-vicultural treatments (De los Santos-Posadas and Bor-ders 2002).

Burger (e.g. 1929, 1945, 1953) was one of the pio-neers of studies on the quantity and structure of treebiomass. His numerous experiments, carried out inSwitzerland, concerned such tree species as Pinusstrobus L., Larix decidua L., and Picea abies (L.)Karst. Recent ecological studies have concentrated onthe quantitative description of the foliage biomass ofthe main forest tree species, in particular Scots Pine.In Finland, important studies on the biomass of Scotspine needles were carried out by Vanninen et al.(1996), Makela and Vanninen (1998), Helmisari et al.(2002), and Lehtonen (2005). In former Czechoslova-kia, empirical equations for estimating foliage biomasswere established by Chroust (1985). Studies on tree-crown biomass, in particular Scots pine foliage bio-mass, in the Ural and Kazakhstan were carried out byHoffman and Usoltsev (2002), in Russia by Monserudet al. (1996). In Germany, Heinsdorf and Krauß

Communicated by Hans Pretzsch

J. Socha (&)Department of Forest Mensuration, Faculty of Forestry,Agricultural University of Cracow, Al. 29 Listopada 46,31-425 Cracow, PolandE-mail: rlsocha@cyf-kr.edu.pl

P. WezykDepartment of Forest Ecology, Laboratory of GIS and RS,Faculty of Forestry, Agricultural University of Cracow,Al. 29 Listopada 46, 31-425 Cracow, PolandE-mail: rlwezyk@cyf-kr.edu.pl

Eur J Forest Res (2007) 126: 263–270DOI 10.1007/s10342-006-0144-4

(1990) elaborate the tables to estimate dry biomass ofScots Pine. In Poland, studies on the foliage biomassof Scots pine (Pinus sylvestris L.) have been carriedout by Lemke (1975, 1983), Lemke and Wozniak(1992), and Lemke and Kazmierczak (1993). The fo-liage biomass of naturally regenerated Scots pine ofyounger age classes has also been studied by Barci-kowski and Loro (1995).

Foliage biomass is difficult to predict because of itsgreat variation and dependence on various site and treeproperties (Lehtonen 2005). Koeper and Richardson(1980) pointed out that the use of allometric equationsfor determining the foliage biomass of Scots pine basedon results obtained in other areas may result in quitesignificant errors, and thus the estimation of biomassproduction in a given area should only be based on localmeasurements, which, however, are time-consuming andcostly to take.

Some methods for foliage biomass estimation arebased on the pipe model theory (Shinozaki et al.1964). According to this theory there is a strongrelationship between foliage biomass and sapwoodarea of the tree.

The most widely used methods for foliage biomassassessment are based on allometric equations with treesize as independent variables and tree biomass asdependent variable. Tree size is usually represented bytree diameter at breast height (dbh) (Lemke 1983; Ba-ker et al. 1984; Eliott and Clinton 1993; Baldwin et al.1997; Makela and Vanninen 1998; Oleksyn et al. 1999),height (Barcikowski and Loro 1995), dbh and height(Chroust 1985; Claesson et al. 2001; Santa Regina andTarazona 2001), crown size (Baldwin et al. 1997; Xuand Harrington 1998), or volume (McCray and Joel1998).

These studies have revealed that the relationship be-tween foliage biomass and tree size does not followlinear trends. However, the majority of equations forleaf biomass calculation use linear or linearized func-tions. Relationships between the different characteristicsof the tree may be described mathematically (Monserudand Marshall 1999). The commonly used model fordescribing allometric relationships is the basic allometricfunction: Y ¼ aX b where a and b are parameters of theallometric function, Y the dependent variable, and Xindependent variable.

This allometric equation is often used to describeboth the total biomass and biomass of various treefractions (Baldwin et al. 1997; Makela and Vanninen1998; Socha and Wezyk 2004).

The purpose of this study was to construct empiricalequations for estimating the foliage biomass of Scotspine, which is the most important forest tree species inPoland (more than 70% of the Polish forests are occu-pied by Scots pine). To achieve this aim, it was necessaryto perform an analysis of dependence of the foliagebiomass of Scots pine on selected biometric character-istics of trees in order to establish the independentvariables for the empirical equations.

Materials and methods

The research described in this paper was performed inthe Niepolomice Forest in 2001 as part of the RTDproject Forest Environmental Monitoring and Man-agement System (FOREMMS; EU 5FP IST). The maingoal of the FOREMMS project was to create a proto-type of the geoinformation system for the managementof European forest resources based on nodes located in:Finland, Italy, and Poland representing the three char-acteristic forest biomes. In Poland the NiepolomiceForest was chosen as the demonstration site of mixedoak–pine stands growing in the temperate climate zone(Pino-Quercetum community). The forested area of theNiepolomice Forest district is now 10,512 ha. The maintree species are: Scots pine (P. sylvestris L.) occupying6,694 ha (66.3%), common oak (Quercus robur L.) andsessile oak (Quercus sessilis L.) occupying together1,952 ha (19.3%), and European black alder (Alnusglutinosa Gaertn.) with an area of 1,093 ha (10.8%). Theremaining 3.1% of the total area is covered by Europeanlarch (Larix europea L.) and lime (Tilia sp.). Forest sitetypes consist mainly of wet coniferous forest, wetdeciduous forest, wet mixed forest, and fresh coniferousforest sites.

Mean annual temperature and mean total annualprecipitation at the Niepołomice Forest are 7.5�C and550 mm, respectively.

A regular (750 · 750 m) grid of 185 monitoring plots(on 113 plots Scots pine was the dominant tree species)was established during the FOREMMS field campaignusing the DGPS method (Wezyk et al. 2001; Wezyk2004). The materials for the present study consist of themeasurement results of the biomass of Scots pine shootswith needles (Fb) and needles alone (F) from 113 aver-age sample trees felled at the FOREMMS randomlyselected sample plots (Fig. 1). In July 2001, for eachmonitoring plot, one sample tree (average dbh andheight) was chosen and felled after all the diameters andheight of trees had been measured in concentric-circleareas (500 and 100 m2). The distribution of sample treesby diameter class is shown in Table 1. After the tree wasfelled, its total length, the length and width of the crown,the biomass of all the branches, and the biomass of allfresh shoots with green needles were measured directlyin the field. To estimate the biomass of fresh shoots withneedles, a mobile electronic scale (accuracy 2 g) wasused. To estimate the biomass of particular crown partsa mixed sample of cut shoots with needles from differentparts of pine crown (heights, branches, and aspects) wastaken. On the same day, a sample of 20 kg (in freshstate), sealed in a hermetic container, was taken to thelaboratory of the Agricultural University of Cracow.The next step was to mix this sample again and takethree subsequent samples, placed in large paper enve-lopes. After determination of the biomass in fresh state(w), the envelopes were placed in a drier for 48 h withforced air circulation at 60�C. The air-dried sample was

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then divided into fractions: shoots, needles, and cones.On the basis of the ratio between wet and dry mass,calculated for particular samples, the total biomass ofshoots with needles and the biomass of the needles ofindividual trees (Fd) were calculated.

For each sample tree, a full analysis of the stem wasperformed. Stem sections were taken at the heights: 0.0,0.5, 1.3, 2.0, 4.0 m, and every 2 m up the stem to the topof the tree. On the basis of this analysis, tree charac-teristics, including age, volume (v), volume increment(Iv) and height increment (Ih), were determined. Thesection taken at 1.3 m was used to determine thediameter increment at breast height (Id) and the basalarea increment (Iba) per year. The data on the foliagebiomass and the values of the biometric characteristics

mentioned above were used to investigate the relation-ships between these variables. On the basis of thisanalysis a group of variables having a significant effecton the quantity of foliage biomass of Scots pine waschosen. These were used to establish the empiricalequation for estimating the foliage biomass of the treespecies. The relationships were modeled using the allo-metric equation (Sit and Poulin-Costello 1994) of ageneral form:

Y ¼ b0Xb11 X b2

2 � � �Xbkk þ e; ð1Þ

where Y is the dependent variable, X1, X2, ..., Xk theindependent variables, b0, b1, b2, ..., bk the equationparameters, k the number of independent variables, ande is the random error of normal distribution; additive

Fig. 1 Regular grid of 185monitoring plots of theFOREMMS project in theNiepolomice Forest, Poland

Table 1 Distribution of sample trees by diameter and height class

Height (m) Dbh (diameter at breast height cm) Total

6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48

6 1 2 38 1 110 1 112 1 114 5 1 1 716 1 118 1 1 220 3 1 1 522 1 1 2 3 1 824 4 4 1 4 2 3 2 2026 5 8 4 4 3 3 1 2828 4 2 8 3 2 2 2 1 2430 1 2 3 1 1 1 1 1032 1 134 1 1Total 1 2 1 1 6 2 3 3 6 7 5 9 15 10 14 11 6 5 3 1 1 1 113

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error was assumed for all equations, and this requiredfulfillment of the condition of homoscedasticity ofresiduals.

In general, in the analysis of allometric relations,residual heteroscedasticity occurs, consisting in an in-crease in the residual variance of the dependent variablewith an increase in the values of independent variable.To obtain the homoscedasticity of residuals, the equa-tion of the allometric function 1 was linearized byfinding the logarithm equation 2:

ln Y ¼ ln b0 þ b1 lnX1 þ b2 lnX2 þ � � � þ bk lnXk þ e ð2Þ

Logarithmic transformation of Eq. 1 allowed the ef-fect of increasing residual variance with the increase ofthe independent variable to be eliminated. However,using the logarithmic form of allometric equation pro-duces a systematic underestimation of the dependentvariable Y when converting the estimated lnY back totheoriginal untransformed scale Y (Zianis, Mencuccini2002). According to Baskerville (1972), an approxima-tion of the corrected estimate is

Yc ¼ eln b0þb1 lnX1þb2 lnX2þ���þbk lnXkþCF; ð3Þ

where CF is the correction factor equal SEE2/2, andSEE is the standard error of estimation:

SEE ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ðln Yi � ln YiÞ2

n� p

s

; ð4Þ

where n is the denote number of observations and p isthe denote number fitted parameters. Equation param-eters of linear models were estimated using the multipleregression technique with STATISTICA software(StatSoft Inc. 2004). Independent variables were selectedon the basis of the adjusted coefficient of determination (R2adj) Eq. 5 (Altman 1991; StatSoft Inc. 2004) and root

mean square error (RMSE) Eq. 6 (Temesgen and Ga-dow 2004).

R2adj ¼ 1� ð1� R2Þ n� 1

n� k � 1

� �

; ð5Þ

where R2 is the coefficient of determination, and n is thenumber of observations

RMSE ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

P

n

i¼1ðYi � YiÞ2

n� k � 1

v

u

u

u

t

: ð6Þ

Y i is the actual observation of the dependent variable,and Yi is the predicted value of the actual observation

Because a strong relationship between the indepen-dent variables, termed collinearity, causes the leastsquares regression coefficients to be unstable: coefficientstandard errors are large, reflecting the imprecision ofestimation of parameters, consequently confidenceintervals for the parameters are broad. The impact of

collinearity on the precision of estimation was capturedby variance inflation factor (VIF) (Fox 1991). VIF wascalculated according to

VIFj ¼1

1� R2j: ð7Þ

The distribution of residual values against valuespredicted according to the equations was graphicallyanalyzed (Fig. 2).

To find out whether growth conditions in the stand,determined on the basis of the forest site type, modifythe relationship between foliage biomass and the bio-metric characteristics of a tree, mixed linear models wereapplied.

Results

It was found that the foliage biomass of Scots pine ischaracterized by relatively high variation. The coefficientof variation for the biomass of the tree shoots withneedles and the biomass of tree needles was about 51%.The biomass of needles, as well as the biomass of freshshoots with needles, was correlated with most of the sizecharacteristics of trees (Table 2). The variation in thefoliage biomass of Scots pine was to a great extent ex-plained by variation in the basic size characteristics oftrees, such as dbh (D), height (H), length of crown (Lc),relative length of crown (Lcr), basal area increment(Iba3), and age (A) (Table 2). The biomass of shoots withneedles, as well as the biomass of needles alone, wascorrelated to the highest degree with tree dbh (Table 2).There was also high correlation of these characteristicswith basal area increment, height, and age of trees(Table 2). A significant correlation was not found be-tween dbh increment and the biomass of needles or thebiomass of shoots with needles (Table 3).

Biometric tree characteristics such as dbh, height,age, length, and width of crown, and annual basal areaincrement are related to one another, and their rela-tionship to foliage biomass may be indirect. To establishthe group of variables having a significant influence onthe quantity of foliage biomass, analysis of multipleregressions was used. This allowed six variables to beidentified as having a significant effect on foliage bio-mass: D, H, A, Lc, and Iba1. Because some of thesecharacteristic are strongly correlated together in finalequations only some were used.

All selected variables were used to create empiricalformulae based on the allometric equation 1. On thebasis of the value of adjusted coefficient of determina-tion and the value of RMSE it was found that thebiomass of shoots with needles, as well as needlesalone, is best described by equations where the crownlength (Lc), age (A), and annual basal area increment(Iba1) of a tree are the independent variables. On thebasis of these variables, equations for estimating thefresh biomass of shoots with needles (Fbw), biomass of

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shoots with needles in air-dry state (Fbd), fresh biomassof needles (Fw), and biomass of needles in air-dry state(Fd) were calculated (Table 4). These equations have thefollowing general form:

Bx ¼ b0 � Lb1c � Ab2 � Ib3

ba1� eCF þ e; ð8Þ

where Bx is the biomass of shoots with needles, needlesin wet or dry state.

As regards the basic statistics ( R2adj and RMSE),

equation in which the dbh and height are used instead ofage give similar results to Eq. 8. In case, when inequations two variables (D and H) were applied, therewas a problem of collinearity. The value of VIF wasequal 7.8. Thus for eliminating the question of collin-earity as independent variable product of D2 and H

(D2H) was applied. In this case, the equations were asfollows:

Bx ¼ b0 � Lb1cr � ðD2HÞb2 � Ibai3 � eCF þ e: ð9Þ

Because measuring tree basal area increment is time-consuming, variants of equations without this charac-teristic were also calculated. In this case it appears thatcrown length, tree height and dbh significantly affect thefoliage biomass quantity of Scots pine. With thesevariables, tree age is an insignificant variable for bothshoots with needles and needles alone. The final equa-tions were as follows:

Bx ¼ b0 � Lb1cr � ðD2HÞb2 � eCF þ e: ð10Þ

Fig. 2 Residuals (actual–predicted) against predicted dryfoliage biomass (for the dataconverted into logarithm) usingEqs. 8, 9, 10 and 11

Table 2 Values of the coefficient of linear correlation between tree size characteristics and the biomass of shoots with needles (Fb) andneedles (F) of Scots pine in wet (w) and dry (d) conditions (correlations calculated on the data transformed logarithmically)

Biomass fraction Biometric tree characteristics

Diameter atbreast height (D)

Height(H)

Crown length Five-year diameterat breast heightincrement (Id5)

Annual basalarea increment(Iba1)

Age

Actual (Lc) Relative (Lct)

Shoots with needles (Fbw) 0.84 0.74 0.52 �0.45 �0.13a 0.72 0.76Shoots with needles (Fbd) 0.86 0.76 0.52 �0.47 �0.18a 0.70 0.78Needles (Fw) 0.83 0.73 0.52 �0.44 �0.15a 0.70 0.75Needles (Fd) 0.85 0.75 0.52 �0.46 �0.18a 0.70 0.78

ainsignificant coefficients of correlation (a = 0.05)

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The RMSE and R2 in Eq. 5 indicate that biomassestimation using equations without the increment ofbasal area (Iba) result in considerably greater error thanequations using this characteristic (Table 4). Not takingthis variable into account in the model causes a reduc-tion in an explained variance fraction amounting to noless than 10% each time.

To facilitate the practical application of the formulae,equations with dbh as independent variables were alsocalculated:

Bx ¼ b0 � Db1 � eCF þ e: ð11Þ

To find out whether site conditions modify thedependence of foliage biomass quantity on the biometriccharacteristics of trees, mixed linear model was applied.The analysis were calculated for sites grouped accordingto soil nutrition (mixed coniferous forests: wet mixedconiferous forest and fresh mixed coniferous forest;mixed deciduous forests: wet mixed deciduous forest andfresh mixed deciduous forest) and according to moisture(fresh: fresh mixed coniferous forest and fresh mixeddeciduous forest; wet: wet mixed coniferous forest andwet mixed deciduous forest).

It was not found that site conditions modify thedependence of foliage biomass quantity on the biometric

characteristics of trees. Both the quantities variabledenoting soil nutrition (SN) and variable denoting sitemoisture (M) in mixed linear models 12, 13 were notsignificant (Table 5).

Bx ¼ b0 � Db1 � SNb2 ; ð12Þ

where SN denotes soil trophicnutrition.

Bx ¼ b0 � Db1 �Mb2 ; ð13Þ

where M denotes site moisture.

Discussion

Due to the large variation in the foliage biomass of Scotspine, even the use of a large number of independentvariables such as dbh, height, age, crown length, andbasal area increment does not fully ensure high estima-tion accuracy. Generally, in practice it is necessary toestimate foliage biomass for a larger number of trees,therefore it is not so important to estimate the biomassof single trees precisely, and it is much more importantnot to make systematic errors. This study showed that inaddition to typical biometric tree characteristics, such asdbh and height, knowledge about the increment of basal

Table 4 Parameters and basic statistics of Eqs. 8, 9, 10, and 11

Biomass fraction (Bx) No. equation Parameters of equation R R2 R2adj RMSE

b0 b1 b2 b3 CF

Shoots with needles (Fbw) 8 105.5014 0.30042 0.57551 0.70442 0.02796 0.925 0.855 0.851 0.23659 24.19228 0.32990 0.41251 0.56085 0.03160 0.914 0.836 0.831 0.251410 0.31265 0.56141 0.56605 – 0.05527 0.843 0.710 0.705 0.332511 0.59320 1.28942 – – 0.05608 0.841 0.707 0.705 0.3349

Shoots with needles (Fbd) 8 28.08155 0.30107 0.61862 0.65444 0.03011 0.920 0.847 0.843 0.24549 5.41727 0.33437 0.44105 0.49666 0.03316 0.912 0.831 0.827 0.257510 0.11516 0.53939 0.57701 – 0.05165 0.857 0.735 0.730 0.321411 0.21832 1.32899 – – 0.05186 0.857 0.735 0.733 0.3221

Needles (Fw) 8 57.27275 0.29897 0.54797 0.64245 0.03320 0.902 0.813 0.808 0.25779 13.50068 0.32870 0.39941 0.50207 0.03564 0.894 0.800 0.794 0.267010 0.27522 0.53596 0.53686 – 0.05452 0.831 0.691 0.685 0.330211 0.52300 1.21105 – – 0.05670 0.824 0.678 0.676 0.3367

Needles (Fd) 8 19.76039 0.27950 0.60056 0.63710 0.03131 0.913 0.833 0.829 0.25029 3.92627 0.31823 0.42627 0.48319 0.03398 0.905 0.819 0.814 0.260710 0.09266 0.51769 0.55855 – 0.05146 0.851 0.723 0.718 0.320811 0.17220 1.28785 – – 0.05185 0.850 0.723 0.720 0.3220

Table 3 Values of the coefficient of linear correlation between tree basal area increment (Iba) and foliage biomass of Scots pine (corre-lations calculated on the data transformed logarithmically)

Biomass fraction Basal area increment

One-year Two-year Three-year Four-year Five-year

Shoots with needles (Fbw) 0.68 0.68 0.66 0.64 0.64Shoots with needles (Fbd) 0.65 0.65 0.63 0.61 0.60Needles (Fw) 0.67 0.66 0.65 0.63 0.62Needles (Fd) 0.66 0.65 0.63 0.61 0.60

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area is very important. This increment may be the resultof interaction between the crown size and volumeincrement of a tree. Foliage biomass and its photosyn-thetic efficiency, in consideration of the site conditions,dictate the amount of assimilative substances producedby a tree, and thus affect the tree volume increment.

During this study, it was also found that tree age issignificantly associated with crown biomass. It can bestated with certainty that this is an indirect effect of thestrong correlation between tree age and tree dimensions.The biomass of the crown, in a similar way to other treeparts, increases with age. In comparison with dbh andheight, which are directly associated with tree size, thevariable ‘‘age’’ proved to be a better indicator of foliagebiomass.

On the basis of initial analyses, it is possible tohypothesize that there is no difference in the foliagebiomass of Scots pine trees growing in different siteconditions. However, similar studies should be per-formed to verify this hypothesis with more variable siteconditions than the Niepolomice Forest.

Conclusions

1. Biomass quantity is most closely connected with treedbh. Basal area increment, age, height and crownlength also explain the variability in the biomass ofScots pine needles to a great extent.

2. Using the biometric characteristics mentioned above,empirical equations for estimating the foliage bio-mass of Scots pine reasonably precisely have been

established. The proportion of variance explained bythe regression models depends on number of inde-pendent variables and varied between 65 and 85%.However, for single trees, the possibility of large er-rors exceeding 50%, should be taken into account.

3. The empirical equations created during this studymay be used for modeling and ecological studies forScots pine stands of Southern Poland. Before theycan be put to practical use on a larger scale, theyshould be verified on independent empirical materialoriginating from different areas of occurrence ofScots pine.

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Table 5 Parameters of mixed linear models Eqs. 12 and 13 to estimate the biomass of shoots with needles and needles with site groups asfixed effect (the influence and significance of fixed effect are described by value and probability level of the b2 parameter)

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Shoots with needles (Fbw) Moisture b0 �5.4385a 33.8227 -0.1608 0.8725b1 1.2876 0.0790 16.2951 0.0000b2 1.0660 7.3334 0.1454 0.8847

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Shoots with needles (Fbd) Moisture b0 13.6434a 32.4994 0.4198 0.6754b1 1.3347 0.0759 17.5788 0.0000b2 �3.2882a 7.0465 �0.4666 0.6417

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Needles (Fw) Moisture b0 �0.1071a 34.0125 �0.0031 0.9975b1 1.2113 0.0795 15.2435 0.0000b2 �0.1173a 7.3746 �0.0159 0.9873

Soil nutrition b0 12.5213a 35.3079 0.3546 0.7235b1 1.2181 0.0807 15.1027 0.0000b2 �2.8571a 7.6599 �0.3730 0.7098

Needles (Fd) Moisture b0 4.5020a 32.5220 0.1384 0.8901b1 1.2902 0.0760 16.9812 0.0000b2 �1.3576a 7.0514 �0.1925 0.8477

Soil nutrition b0 12.9342a 33.7586 0.3831 0.7023b1 1.2958 0.0771 16.8024 0.0000b2 �3.1877a 7.3237 �0.4353 0.6642

aParameters not significant at 0.05 significance level

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