DIGITALNA ARHIVA ŠUMARSKOG LISTA
prilagođeno pretraživanje po punom tekstu
ŠUMARSKI LIST 11-12/2009 str. 27 <-- 27 --> PDF |
IZVORNI I ZNANSTVENI ČLANCI – ORIGINAL SCIENTIFIC PAPERS Šumarski list br. 11–12, CXXXIII (2009), 589-603 UDK 630* 165 + 561 (001) DIAMETER STRUCTURE MODELS OF BLACK POPLAR SELECTED CLONES IN THE SECTION AIGEIROS (DUBY) OBTAINED BYTHE WEIBULLDISTRIBUTION MODELI DEBLJINSKE STRUKTURE SELEKCIONIRANIH KLONOVA CRNE TOPOLE SEKCIJE AIGEIROS (DUBY) DOBIVENI WEIBULL-OVOM DISTRIBUCIJOM 1 23 Siniša ANDRAŠEV, Martin BOBINAC, Saša ORLOVIĆ ABSTRACT: The present study was performed in an experimental plantation with six 20-year-old black poplar clones in the Section Aigeiros(Duby). The diameter structure models were constructed using the Weibull probability density distribution with three parameters based on periodical measurements of diameters at breast height. The unidentified parameters were calculated by the so-called “hybrid system” (Knoebel, et al, 1986): location parameter (a) was calculated by percentile method, scale parameter (b) and shape parameter (c) were calculated by moments method. The applied method of estimating the location parameter (a) showed that in 90.6 % of the study sample, the parameter “a” ranged between 50 and 90 %, and in 52.4 % of the sample, “a” ranged from 80 to 90 % of the minimal diameter. With higher plantation ages, location parameter (a) and scale parameter (b) also increased with small oscillations, which was confirmed by the significance of the correlation coefficient of 0.71 and 0.73 respectively. This was shown by the shift of the curve of diameter structure model to the right, towards larger diameters, and in a wider range of diameters at breast height with a lower relative frequency of the modal degree. In the initial period, F-ratio of all three parameters of diameter structure model decreased and reached the minimal value in the eighth year, and the predominantly increasing trend started in the twelfth year, which points to the changes in diameter structure of the study clones depending on the age. The plantation growth elements (dg, G) and the Kolmogorov-Smirnov test, as well as the analysis of variance test and LSD test for the percentage of the number of trees with diameters at breast height above 40 cm, confirmed the grouping of diameter structure models of the study poplar clones in two groups. This makes it possible to define the differentiated management procedures with individual groups. Key words:black poplar, clones, diameter structure, Weibull distribution. 1. INTRODUCTION – Uvod The main parameters which characterise poplar plan-bioecological and development-production characteritation production are: poplar clone (cultivar) and its stics, the site with its specificities, and the technologies of plantation establishment, tending and protection, inc 1 Dr. Siniša Andrašev, research associate, Institute of Lowland Forestry and Environment,Antona Čehova 13d, 21000 Novi Sad, luding also plantation density depending on the specific Serbia; E-mail: andrasev@uns.ac.rs purpose.All the above parameters are interdependent, 2 Dr. Martin Bobinac, assistant professor, University of Belgrade but the correct selection of poplar cultivar is of primary – Faculty of Forestry, Kneza Višeslava 1, 11030 Belgrade, importance for the optimal use of site potential. Serbia; E-mail: mbobinac@EUnet.rs 3 Dr. Saša Orlović, principal research fellow, Institute of Lowland Compared to natural ecosystems, poplar plantations Forestry and Environment,Antona Čehova 13d, 21000 Novi Sad, of selected new cultivars and clones ensure multiple Serbia; E-mail: sasao@uns.ac.rs |
ŠUMARSKI LIST 11-12/2009 str. 28 <-- 28 --> PDF |
S.Andrašev, M. Bobinac, S. Orlović: DIAMETER STRUCTURE MODELS OF BLACK POPLAR SELECTED ... Šumarski list br. 11–12, CXXXIII (2009), 589-603 increases in the dendromass quantity and value. By the establishment of intensive plantations after the Second World War in Serbia, in a relatively short period (20–25 years), annual poplar and willow felling volume increased 12 times, and by improving the assortment structure, the value of wood volume increased almost 20 times compared to the pre-war period (Marković, et al., 1995). However, plantation establishment with one clone over large areas soon resulted in susceptibility to pathogen and pest attacks. For this reason, one of the strategic directions of further poplar research was the continuing creation (selection) of new poplar clones and their putting to production. These processes were accompanied by the quantification of productivity at the designated sites and for the selected plantations management procedures. The quantification of differences between genotypes is usually defined by mean values of growth elements: diameter (d), height (h), and the derived elements, basal area (G), and volume (V).Also, the study of internal stand (plantation) structure makes it possible to analyse the state and to project the future development which leads to a more reliable identification of productivity differences. In this process, modern forest management planning applies the models of tree and stand (plantation) growth, based on real and testable data which also include the data on ecological conditions and growth characteristics of forest trees.The first step in the design of stand models is the model of diameter structure. Diameter structure modelling in even-aged stands (and plantations) applies theWeibull probability density function.The mathematical model of the function was defined by Weibull,(1951) in his study of the reliability of material hardness. It was introduced to forestry by Bailey andDell (1973) who constructed the model of stand diameter structure. Since then, theWeibull distribution has been widely implemented in forestry because it can describe a wide range of unimodal distributions and it can be adapted to both negative and positive skewness (Bailey and Dell, 1973; ......, 1984;Zarnoch andDell,1985;Knowe, et al., 1994;Kotar,2005). AccordingtoBailey andDell, (1973), ...... (1984), a special characteristic of Weibull distributionis the fact that its parameters have a biological interpretation. The significance of the Wei- bull distribution in the construction of diameter structure model in poplar plantations was reported by Andraševet al.(2003, 2004),Andrašev(2008). The objective of this study was to investigate the suitability of theWeibull distribution for the construction of diameter structure models of newly selectedpoplar clones, SectionAigeiros(Duby), by applying the so-called “hybrid system”of predicting the model parameters from the sample.Also, the objective was to study the change in model parameters depending on plantation age and poplar clone, and also their relation to plantation growth elements (dg ,G). 2. MATERIAL – Objekt istraživanja The research was performed in a 20-year-old test plantation consisting of several clones (cultivars) of black poplar in the SectionAigeiros(Duby). Theplantation is located on the experimental field of the Institute for Lowland Forestry and Environment (former Poplar Research Institute) near Novi Sad, planting space 5 × 5 m (400 trees per hectare), plant type 2+0. The plantation soil is fluvisol, sandy-loamy form (Škorić et al.,1985) and can be considered as medium suitable for poplar growing. The following poplar clones (cultivars) were researched: 1S (Populus deltoidesBartr. ex Marsh.) – cultivar 6-36 registered in Serbia in 1987; 2NS (Populus deltoidesBartr. ex Marsh.) – cultivar 1-3 registered in Serbia in 1998; 3NS (Populus × euramericana (Dode) Guinier) 11-8 × (Populus deltoidesBartr. ex Marsh.) – cultivar registered in Serbia in 1998; 3 Pannonia (Populus × euramericana (Dode) Guinier) – cultivar registered in Serbia in 1998; 5 PE 19/66 (Populus deltoidesBartr. ex Marsh.) – in selection procedure; 6S(Populus deltoidesBartr. ex Marsh.) – in selec 6-7 tion procedure. Each clone in the test plantation consisted of six rows, with 20–25 trees per row.The fringe rows were not included in measurement and processing, because of the mutual influences. From the aspect of the experiment, each row represents a replicate (altogether 4 replicates) for the statistical processing of the results. 3. METHOD – Metoda rada Diameters at breast height of all trees were periodically measured (to the nearest 1mm) after one, two, five, eight, twelve, seventeen and twenty years from the test plantation establishment. The number of trees in the plantation decreased over time due to different causes: after 20 years, minimum 85%of the initial num ber of trees remained in each row (replicate) (Table 1). Their diameters measured at the above ages were used for the construction of the diameter structure model.This was done to avoid the impact of changes in parameters due to the decrease in the number of trees.As the same trees were measured throughout the study period, the parameter changes in diameter structure models can mostly be assigned to the process of tree growth, i.e. to the specific |
ŠUMARSKI LIST 11-12/2009 str. 31 <-- 31 --> PDF |
S.Andrašev, M. Bobinac, S. Orlović: DIAMETER STRUCTURE MODELS OF BLACK POPLAR SELECTED ... Šumarski list br. 11–12, CXXXIII (2009), 589-603 The clones were differentiated by mean diameter in the fifth year after planting and it lasted to the end of the study period of 20 years. The clone differentiation per attained basal areas per hectare (G), which indicates indirectly the differences in volume per hectare, also, occurs in the fifth year and lasts through the eighth year (Table 3, Diagram 1b). At the age of 12, the values of basal area per hectare were 2 -1 very close for all six study clones (24.2–26.3 m·ha ) with F-ratio of the analysis of variance amounting to only 0.53.With the increasing plantation age, the differences between clones in basal areas per hectare incre ase and at the age of 20, the differences were significant at the risk level of 0.05. 2 -1 a)Stand quadratic mean diameter d(cm) b)Basal area per hectare, G (m·ha) g Srednji promjer po temeljnici dg(cm) Temeljnica po hektaru G (m2·ha-1) Diagram 1 Mean values of the stand quadratic mean diameter (dg) and total basal area per hectare (G) of the clones depending on plantation age. Grafikon 1. Srednje vrijednosti prsnog promjera po temeljnici (dg) i ukupne temeljnice po hektaru (G) istraživanih klonova u zavisnosti od starosti nasada Table 3 Basal area per hectare (G) and the results of the analysis of variance test and LSD test at the risk level of 0.05 for the clones per years of measurement. Tablica 3.Temeljnica po hektaru (G) ) i rezultati testa analize varijance i testa NZR na razini rizika od 0,05 istraživanih klonova po godinama izmjere. Clone Klon Plantation age after planting –Starost nasada nakon sadnje 1 year 1. god. 2 years 2. god. 5 years 5. god. 8 years 8. god. 12 years 12.god. 17 years 17. god. 20 years 20. god. Gg [m2 ·ha-1] S6-36 0.27(0.02) 1 bc 2 1.31 (0.11) a 9.10 (0.73) b 16.83(0.55) bc 24.34 (1.01) a 33.67(1.22)abc37.63 (1.42) bc NS1.3 0.32 (0.03) ab 1.24 (0.11) a 10.47 (0.99) a 18.69(2.32) ab 24.19 (3.17) a 31.56(4.32) bc 36.13 (5.42) bc NS11-8 0.24 (0.06) b 1.22 (0.17) a 9.35 (1.13) ab 18.12(1.65) ab 25.70 (2.40) a 35.10(2.90) ab 40.31 (2.92) ab Pannonia 0.27 (0.01) bc 1.33 (0.12) a 7.62 (0.69) c 15.67 (0.80) c 24.32 (1.15) a 34.23(1.62)abc38.29 (2.42) bc PE19/66 0.34 (0.06) a 1.48 (0.14) a 10.57 (0.12) a 19.12 (1.05) a 26.30 (1.64) a 37.09 (3.08) a 44.70 (4.36) a S6-7 0.28 (0.01) ab 1.46 (0.05) a 10.34 (1.32) ab17.99 (1.77) ab 24.61 (3.74) a 30.14 (4.09) c 34.32 (4.11) c F 2.15ns 1.85ns 5.54** 2.94* 0.53ns 2.59ns 3.85* 1 Values in parentheses represent the standard deviation –Vrijednosti u zagradi predstavljaju standardnu devijaciju. 2 The same letters indicate that there is no statistically significant differences between the clones tested by least significant differences at the risk level of 0.05 – Ista slova znače da ne postoje statistički značajne razlike između klonova po testu najmanje značajne razlike na razini rizika od 0,05. ns* ** non significant –nije signfikantno; significant at the risk level of 0,05 –signfikantno na razini rizika od 0,05; significant *** at the risk level of 0,01 –signfikantno na razini rizika od 0,01; significant at the risk level of 0,001 –signfikantno na razini rizika od 0,001. |
ŠUMARSKI LIST 11-12/2009 str. 29 <-- 29 --> PDF |
S.Andrašev, M. Bobinac, S. Orlović: DIAMETER STRUCTURE MODELS OF BLACK POPLAR SELECTED ... Šumarski list br. 11–12, CXXXIII (2009), 589-603 response to environmental conditions (primarily soil conditions and tree competition) of each genotype. The sample of trees used for the construction of the diameter structure model (total 168 samples) comprised the measured diameters at breast height (mean value of two cross measurements) in each row (4 repetition),for each clone (6 clones) and measurement year (7 years). Basal area, as the sum of basal areas of all trees, and the stand quadratic mean diameter were calculated for each tree samples. Table 1 Number of trees of studied clones by repetitions after planting and after 20 years. Tablica 1.Broj stabala istraživanih klonova po ponavljanjima pri osnivanju nasada i nakon 20 godina. Clone Klon Number of trees after planting per repetitions Broj stabala nakon sadnje po ponavljanjima Number of trees after 20 years per repetitions Broj stabala nakon 20 godina po ponavljanjima I II III IV I II III IV S 6-36 25 25 25 25 23 24 24 24 NS 1.3 22 22 22 22 21 20 21 20 NS 11-8 25 25 25 25 23 23 24 23 Pannonia 25 25 25 25 22 24 22 24 PE19/66 20 20 20 20 19 17 19 19 S 6-7 25 25 25 25 24 23 22 23 The selected model was the Weibull distribution with three parameters.The mathematical model of the Weibull distribution is defined as follows: (1) where:a– location parameter;b– scale parameter; c – shape parameter. The mathematical model of the Weibull cumulative distribution is expressed as: (2) Location parameter (a) defines the location distribution in the coordinate system, i.e. its distribution along the abscissa. Scale parameter (b) is equal to 63% of the distribution of unknown value (x) in the increasing order, i.e. about 63%of the trees have diameter at breast height lower than the sum of parameters “a”and “b”. Shape parameter (c) defines the distribution skewness: forc<1 the distribution decreases, and forc>1 it has bell shape. In the interval 1 and for c=3.6 it approximates the normal probability density function (PDF). If the location parameter (a) is equal to zero the mathematical model turns into the so-called two-parameter model of theWeibull distribution, defined by the expression: The parameters of the Weibull probability density function can be estimated in several ways (from sample trees), depending on the desired estimation of two (b, c) or all three parameters (a,b,c).The unidentified parameters of the Weibull distribution were estimated using the so-called “hybrid system”, i.e. the method of moments estimation in combination with the percentile method (Knoebel, et al, 1986). Location parameter (a)in diameter structure modelling is directly related to minimal diameter and can vary from 0 (zero) todmin. So the parameter “a” was calculated by the percentile method, with the following percentiles of the minimal diameter: 0.00; 0.01; 0.05; 0.10; 0.15; 0.20; 0.25; 0.30; 0.35; 0.40; 0.45; 0.50; 0.55; 0.60; 0.65; 0.70; 0.75; 0.80; 0.85; 0.90; 0.95; 0.99; 1.00. Scale parameter (b) and shape parameter (c) were estimated by the moments method.They were estimated by subtracting the measured values (diameters at breast height) from the previously defined parameter “a”.This method is based on the following equations – - 2 of the first (x) and the second (x) common moment of theWeibull two-parameter distribution: (5) (6) where.(·) – gamma function. The assessed variance () of theWeibull distribution is expressed as: (3) (7) and the coefficient of variation (): and the cumulative model: (8) (4) |
ŠUMARSKI LIST 11-12/2009 str. 30 <-- 30 --> PDF |
S.Andrašev, M. Bobinac, S. Orlović: DIAMETER STRUCTURE MODELS OF BLACK POPLAR SELECTED ... Šumarski list br. 11–12, CXXXIII (2009), 589-603 By calculating the first and the second common mo-The percentiles of minimal diameter were selected 2 ment, and also the coefficient of variation from the sample and by inserting in formula 8, the coefficient of variation is the function of only one parameter (c), so it can be estimated by an iteration procedure.The combination of secant method and bisection method was ap -6 plied with the previously set precision of 10 (Conte and deBoor,1980). The value of parameter “c” was applied to obtain the value of parameter “b”in the relation: (9) Parameter “a”was calculated for each of the above percentiles in each replicate and the parameters “b”and “c”by the moments method.Then the empirical diameter structure and the model were compared usingAnder 2 son-Darling statistic (A) (Anderson andDar ling, 1954): (10) where:F(x)– cumulative model of diameter structure; n– number of samples. based on the minimal value ofA statistic in all 4 replicates within the same clone and plantation age. For each of the selected percentiles of minimal diameter within each clone and plantation age, all three parameters of theWeibull distribution were re-estimated for each replicate. The diameter structure model and the empirical distribution were tested by non-parametric Kolmogorov-Smirnov test, using |D| statistics: (11) where:F1(x)– cumulative model of diameter structure; F2(x)– empirical cumulative diameter structure in the increasing order. The obtained parameters of theWeibull distribution per individual replicates were applied in the assessment of differences between the study clones at certain ages (years after planting), using the analysis of variance test and the least significant difference test (LSD), at the 5%risk level. Finding the value of the unknown parameters of the model ofWeibull diameter distribution, by the above method, was performed programming inVisual Basic, which is an integral part of the Excel package. For a statistical assessment STATISTICA, ver. 7.0 software package was used. 4. RESULTS – Rezultati istraživanja 4.1. Growth elements of the study clone plantations – Elementi rasta nasada istraživanih klonova The clones attained close stand quadratic mean dia-quence of the uniform dimensions of the applied plan- meters (dg) only in the first and the second years after ting material, and also of the low increment, especially planting (Table 2, Diagram 1a), which is the conse-in the first year after planting (Andrašev etal. 2006). Table 2 Stand quadratic mean diameter (d) and the results of the analysis of variance test and LSD test at the risk level of g 0.05for the clones per years of measurement. Tablica 2.Srednji promjer po temeljnici (dg) i rezultati testa analize varijance i testa NZR na razini rizika od 0,05 istraživanih klonova po godinama izmjere Clone Klon Plantation age after planting -Starost nasada nakon sadnje 1 year 1. god. 2 years 2. god. 5 years 5. god. 8 years 8. god. 12 years 12.god. 17 years 17. god. 20 years 20. god. dg [cm] S 6-36 2.9 (0.06) 1 ab 2 6.5 (0.16)ab 17.2 (0.57)c 23.4 (0.48)cd 28.1 (0.39)b 33.1 (0.88)bc 35.0 (1.03)bc NS 1.3 3.3 (0.08)a 6.5 (0.14)ab 18.7 (0.79)ab 24.9 (1.11)b 28.5 (1.49)b 32.4 (1.77)bc 34.6 (2.16)bc NS 11-8 2.8 (0.24)b 6.2 (0.36)b 17.7 (1.09)bc 24.7 (0.90)b 29.4 (1.14)ab 34.4 (1.25)b 36.8 (1.20)b Pannonia 3.0 (0.16)ab 6.5 (0.22)ab 15.9 (0.50)d 22.8 (0.15)d 28.4 (0.37)b 33.7 (0.89)b 35.6 (1.31)bc PE19/66 3.3 (0.13)a 6.9 (0.24)a 19.0 (0.56)a 26.4 (0.61)a 31.0 (1.05)a 36.7 (1.37)a 40.3 (1.79)a S 6-7 3.0 (0.09)ab 6.8 (0.20)ab 18.4 (0.87)ab 24.2 (0.89)bc 28.2 (1.80)b 31.3 (1.83)c 33.7 (2.05)c F 2.29 ns 1.93 ns 10.73 *** 11.93 *** 3.68 * 7.65 *** 8.06 *** 1 Values in parentheses represent the standard deviation –Vrijednosti u zagradi predstavljaju standardnu devijaciju. 2 The same letters indicate that there is no statistically significant differences between the clones tested by least significant differences at the risk level of 0.05 – Ista slova znače da ne postoje statistički značajne razlike između klonova po testu najmanje značajne razlike na razini rizika od 0,05. ns* ** non significant –nije signfikantno; significant at the risk level of 0,05 –signfikantno na razini rizika od 0,05; significant *** at the risk level of 0,01 –signfikantno na razini rizika od 0,01; significant at the risk level of 0,001 –signfikantno na razini rizika od 0,001. |
ŠUMARSKI LIST 11-12/2009 str. 32 <-- 32 --> PDF |
S.Andrašev, M. Bobinac, S. Orlović: DIAMETER STRUCTURE MODELS OF BLACK POPLAR SELECTED ... Šumarski list br. 11–12, CXXXIII (2009), 589-603 Test results of the analysis of variance of repeated measurements showed a high (G) and very high (dg) significant interactions clone×year which indicates that the investigated clones had different increments of the quadratic mean diameterand total basal area per hectare in the study period (Table 4, Diagram 1). Throughout the period of 20 years, the clone PE 19/66 attained the best results both in stand quadratic mean diameter (dg), and in total basal area per hectare (G) and it is differentiated from the other clones by LSD test at the 5%risk level. Clone Pannonia attained the lowest sizes of the stand quadratic mean diameter and the total basal area per hectare in the period to the eighth year. In further development, its increment was more intensive compared to other clones and at the age of 20 years, its mean diameter and total basal area per hectare were greater compared to the clones S , NS and S . 6-7 1-3 6-36 The growth of clone NS was also more intensive 11-8 with the increased age. Table 4 Test results of the analysis of variance of repeated measurements ofthe quadratic mean diameter and total basal area per hectare. Tablica 4.Rezultati testa analize varijance ponovljenih mjerenja srednjeg promjera po temeljnici i ukupne temeljnice po hektaru. Sum of Square Degr. of Freed. Mean Square F p Stand quadratic mean diameter - d g [cm]– Srednji promjer po temeljnici - dg[cm] Intercept 77431.36 1 77431.36 17478.1 0 Clone 147.31 5 29.46 6.65 0.00114 Error 79.74 18 4.43 Year 23945.81 6 3990.97 8612.37 0 Clone ×Year 120.13 30 4.00 8.64 0 Error 50.05 108 0.46 Basal area per hectare – G [m 2 ·ha -1 ]– Temeljnica po hektaru – G [m2·ha-1] Intercept 50759.86 1 50759.86 1461.36 0 Clone 134.79 5 26.96 0.77614 0.57951 Error 625.22 18 34.73 Year 30971.14 6 5161.86 1267.97 0 Clone ×Year 240.87 30 8.03 1.97228 0.00602 Error 439.66 108 4.07 4.2. Diameter structure models obtained by the weibull distribution Modeli debljinske strukture dobiveni weibull-ovom distribucijom 4.2.1. Location parameters (a) of the Weibull diameter structure model Definiranje parametara položaja (a) modela Weibull-ove debljinske strukture Table 5 presents the percentile minimum diameter son-Darling statistics of studied clones in certain years of with a minimum value of Anderson-Darling statistics surveying. Diagram 2 shows the percentage of the per 2 (A), and mean values and standard deviations ofAnder-centiles of minimal diameter for the definition of location 2 Table 5 Percentile values of the minimum diameter (%d ) that have the least value ofAnderson-Darling (A) statistic of min examined clones by years of survey. Tablica 5.Vrijednost percentila minimalnog promjera (%dmin) koji imaju najmanju vrijednost Anderson-Darling statistikue (A2) istraživanih klonova po godinama izmjere. Clone Klon %d min A 2 1 Age of the plantation after planting Starost nasada nakon sadnje Age of the plantation after planting Starost nasada nakon sadnje 1. 2. 5. 8. 12. 17. 20. 1. 2. 5. 8. 12. 17. 20. S 6-36 0.85 0.90 0.85 0.85 0.90 0.90 0.90 0.33(0,15) 2 0.60 (0,06)0.66 (0,21) 0.67 (0,12) 0.49 (0,29) 0.28 (0,10) 0.31 (0,16) NS 1.3 0.90 0.90 0.85 0.75 0.65 0.65 0.55 0.36 (0,17) 0.26 (0,03)0.71 (0,26) 0.46 (0,23) 0.59 (0,21) 0.37 (0,17) 0.51 (0,39) NS 11-8 0.60 0.55 0.75 0.80 0.80 0.85 0.85 0.71 (0,25) 0.43 (0,27)0.51 (0,10) 0.46 (0,11) 0.43 (0,19) 0.45 (0,10) 0.38 (0,04) Pannonia 0.10 0.45 0.70 0.85 0.90 0.80 0.75 0.56 (0,28) 0.50 (0,26)0.43 (0,14) 0.56 (0,27) 0.59 (0,31) 0.20 (0,03) 0.21 (0,03) PE19/66 0.80 0.70 0.90 0.90 0.90 0.70 0.60 0.23 (0,06) 0.36 (0,04)0.60 (0,21) 0.39 (0,27) 0.36 (0,13) 0.36 (0,09) 0.28 (0,08) S 6-7 0.45 0,70 0.95 0.80 0.75 0.60 0.60 0.23 (0,06) 0.29 (0,01) 0.55 (0,11) 0.57 (0,29) 0.55 (0,37) 0.55 (0,41) 0.40 (0,24) 1 mean values ofAnderson-Darling statistic– srednje vrijednosti Anderson-Darling statistike. 2 Values in parentheses represent the standard deviation –Vrijednosti u zagradi predstavljaju standardnu devijaciju. 594 |
ŠUMARSKI LIST 11-12/2009 str. 33 <-- 33 --> PDF |
ns 4.2.2. Comparison of parameters of diameter structure model between clones Usporedba parametara modela debljinske strukture između klonova Depending on plantation age, the results of the analy-structure model showed the decreasing trend and the misis of variance test showed mostly significant differen-nimal value occurred in the eighth year, and the predoces between the parameters of Weibull diameter minantly increasing trend started in the twelfth year. In structure model (Tables 6, 7 and 8). In the initial period, the eighth year, there were no significant differences F-ratio of all three parameters of theWeibull diameter between parameter “c”of the diameter structure mo del, Table 6 Mean values of location parameter (a) of theWeibull diameter structure model and the results of the analysis of variance test and LSD test at the risk level of 0.05 of study clones per years of measurement. Tablica 6.Srednje vrijednosti parametra položaja (a) modela Weibull-ove distribucije prsnih promjera i rezultati testa analize varijance i testa NZR na razini rizika od 0,05 istraživanih klonova po godinama izmjere. Clone Klon Plantation age after planting -Starost nasada nakon sadnje 1 year 1. god. 2 years 2. god. 5 years 5. god. 8 years 8. god. 12 years 12.god. 17 years 17. god. 20 years 20. god. S6-36 1,67 (0.09) 1 b 2 4,65 (0.30) a 12,75 (0.69) b 17,42 (0.85) b 22,72 (0.86) a 26,56 (0.98) a 27,98 (1.12) a NS1.3 2,23 (0.20) a 4,81 (0.43) a 13,18 (1.77) b 15,19 (2.48) c 14,62 (2.88) c 15,71 (2.36) c 13,9 (1.98) e NS11-8 0,91 (0.18) c 2,54 (0.20) d 10,88 (0.75) c 16,4 (1.39) bc 18,4 (2.69) b 23,18 (3.74) b 24,63 (4.09) b Pannonia 0,16 (0.01) d 2,10 (0.12) e 9,1 (0.57) d 17 (0.00) bc 22,5 (1.27) a 23,08 (1.31) b 22,29 (1.41) bc PE19/66 2,09 (0.02) a 4,05 (0.15) b 15,98 (0.45) a 20,92 (0.45) a 24,75 (0.52) a 21,08 (0.76) b 19,59 (0.73) cd S6-7 0,76 (0.05) c 3,46 (0.36) c 15,2 (1.10) a 16,6 (1.20) bc 17,62 (2.33) b 15,34 (2.17) c 16,41 (2.43) de F 190.29*** 61.1*** 27.11*** 8.75*** 14.88*** 17.45*** 21.66*** 1 Values in parentheses represent the standard deviation– Vrijednosti u zagradi predstavljaju standardnu devijaciju. 2 The same letters indicate that there is no statistically significant differences between the clones tested by least significant differences at the risk level of 0.05– Ista slova znače da ne postoje statistički značajne razlike između klonova po testu najmanje značajne razlike na razini rizika od 0,05. nsnon significant –nije signfikantno; * significant at the risk level of 0,05 –signifikantno na razini rizika od 0,05; ** significant at the risk level of 0,01 –signfikantno na razini rizika od 0,01; *** significant at the risk level of 0,001 – signifikantno na razini rizika od 0,001. |
ŠUMARSKI LIST 11-12/2009 str. 34 <-- 34 --> PDF |
S.Andrašev, M. Bobinac, S. Orlović: DIAMETER STRUCTURE MODELS OF BLACK POPLAR SELECTED ... Šumarski list br. 11–12, CXXXIII (2009), 589-603 which points out the changes in diameter structure of the study clones depending on the age. With higher plantation ages, location parameter (a) and scale parameter (b) also increased with small oscillations, which was confirmed by the significance of the correlation coefficient of 0.71 and 0.73 respectively (Diagram 3).This was shown by the shift of the curve of diameter structure model to the right, towards larger diameters, and in a wider range of diameters at breast height with a lower relative frequency of the modal degree (Diagram 4).The changes in shape parameter (c) were smaller, which was confirmed by the correlation coefficient of 0.36 (Diagram 3). However, its significance at the risk level of 0.001 indicates the increasing trend with plantation age, i.e. the change in the shape of diameter structure positive skewness, or approximately normal distribution, to the negative skewness. Table 7 Mean values of scale parameter (b) of theWeibull diameter structure model and the results of the analysis of variance test and LSD test at the risk level of 0.05 of study clones per years of measurement. Tablica 7.Srednje vrijednosti parametra skaliranja (b) modela Weibull-ove distribucije prsnih promjera i rezultati testa analize varijance i testa NZR na razini rizika od 0,05 istraživanih klonova po godinama izmjere. Clone Klon Plantation age after planting –Starost nasada nakon sadnje 1 year 1. god. 2 years 2. god. 5 years 5. god. 8 years 8. god. 12 years 12.god. 17 years 17. god. 20 years 20. god. S6-36 1,37 (0.18) 1 c 2 1,96 (0.48) c 4,83 (0.61) bc 6,46 (0.53) c 5,93 (0.56) c 7,11 (0.18) c 7,64 (0.16) d NS1.3 1,16 (0.27) c 1,87 (0.41) c 5,99 (1.74) ab 10,51 (1.76) a 14,87 (1.59) a 17,9 (0.96) a 22,22 (0.57) a NS11-8 1,94 (0.08) b 3,89 (0.22) ab 7,38 (0.83) a 8,94 (0.88) b 11,88 (1.99) b 12,13 (2.97) b 13,27 (3.46) c Pannonia 2,76 (0.24) a 4,42 (0.29) a 7,3 (0.59) a 6,33 (0.14) c 6,49 (1.36) c 11,43 (1.57) b 14,36 (1.96) c PE19/66 1,46 (0.24) c 3,25 (0.57) b 3,59 (0.58) c 5,99 (1.11) c 6,81 (1.47) c 16,76 (2.09) a 22,04 (2.59) a S6-7 2,5 (0.32) a 3,99 (0.59) a 3,42 (0.82) c 8,18 (0.61) b 11,41 (1.11) b 16,94 (1.04) a 18,34 (1.21) b F 30.65*** 23.56*** 13.51*** 13.31*** 26.83*** 23.97*** 31.58*** 1 Values in parentheses represent the standard deviation – Vrijednosti u zagradi predstavljaju standardnu devijaciju. 2 The same letters indicate that there is no statistically significant differences between the clones tested by least significant differences at the risk level of 0.05 – Ista slova znače da ne postoje statistički značajne razlike između klonova po testu najmanje značajne razlike na razini rizika od 0,05. nsnon significant –nije signifikantno; * significant at the risk level of 0,05 –signifikantno na razini rizika od 0,05; ** significant at the risk level of 0,01 –signifikantno na razini rizika od 0,01; *** significant at the risk level of 0,001 –signfikantno na razini rizika od 0,001. Table 8 Mean values of shape parameter (c) of the Weibull diameter structure model and the results of the analysis of variance test and LSD test at the risk level of 0.05 of study clones per years of measurement. Tablica8.Srednje vrijednosti parametra oblika (c) modelaWeibull-ove distribucije prsnih promjera i rezultati testa analize varijance i testa NZR na razini rizika od 0,05 istraživanih klonova po godinama izmjere. Clone Klon Plantation age after planting –Starost nasada nakon sadnje 1 year 1. god. 2 years 2. god. 5 years 5. god. 8 years 8. god. 12 years 12.god. 17 years 17. god. 20 years 20. god. S6-36 2,235(0.20)1 b2 2,044 (0.27) b3,714(0.59)abc 4,373 (1.37) a 2,971 (0.45) c 3,618 (0.86) b 3,519 (0.81) b NS1.3 2,084 (0.57) b 2,513 (0.68) b 4,146(1.39) ab 4,963 (1.06) a 5,398 (1.09) a 5,131 (1.57) b 5,123(0.99) ab NS11-8 3,099 (0.95) b 4,451 (1.03) a 4,831(1.16) ab 4,74 (1.56) a 4,415(1.18) ab 3,556 (0.80) b 3,493 (0.64) b Pannonia 5,378 (1.90) a 5,133 (0.93) a 5,04 (0.98) a 4,077 (0.46) a 3,425(0.70) bc 5,539(1.44) ab 5,712(1.42) ab PE19/66 2,95 (0.40) b 4,961 (0.58) a 3,53 (0.59) bc 3,372 (0.19) a 3,228(0.30) bc 5,618(0.70) ab 6,563 (1.07) a S6-7 4,677 (1.00) a 4,175 (0.89) a 2,378 (0.79) c 4,949 (1.30) a 5,69 (1.46) a 7,986 (3.86) a 7,287 (3.09) a F 7.12*** 11.23*** 4.08* 1.23ns 5.88** 2.98* 3.96* 1 Values in parentheses represent the standard deviation – Vrijednosti u zagradi predstavljaju standardnu devijaciju. 2 The same letters indicate that there is no statistically significant differences between the clones tested by least significant differences at the risk level of 0.05 – Ista slova znače da ne postoje statistički značajne razlike između klonova po testu najmanje značajne razlike na razini rizika od 0,05. nsnon significant –nije signifikantno; * significant at the risk level of 0,05 –signifikantno na razini rizika od 0,05; **significant at the risk level of 0,01 –signifikantno na razini rizika od 0,01; *** significant at the risk level of 0,001 – signifikantno na razini rizika od 0,001. The differences between the parameters of the Wei-gnificant difference test at the 5%risk level grouped bull diameter structure model of poplar clones per the study clones in several groups. years of measurement were significant, and the least si |
ŠUMARSKI LIST 11-12/2009 str. 35 <-- 35 --> PDF |
S.Andrašev, M. Bobinac, S. Orlović: DIAMETER STRUCTURE MODELS OF BLACK POPLAR SELECTED ... Šumarski list br. 11–12, CXXXIII (2009), 589-603 Plantation age affects the trend of parameters of the diameter structure model. In the initial period of plantation development (five years) there was a sharp increase in the location parameter (a), after which its trend changed depending on the clone. In the initial period, the increase in the scale parameter (b) of theWei- bull diameter structure model was lower and also the differences between the clones were lower. The increase in parameter “b” in the following period was considerably greater in the majority of the clones, but the clone S showed the trend of a very slow increase. 6-36 The differences between the study clones were the lowest in the shape parameter (c). Diagram 3 Changes in the mean values of the parameters of the Weibull diameter structure model depending on plantation age. Grafikon 3. Promjena srednjih veličina parametara modela debljinske strukture po Weibull-u u zavisnosti od starosti nasada 4.2.3. Construction of the Weibull diameter structure model Konstrukcija modela debljinske strukture po Weibull-ovoj distribuciji Diagram 4 presents the models of diameter structu-Aiming at the objective assessment of similarities res of the study clones per years.The Diagram shows and differences between the Weibull diameter structure the changes in the shape of diameter structure with models of poplar clones, the non-parametric Kolmogoadvancing age, as well as the differences between the rov-Smirnov test was applied at the plantation age of clones. It can be concluded that some clones had simi-17 and 20 years (Table 9). The test results showed silar models of diameter structure, especially in the pe-gnificant differences only between diameter structure riod after the age of 12, which indicates the possibility models of the clone PE 19/66 and the clones S , NS , 6-7 1-3 th of their grouping in the definition of management pro- S in the 17 year, and between the clone PE 19/66 6-36 th 6-7 1-3 6-36 cedures. and clones S , NS , S and Pannonia in the 20 year. Table 9 Value of |D| statistics by Kolmogorov-Smirnov test and the comparison of differences in the Weibull diameter th th structure models in the 17 and 20 year of poplar plantation age. Tablica 9.Vrijednosti |D| statistike po testu Kolmogorov-Smirnova i usporedba razlika modela debljinskih struktura po modelu Weibull-a u 17. i 20. godini starosti nasada istraživanih klonova topola. Clone –Klon 20 years –20. godina S 6-36 NS 1-3 NS 11-8 Pannonia PE 19/66 S 6-7 17 years S 6-36 -0.2039 ns 0.28 ns 0.1454 ns 0.6623 ** 0.18 ns NS 1-3 0.1993 ns -0.1925 ns 0.195 ns 0.5266 ** 0.1941 ns NS 11-8 0.2626 ns 0.1963 ns -0.1718 ns 0.3923 ns 0.35 ns 17. godina Pannonia 0.1771 ns 0.24 ns 0.1529 ns -0.5641 ** 0.2641 ns * * ns ns *** PE 19/66 0.5758 0.4972 0.3131 0.4661 -0.7144 S 6-7 0.2525 ns 0.1988 ns 0.3939 ns 0.3875 ns 0.6869 *** - nsnon significant– nije signifikantno; *significant at the risk level of 0,05– signifikantno na razini rizika od 0,05; **significant at the risk level of 0,01– signifikantno na razini rizika od 0,01; ***significant at the risk level of 0,001 –signifikantno na razini rizika od 0,001. |
ŠUMARSKI LIST 11-12/2009 str. 36 <-- 36 --> PDF |
S.Andrašev, M. Bobinac, S. Orlović: DIAMETER STRUCTURE MODELS OF BLACK POPLAR SELECTED ... Šumarski list br. 11–12, CXXXIII (2009), 589-603 Diagram 4 Models of diameter structure of the study clones depending on plantation age. Grafikon 4. Modeli debljinske strukture istraživanih klonova u zavisnosti od starosti nasada. Table 10 Mean values of the percentage of the number of trees with diameters at breast height above 40 cm (N [%]) d>40cm and the results of the analysis of variance test and LSD test at the 5%risk level. Tablica 10.Srednje vrijednosti učešća broja stabala prsnih promjera većih od 40 cm (Nd>40cm[%]) i rezultati testa analize varijance i testa NZR na razini rizika od 5%. Age Clone –Klon S 6-36 NS 1-3 NS 11-8 Pannonia PE 19/66 S 6-7 F 1 Starost Nd>40cm [%] 17 years 0.0 c 2 1.4 bc 4.4 ab 0.4 bc 13.3 a 0.0 c 5.31 ** 20 years 1.0 d 11.3 bc 19.1 b 4.5 cd 50.0 a 0.8 d 12.1 *** 1 The comparison was preceded by the transformation arcsin aiming at the homogenisation of the variances (%Nd>40cm)1 –Usporedba je izvršena uz prethodnu transformaciju arcsin (%Nd>40cm)1u cilju homogenizacije varijanci. 2 The same letters indicate that there is no statistically significant differences between the clones tested by least significant differences at the risk level of 0.05 – Ista slova znače da ne postoje statistički značajne razlike između klonova po testu naj manje značajne razlike na razini rizika od 0,05. ns* ** non significant –nije signifikantno; significant at the risk level of 0,05 –signifikantno na razini rizika od 0,05; signifi *** cant at the risk level of 0,01 –signifikantno na razini rizika od 0,01; significant at the risk level of 0,001 –signifikantno na razini rizika od 0,001. |
ŠUMARSKI LIST 11-12/2009 str. 37 <-- 37 --> PDF |
S.Andrašev, M. Bobinac, S. Orlović: DIAMETER STRUCTURE MODELS OF BLACK POPLAR SELECTED ... Šumarski list br. 11–12, CXXXIII (2009), 589-603 The practical significance of the obtained models is best seen by the example of estimating the percentage of the number of trees with diameters at breast height above 40 cm.The diameter at breast height above 40 cm makes it possible to produce the best quality veneer logs (Pudar, 1986; Krznar,1987), so the share of such trees indicates indirectly the plantation value. Table 10 presents the mean relative percentage of the number of trees with diameters at breast height above 40 cm from the diameter structure model and the results of the analysis of variance test and LSD test at the 0.05 risk level.The analysis of variance points out the signi th ficant differences between the clones, both in the 17 th and in the 20 year. Significantly the highest percentage of the number of trees with diameters at breast height above 40 cm was attained by the clone PE 19/66, and the lowest percentage by the clones S and S . 6-7 6-36 5. DISCUSSION – Rasprava The researched plantation of six newly selected clones showed different values of stand quadratic mean diameter (dg) and total basal area per hectare (G) at the end of the study period (20 years). Based on the results of LSD test at the 5%risk level, the clones were grouped in several production groups.Also, the periodical measurements of diameter at breast height showed different diameter growth of the clones depending on the age. In the initial period, the clonesPopulus deltoides Bartr. ex Marsh. (S , NS , PE 19/66, NS , S ) developed more intensively than the clone Pannonia (Populus × euramericana (Dode) Guinier). In the later period, Pannonia developed more intensively and the clones ofP.deltoidesBartr. ex Marsh. showed the differentiation. The different growth characteristics of the clonesP.deltoidesBartr. ex Marsh. and P.×euramericana( Dode) Guinier, prevent the reliable productivity differentiation of the clones before the ages of 16–18 years at plantation density of 400 trees per hectare (Andrašev, 2008). Taking into account the above facts, the differentiation of study poplar clones by total basal area per hectare (G) and stand quadratic mean diameter (dg) at the ages of 17 and 20 years showed (LSD test) that clone PE 19/66 can be classified in one group, and the other clones in the other group. The constructed Weibull models of diameter structure, and the derived percentage of the number trees with diameters at breast height above 40 cm (Nd>40cm [%]) confirmed thegrouping of the clones in two groups, as well as based on growth elements (G,dg), which point out their implementation in productive differentiation. The study results refer to six black poplar clones, SectionAigeiros(Duby), four of which were registered as cultivars in Serbia, and the other two are still undergoing the selection procedure.The registered poplar clones (S , NS , NS and Pannonia) attained similar 6-7 1-3 11-8 6-36 6-36 1-3 11-8 plantation growth elements (dg ,G), and diameter structure, which was confirmed by statistical tests.The other two clones which were in selection procedure (S and 6-7 PE 19/66) attained significant differences in growth elements and plantation structure.Clone S did not have 6-7 significantly lower values of growth elements and structure compared to registered clones. However, clone PE 19/66 attained a significant advantage in the elements of growth and structure compared to the registered clones at the plantation age of 20 years, which, according toMarkovićet al.(1997) andAndrašev (2008), can be taken as the rotation period for the density of 400 trees per hectare, so this clone is a reliable candidate for a soon registration and putting in mass production. The study results indicate that theWeibull diameter structure model can be successfully applied in the estimation of diameter structure of the newly selected poplar clones at different plantation ages. The application of the model of theWeibull three- parameter distribution, especially the calculation of the location parameter (a), was made difficult and it was evaluated in different ways: using different mathematical expressions (Zarnoch andDell,1985), fixed values of location parameter 0 or d , the percentiles of min minimal diameter, with frequent value 50%·d (Bai min ley and Dell, 1973, Knoebel, et al, 1986, Lei, 2008). Our research indicates that the choice of location parameter (a) inWeibull distribution should not be uniformly defined, and that further research is necessary aiming at reliable methods of diameter structure modelling in poplar plantations. Taking into account the so-called “biological”interpretation of the calculated parameters, it can be concluded that location parameter (a) is the minimal diameter in the plantation (but not also in the sample based on which it is predicted). In most clones, location parameters depending on the age show an increasing trend; in the initial period the trend is sharp (till the age of 5), and later on it is slower or more intensive, depending on the clone.The above can be related to the so-called “solitary growth”in the initial period before crown closure (from fifth to eighth year) and the so-called “stand growth”with the competitive impact of trees.The observed significant drop of location parameter (a) in the clone PE 19/66 is the consequence of the applied method and it shows that in periodical measurements the so-called “biological component”should be “incorporated” in its definition. The scale parameter (b) is in high correlation (R=0.884) with the variability of diameters at breast |
ŠUMARSKI LIST 11-12/2009 str. 38 <-- 38 --> PDF |
S.Andrašev, M. Bobinac, S. Orlović: DIAMETER STRUCTURE MODELS OF BLACK POPLAR SELECTED ... Šumarski list br. 11–12, CXXXIII (2009), 589-603 height, represented by standard deviation (sd). Its change depending on plantation age, with a high value of the correlation coefficient (R=0.74), points to the differentiation process of the trees in the plantation. The parameters of the Weibull diameter structure model (a,b,c) of the study poplar clones, according to the analysis of variance F-ratio, decrease till the age of 8, and then they increase.Asimilar F-ratio trend was shown by the stand quadratic mean diameter (dg) and total basal area per hectare (G), with the minimal F- ratio at the age of 12.As the parameters describe the internal plantation structure, the earlier change in parameters compared to growth elements indicates the growth changes in the trees of different categories (diameters), which enables the adequate evaluation of the plantation state and future development. The quantification of similatities and differences in the location, scale and shape of diameter structure during the development of the plantations of different clones contributes to the advanced study of plantation development and can be applied in the construction of the growth model of selected clones, and their production differentiation. The assessment of the effects of clone and plantation age on diameter structure enables a more reliable construction and estimation of the future structure, and also its incorporation in growth models. 6. CONCLUSIONS – Zaključci Based on the research of 20-year old test plantation consisting of several newly selected clones of black poplar, Section Aigeiros(Duby), which are either registered or are in the selection procedure, we can conclude as follows: – there are significant differences in growth elements (dg, G) between individual clones in the test plantation at the end of the study period of 20 years, which provides the basis for their production differentiation; – periodical measurements of diameters at breast height showed different growth of the clones depending on the age: in the initial period of development, the clonesPopulus deltoidesBartr. ex Marsh. (S , 6-7 NS , PE 19/66, NS , S ) developed more inten 1-3 11-8 6-36 sively than the clone Pannonia (Populus×euramericana( Dode) Guinier), and later on Pannonia had a more intensive growth, while the clones ofP.deltoidesBartr. ex Marsh. showed the differentiation; – theWeibull distribution model is suitable for diameter structure modelling of the study poplar clones at different plantation ages, and the applied method of predicting the location parameter (a) of theWeibull distribution model showed that in 90.6 % of the study sample, the parameter “a”ranged between 50 and 90%, and in 52.4% “a”ranged from 80 to 90% of the minimal diameter; – with higher plantation ages, location parameter (a) and scale parameter (b) also increased with small oscillations, which was confirmed by the significance of the correlation coefficient of 0.71 and 0.73 respectively. This was shown by the shift of the curve of diameter structure model to the right, towards larger diameters, and in a wider range of diameters at breast height with a lower relative frequency of the modal degree; – in the initial period, F-ratio of all three parameters of theWeibull diameter structure model decreased and reached the minimal value at the age of eight, and the predominantly increasing trend started at the age of twelve, which points to the changes in diameter structure of the clones depending on the age; – the constructed models of poplar clone diameter structure show the clone grouping in two groups, which was confirmed by the non-parametric Kolmogorov- Smirnov test, the analysis of variance test, and LSD test for the percentage of the number of trees with diameters at breast height above 40 cm. This emphasises the possibility and the need of their grouping in the definition of management procedures. 7. REFERENCES – Literatura Anderson,T.W.,D.A.,Darling,1954: ATest of goodness-of-fit. Journal of theAmerican StatisticalAssociation, 49: 765–769,Alexandria, USA. Andrašev,S., S.Rončević, M.Bobinac,2003: Uticaj gustine sadnje na debljinsku strukturu klonova crnih topola S 6-7 i M-1 (SekcijaAigeiros (Duby)). Glasnik Šumarskog fakulteta, 88: 7–16, Beograd. Andrašev,S., M. Vučković, S.Rončević, M. Bobinac,2004: Mogućnost modelovanja debljinske strukture i izračunavanje zapremine za sada klonova crnih topola. Glasnik Šumarskog fakulteta 90: 37–51, Beograd. Andrašev,S., M. Vučković, S.Rončević, M. Bobinac,2006: Modeli rasta stabala crnih topola sekcije Aigeiros (Duby). Glasnik Šumarskog fakulteta 94: 81–90, Beograd. Andrašev,S., 2008: Razvojno proizvodne karakteristike selekcionisanih klonova crnih topola (sekcija Aigeiros Duby) u gornjem i srednjem |
ŠUMARSKI LIST 11-12/2009 str. 39 <-- 39 --> PDF |
S.Andrašev, M. Bobinac, S. Orlović: DIAMETER STRUCTURE MODELS OF BLACK POPLAR SELECTED ... Šumarski list br. 11–12, CXXXIII (2009), 589-603 Podunavlju. Disertacija, Šumarski fakultet Uni-Forest Science, 54 (12): 566–571,Prague, Czech verziteta u Beogradu, p. 427. Republic. Bailey, R.L., T.R.,Dell,1973: Quantifying diame-Marković,J., Z. Pudar, S. Rončević,1995: ter distributions with the Weibull function. Fo-Zna čaj proizvodnje drveta topola i vrba kao sirorest Scienece 19 (2): 97–104, Bethesda, USA. vinske osnove za industriju celuloze i papira u Jugoslaviji. Radovi Instituta za topolarstvo, br. Conte, S. D, C.deBoor,1980: Elementary numeri26: 5–19, Novi Sad. cal analysis, algorithmic approach. Third edition. McGraw-Hill Book Company, p 432, New Marković,J., S. Rončević, Z. Pudar,1997: York. Izbor razmaka sadnje pri osnivnju zasada topola. Topola, 159/160: 7–26, Novi Sad. ......, .. .., 1984: ............. ........ .. ........ . ....... ....... ......... Pudar,Z., 1986: Ekonomski aspekti proizvodnje dr..........., 2: 65–70, ......, ..... veta topole, Populus × euramericana (Dode) Kotar, M., 2005: Zgradba, rast in donos gozda na Guinier, cl. I-214 u zasadima različite gustine. ekoloških in fizioloških osnovah. Zveza gozdar- Radovi Instituta za topolarstvo, 17: 1–121, Novi skih društev Slovenije in Zavod za gozdove Slo- Sad. venije, p. 500. Ljubljana. StatSoft Inc., 2006: STATISTICA(data analysis soft- Knoebel, B. R., H. E. Burkhart, D. E. Beck, ware system).Version 7.1. 1986: A growth and yield model for thinned Škorić,A., G.Filipovski, M.Ćirić,1985: Klastands of yellow-poplar. Forest-Science-Mo no si fikacija zemljišta Jugoslavije. Akademija nau graph 27. p. 62, Bethesda, USA. ka i umjetnosti Bosne i Hercegovine; Posebna Knowe, S.A., G. S.Foster, R. J.Rousseau,W. izdanja, knjiga LXXVIII; Odeljenje prirodnih i matematičkih nauka, knjiga 13: 1–72, Sarajevo. xing study: predicted diameter distributions. L.Nance,1994: Easter cottonwood clonal mi- Weibull,W.,1951:Astatistical distribution function Can. J. For. Res, 24: 405–414, Ottawa, Canada. of wide applicability. Journal of applied mechaKrznar, A., 1987: Utjecaj debljinske strukture na vri nics, 18: 293–297, NewYork, USA. jednost sastojine. Šumarski list, 10–12: 631–344, Zarnoch, S.J., T.R.Dell,1985:An evaluation of Zagreb. skewness and maximum likelihood estimators of Lei,Y.,2008: Evaluation of three methods for estima- Weibull parametrs. Forest Science, 31: 260–268, ting theWeibull distribution parameters of Chi- Bethesda, USA. nese pine (Pinus tabulaeformis). Journal of SAŽETAK: Cilj rada je utvrditi pogodnost Weibull-ove distribucije za konstrukciju modela debljinske strukture više klonova topola sekcije Aigeiros (Duby), uz primjenu tzv. “hibridnog sustava” nalaženja parametara modela iz uzorka, pri čemu se za nalaženje nepoznatog parametra lokacije (a) modela koristi više percentila minimalnog promjera u rasponu od 0÷dmin. Također, cilj rada je ispitati promjenu parametara modela u zavisnosti od starosti nasada i klona topole, kao i njihov odnos s elementima rasta nasada (dg, G). Istraživanja su obavljena u pokusnom nasadu starom 20 godina, koji se sas toji od više klonova (sorti) crnih topola sekcije Aigeiros (Duby): S6-36, NS1-3, NS11-8, Pannonia, PE 19/66 i S6-7. Nasad je osnovan na zemljištu tipa fluvisol, pjeskovito-ilovaste forme, pri razmaku sadnje od 5 × 5 m (400 stabala po hektaru), sa sadnicama tipa 2+0. U pokusnom nasadu svaki klon ima četiri reda (ponavljanja) i po 20–25 biljaka u svakom redu. U pokusnom nasadu su periodično mejreni prsni promjeri svih stabala (s točnošću od 1 mm), nakon prve, druge, pete, osme, dvanaeste, sedamnaeste i dvadesete godine od osnivanja. Mjereni prsni promjeri stabala u svakom redu, za svaki istraživani klon i godinu izmjere, predstavljali su uzorak stabala za konstrukciju modela debljinske struk ture (ukupno 168 uzoraka). Za svaki uzorak stabala izračunata je temeljni ca, kao zbroj temeljnica svih stabala, te izračunat srednji promjer po temeljnici. Kao model izabrana je Weibull-ova distribucija s tri parametra, čija je funkcija gustoće definirana izrazom (1), a kumulativne distribucije izrazom |
ŠUMARSKI LIST 11-12/2009 str. 40 <-- 40 --> PDF |
S.Andrašev, M. Bobinac, S. Orlović: DIAMETER STRUCTURE MODELS OF BLACK POPLAR SELECTED ... Šumarski list br. 11–12, CXXXIII (2009), 589-603 (2). Za nalaženje nepoznatih parametara Weibull-ove distrbucije korišten je tzv. “hibridni sustav”, odnosno metoda momenata u kombinaciji s metodom percentila (Knoebel, et al, 1986). Parametar položaja (a) dobiven je po metodi percentila, pri čemu su korišteni sljedeći percentili minimalnog promjera: 0,00; 0,01; 0,05; 0,10; 0,15; 0,20; 0,25; 0,30; 0,35; 0,40; 0,45; 0,50; 0,55; 0,60; 0,65; 0,70; 0,75; 0,80; 0,85; 0,90; 0,95; 0,99; 1,00. Parametri skaliranja (b)i oblika (c) dobiveni su po metodi momenata, pri čemu je za njihovo nalaženje izvršeno oduzimanje mjerenih veličina (prsnih promjera) od prethodno definiranog parametra “a”. Ova metoda zasniva se na jednadžbama prvog (x-) i drugog (x–2) običnog momenta Weibull-ove dvoparametarske distribucije (5, 6). Procijenjena varijanca (s2) Weibull-ove distribucije definirana je izrazom (7), a koeficijent varijacije (cv) izrazom (8). Nalaženjem prvog i drugog običnog momenta, kao i koeficijenta varijacije iz uzorka i stavljanjem u formulu 8, koeficijent varijacije je funkcija samo jednog parametra (c), te se može dobiti postupkom iteracije. U radu je korištena kombinacija metode sekante i metode polovljenja intervala uz unaprijed zadanu točnost od 10-6(Conte i de Boor, 1973). Dobivena veličina parametra „c“ poslužila je da se dobije veličina parametra “b” iz relacije (9). Za svaki od navedenih percentila u svakom ponavljanju dobiven je parametar „a“ modela, a metodom momenata parametri “b” i “c”. Zatim je izvršena usporedba empirijske debljinske strukture i modela primjenom Anderson-Darling statistike (A2) (Anderson i Darling, 1954) po formuli (10). Izbor percentila minimalnog promjera izvršen je na temelju minimalne veličine A2statistike za sva 4 ponavljanja u okviru istog klona i starosti nasada. Za svaki od izabranih percentila minimalnog promjera u okviru svakog klona i starosti nasada izvršeno je ponovno nalaženje sva tri parametra Weibull-ove distribucije za svako ponavljanje. Stupanj slaganja modela debljinske strukture i empirijske distribucije izvršen je neparametarskim testom Kolmogorov-Smirnova, nalaženjem |D| statistike (11). Dobiveni parametri Weibull-ove distribucije po pojedinim ponavljanjima korišteni su za utvrđivanje razlika između istraživanih klonova u pojedinim starostima (godina nakon sadnje), pri čemu je korišten statistički test analize varijance i test najmanje značajne razlike (NZR), na razini rizika od 5 %. Istraživani klonovi ostvarili su značajne razlike u elementima rasta (dg, G) na kraju istraživanog razdoblja od 20 godina, što pruža osnovu za njihovo proizvodno diferenciranje. Na osnovi periodičnih izmjera prsnih promjera utvrđen je različit rast istraživanih klonova u debljinu, u zavisnosti od starosti: u početnom razdoblju razvoja klonovi Populus deltoides Bartr. ex Marsh. (S6-7, NS1-3, PE 19/66, NS11-8, S6-36) rastu intenzivnije od klona Pannonia (Populus × euramericana (Dode) Guinier), a kasnije klon Pannonia ima intenzivniji rast, dok između klonova P. deltoides Bartr. ex Marsh. dolazi do međusobnog diferenciranja. Tijekom cijelog razdoblja od 20 godina klon PE 19/66 ostvario je najveće veličine, kako srednjeg promjera po temeljnici (dg), tako i ukupne temeljnice po hektaru (G) i izdvaja se od ostalih klonova po testu NZR na razini rizika od 5 % (tablice 1, 2, grafikon 1). Model Weibull-ove distribucije pokazao se pogodnim za modeliranje debljinske strukture istraživanih klonova topola u različitim starostima nasada, a primijenjena metoda nalaženja parametra položaja (a) modela Weibull-ove distribucije pokazala je da se u 93,1 % istaživanog uzorka parametar „a“ nalazi o rasponu od 50–90 %, a u 54,2 % u rasponu od 80–90 % minimalnog promjera uzorka (grafikon 2). Usporedbom modela kumulativne distribucije i empirijske kumulativne distribucije neparametarskim testom Kolmogorov- Smirnova, povrđena je sličnost kod svih 168 uzoraka. Uz male oscilacije s povećanjem starosti nasada povećavaju se parametri položaja (a) i skaliranja (b), što je potvrđeno koeficijentom korelacije od 0,71 i 0,73 (grafikon 3). Tose manifestira u pomicanju krivulje modela debljinske |
ŠUMARSKI LIST 11-12/2009 str. 41 <-- 41 --> PDF |
S.Andrašev, M. Bobinac, S. Orlović: DIAMETER STRUCTURE MODELS OF BLACK POPLAR SELECTED ... Šumarski list br. 11–12, CXXXIII (2009), 589-603 strukture udesno k većim promjerima i u širem rasponu prsnih promjera s manjom relativnom frekvencijom modalnog stupnja (grafikon 4). Promjene para- metra oblika raspodjele (c) manje su izražene, što potvrđuje iznos koeficijenta korelacije od 0,36 (grafikon 3). Međutim, njegovo značenje na razini rizika od 0.001 ukazuje na trend povećanja sa starošću nasada, odnosno na promjenu oblika debljinske strukture. U početnom razdoblju koda sva tri parametra modela debljinske strukture po Weibull-u F-količnik ima trend opadanja i dostizanja minimalne vrijednosti u osmoj godini, a u dvanaestoj godini pokazuje porast, odnosno pretežito trend povećanja, što ukazuje na promjene u debljinskoj strukturi istraživanih klonova u zavisnosti od starosti. Konstruirani modeli debljinske strukture istraživanih klonova topola pokazuju grupiranje klonova u dvije grupe, što je potvrđeno neparametarskim testom Kolmogorov-Smirnova, kao i testom analize varijance i testom NZR za učešće broja stabala prsnih promjera debljih od 40 cm, te ukazuje na mogućnost i potrebu njihovog grupiranja pri definiranju odgovarajućih gospodarskih postupaka Ključne riječi:crna topola, klonovi, debljinska struktura, Weibulova funkcija gustoće |