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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


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


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:


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


son-Darling statistic (A) (Anderson andDar ling,


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:


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


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

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
17 years
17. god.
20 years
20. god.
dg [cm]
2.9 (0.06)
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
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
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
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


Values in parentheses represent the standard deviation –Vrijednosti u zagradi predstavljaju standardnu devijaciju.


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.