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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


ficant differences between the clones, both in the 17


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 .

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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

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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


PE 19/66) attained significant differences in growth elements
and plantation structure.Clone S did not have


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

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


minimal diameter, with frequent value 50%·d (Bai


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