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ŠUMARSKI LIST 1-2/2005 str. 64     <-- 64 -->        PDF

J. Zelić: PRILOG MODELIRANJU NORMALITETA REGULARNIH SREDNJODOBNIH BUKOVIH ... Šumarski list br. 1–2, CXXIX (2005), 51-62
V u k e l i ć , J. i Đ. R a u š , 1998: Šumarska fitocenolo- Z e l i ć , J., 2000: Prilog raspravi o teoriji rasta, prirasta
gija i šumske zajednice u Hrvatskoj, Sveučilište i održivog razvoja, Šumarski list 9-10, str.
u Zagrebu, Zagreb. 515–531.


SUMMARY: The article presents a model of a normal, 70-year-old beech stand
(EGT–II–D–10) covering 1 ha in the compartment 58a of the management unit
“Južni Papuk”.


Under the assumption that the past stand management was based on professional
principles, the breast diameter distribution shows a characteristic structure
of regular stands. According to the earlier method of regular stand management,
the distribution curve of breast diameters is bell-shaped.


The breast diameter distribution (thickness degree of 1 cm) was equalised with
Beta-function.


N = f (d) = 0,04305 * .((d – 9,5) 0,52723 * (50,5 – d) 1,4603))


The transitional probability matrix was used in the graphic part of modelling
the normal diameter structure (pi,j ).


The order of recording breast diameters in an area of 1 ha takes the shape of
Lorenz’s strange attractor. The so-called untrue observables (Ruelle and Takens)
were used for the second and the third variable (y,z).


The probability distribution by thickness degrees is as follows:


There are a total of 551 trees per hectare.
As measures of aberration from the normal breast diameter distribution (the
median, the first and the second exponents of Beta-distribution, the asymmetry
coefficient and the flatness coefficient), the parameters show that the egualised
distribution curve is asymmetrical on the left (positive) side.


The asymmetry coefficient Pj = + 0,3475, and the flatness coefficient


P2 = 2,4337(-05663).


After classifiing the stands according to site class and age, the relevant structural
biometric parameters should be determined and compared with the suggested
model in terms of tree number distribution and volume per hectare.


Key words: unmixed regular beech forest, model of middle-aged forest, normal
models, distribution of diameter at breast height, strange attractor, the transitional
probability matrix, beta-function, the asymmetry coefficient and the fiatness
coefficient