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ŠUMARSKI LIST 5-6/2016 str. 50     <-- 50 -->        PDF

Richards’s and Todorović’s functions have almost identical growth curves and statistical features. Contrary to the observed deficiency in Korf’s and Schumacher’s functions, which occurs in the initial period of growth curves, the deficiency in Todorović’s and Chapman-Richards’ functions is linked to the fact that the growth curves of these functions reach asymptote relatively early, though empirical data show upward flow even at the age of 140 (Figure 1). So, although it has been often proved to be very suitable to describe growth in height (Wang and Payandeh 1995; Álvarez González et al. 2005; Zlatanov et al. 2012 etc.), Chapman-Richards’ function was not flexible enough to represent the analyzed height growth of beech tress. Also, it seems that the current height increment of Todorović’s model (age of 37) is reached quite late. Namely, the culmination of the current height increment of beech at the sites of medium productivity should be expected around the age of 30 (Stajić 2010). Korsun’s function proved to be the best one with regard to statistical indicators and growth flow. The only ’’disadvantage’’ of Korsun’s function could be found in the time of culmination of the current height increment (age of 21), which likely occurs somewhat earlier than in reality. However, it should nevertheless be underlined that in undisturbed stand conditions the height growth of beech can be relatively fast, with a large initial increment (Lukić et al. 2003). Bearing in mind all of the above-mentioned, Korsun’s function was definitely selected and the set of anamorphic site index curves was constructed (Figure 2).
As noted, site index studies have not been intensively performed in Serbia. Ratknić (1998) presented beech site indices for the area of western Serbia. In doing so, he applied Todorović’s function in fitting the height-age empirical values obtained from the stem analysis method. Ratknić (1998) used the reference age of 150 years for the site index construction, which is considered partly inappropriate given that the currently prescribed rotation length in pure even-aged beech forests in Serbia is less than 150 years. In addition, the culmination of the current height increment on poor sites occurs earlier compared to more productive sites. For example, the culmination of current height increment, according to Ratknić’s instructions, occurs for the first three site classes at the age of 30, for the site class VI at the age of 28, and at the age of 24 for the site class VIII. This statement can be considered inadequate according to the present-day knowledge. Namely, it is well known that the better the site, the earlier the current height increment in even-aged stands culminates and the amount at the moment of culmination is greater (Sloboda 1971; Kramer 1988; Vučković 1989; Stajić 2010). By summarizing the available information about the method of site index construction provided by Ratknić, it remains unclear whether the author has developed anamorphic or polymorphic site index curves.
CONCLUSIONS
ZAKLJUČCI
The site index curves developed in this study are anamorphic site curves. In the procedure of their forming only asymptote coefficients were changed (shape parameters were constant) resulting in site index curves with the same shape. This fact causes the main drawback of anamorphic site index curves – the same age of the current height increment culmination. It means that the current height increment of different site classes culminates at the same time regardless of the quality of the site. However, this assumption cannot be considered biologically totally justified.
The results of the conducted study show that Korsun’ growth model best fits the dominant beech height-age relations and therefore this model was implemented for the construction of site index curves in pure beech stands in the studied region. It must be also noted that the obtained growth model and site index curves should be used within the empirical data set (up to the age of 140). Namely, the model was parameterized on trees whose age in most cases did not exceed 140 years.
Although the determined site indices are burdened with aforementioned limitations, this study is of considerable significance for the Serbian beech forest sector. In a sense, bearing in mind the large sample with mainly well-distributed sample units pre age and site classes, this research is the first extensive research of beech forest sites according to productivity. In addition, this method of stratifying the sites according to quality has been performed for the first time on the basis of site indices calculated from temporary sample plots. The obtained knowledge is useful for effective forest management and decision making in forest management planning, forest policy, and ecology. Of course, future studies should be undertaken in order to expand the database and knowledge on the dominant beech height-age relationships in the studied region and another well-known procedure of site indices construction – polymorphic site index curves – should be applied. In this way, the obtained polymorphic site index curves can be also very helpful in the development of appropriate silvicultural treatments, general classification of sites with regard to their quality and sustainable management of these forests. In that context, the obtained results should be considered as a preliminary stage of site index studies for beech in Serbia.
ACKNOWLEDGEMENT
ZAHVALA
This paper was realized as a part of the project ’’Creating of normal models for selection forests and establishing a normal state for high even-aged beech stands in Serbia (creating of yield and growth tables)’’, financed by the Ministry of Agriculture, Forestry and Water Management for the period 2013–2015.