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available data. In fact, three distinct sources of height–age data for site index curves constructions have been widely used in literature (Clutter et al. 1983): temporary sample plots, stem analyses data, and permanent sample plots. The data on the height of trees at different ages (temporary sample plots) is the least usable. It does not provide completely valid information on the real height growth of individual stands, but in the absence of other data, it is still often used (Nanang and Nunifu 1999). Nonetheless, height observations (and sometimes age) are subject to the sampling and measurement error (García 2011) and the so-called ’’age trend’’ (Socha et al. 2016), which can cause a bias in the data from temporary sample plots. Another shortage of this data is the need to make the assumption that all sites are equally sampled at all ages (Monserud 1984). This type of height-age data was used to construct the existing anamorphic site index curves for beech in Serbia (Stajić et al. 2016). In the procedure of their construction, asymptote coefficients of growth curve models are only changed resulting in site index curves with the same shape, causing the main drawback of anamorphic site index curves – the same age of the current height increment culmination. This assumption cannot be considered biologically totally justified and it is well-known that the better the site is, the earlier the current height increment culminates in even-aged stands and the greater the increment value at the moment of culmination is (Sloboda 1971, Kramer 1988, Vučković 1989, Stajić 2010). To account for differences in the height growth pattern per site, the dominant height growth is commonly modelled by polymorphic site index functions (Mamo, Sterba 2006).
In spite of the relevance of site productivity estimations for forest management, studies on site productivity assessment regarding site index curves have not been carried out very intensively, both in Serbia and in the entire Region of former Yugoslavia. In majority countries, a classification of site productivity in has been conducted either by applying the mean height-diameter relations or the mean height-age relations (see Stajić et al. 2016). In order to improve the existing system of site classification according to productivity, to harmonize it with the dominant mode of site productivity estimation in Europe and to create opportunities for the comparison of the obtained results in Serbia with the results of site index investigations from other countries, it is necessary to establish site index curves for the main tree species. It is especially important for European beech (Fagus sylvatica L.), which represents the most important and one of the most productive tree species in Serbia (Vučković and Stajić 2005). Its productivity largely depends on the silviculture method employed in its forests. Generally, for high-quality beech wood production forestry practices and especially thinings have a special importance (Usta et al. 2019). In addition, the distance between the trees and their optimal number, and consequently the optimal size of tree growth space are also of importance for the achievement of the optimal site and stand productivity in beech forests (Lukić 1988, Vučković and Stajić 2003, Zelić 2005). Nevertheless, the wide vertical and horizontal distribution of beech on different bedrocks and in various soil evolution stages has caused large differences in the productivity of beech forests (Vučković and Stajić 2005). Previous studies of pure and mixed stands of beech don’t provide enough data for a complete overview and classification of sites and stands according to the actual and potential level of production (Stajić et al. 2016). Accordingly, aim of this study was (1) modelling the beech dominant height-age relationships, (2) constructing polymorphic site index curves for beech in the central and eastern areas of its distribution in Serbia and (3) making some comparisons with beech height-age data from surrounding countries.
MATERIAL AND METHODS
MATERIJAL I METODE
The research was conducted in beech stands in the Žagubica – ŽA, eastern Serbia (latitude: 44°10’3” N, longitude: 21°51’43” E) and Rudnik mountain – RU, central Serbia (latitude: 44°8’25” N, longitude: 20°29’33”E) regions, with about 15,000 ha and 7,000 ha of total forest area, respectively. The stands belong to the complex of a montane beech forest. The altitude ranges from 650 to 1,250 m (ŽA) and from 690 to 1,080 m (RU). The parent rock of the management unit consists of limestone and amphibolic and clay shales. Soil types include shallow, medium and deep soils on different limestone and brown acid soils. The average annual temperatures for ŽA and RU are 9.8°C and 7.7°C, respectively. The annual precipitation for ŽA and RU are of 682 mm and 742 mm, respectively
A set of 62 (ŽA) and 64 (RU) dominant beech trees were used to obtain suitable height-age data. Trees were selected to cover a wide range of ages and site conditions throughout the analyzed beech forest complexes. In fact, we were selectively looking for stands or parts of stands of different age and with different site conditions over the regions, in which we felled the tallest trees. In order to get a deeper insight into the height increment relationships as precisely as possible, especially in youth, each tree was felled and cross-sectioned at every 1 m in the first 10 m of the trunk and, thereafter, at 2 m intervals up to the terminal peak of a tree. To estimate the height from the stem analysis data, using Carmean’s procedure (Newberry 1991), annual rings on each disc were precisely measured and counted.
The first step in producing polymorphic fixed base-age site index curves was to develop a guide curve fitting tree height data depending on age. According to the fitted height values at the age of 100 from the guide curves obtained (≈25 m) and the calculated standard deviations of heights at the age