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TREE VOLUME MODEL ESTIMATES AND NEAREST NEIGHBOR ANALYSIS IN THE STANDS OF SCOTS PINE ( Pinus sylvestris L.) IN THE CENTRAL PART OF RODOPE MOUNTAINMODELI PROCJENE VOLUMENA STABALA TE ANALIZA STRUKTURNIH ODNOSA METODOM NAJBLIŽIH SUSJEDA U SASTOJINAMA OBIČNOG BORA ( Pinus sylvestris L.) U SREDIŠNJEM MASIVU RODOPAKyriaki Kitikidou, Elias Milios, Ioannis Lipiridis Summary Scots pine ( Pinus sylvestris L.) is a native species of Europe and Asia, important for its timber. The aim of this study was to develop volume estimation models for the Scots pine in the central part of the Rhodope mountains (Northeastern Greece). For each sampled tree the three nearest trees were examined, applying nearest neighbor analysis. For the Scots pine of the central part of the Rhodope mountains, regression models, which estimate the volume using breast height diameter and total height as predictor variables, were fitted. In addition, nearest neighbor analysis was applied to examine possible effects on form factor of nearest trees and their distances to sampled trees. Three site types were distinguished in the research area, A, B, C (good, medium, and poor site qualities). For the site type C it wasn’t possible to develop a volume estimation model. For the rest of the sites the selected models are: For site type Α: , R^{2} = 0.7653, standard error = 0.3096, for site type B: , R^{2} = 0.8146, standard error = 0.3379, for the total area: , R^{2} = 0.8377, standard error = 0.3039. There is not a clear effect of the distance of the nearest trees on the form factor of sampled trees. This study lead to the development of volume estimation models for site types A, B, and for the whole study area. Nearest neighbor analysis showed that the species and dimensions of the nearest trees had different influence in the form of trees.Keywords: Pinus sylvestris, Greece, volume model estimation, nearest neighbor analysis.1. Introduction Uvod Scots pine ( Pinus sylvestris L.) is a native species of Europe and Asia, spreading west to Scotland, Ireland and Portugal, east to eastern Siberia, south to the mountains of Caucasus and far north, as well as inside the Arctic Circle in Scandinavia. In the North appears in altitude 0-1000 m, while in South orientation is at higher altitudes, 1200–2600 m (Mirov 1967, Farjon 2005). The species is easily recognized, based on quite short, turquoise needles and orange bark. The tree wood is known as red wood, is reddish and hard and used for paper pulp, building construction and shipbuilding (Mirov 1967, Farjon 2005). |

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Given that the objective of “timber management” type of forestry is to provide the optimal combination of quantity and quality of timber products that will maximize economic profit, the development of accurate and flexible models is necessary to provide the information required. The variable used in decision-making regarding timber management is volume. The total volume of trees is commonly estimated from regression models using the breast height diameter and the total height as predictors (Van Laar and Akça 2007). In this study, randomly selected Scots pine trees from the central part of the Rhodope Mountains were measured. Data collected were used as input for the development of regression models that estimate the total tree volume. Development of such models is particularly important, because there are no other models for Scots pine for that area. Also, the effect of nearest trees to sample trees was examined, in an attempt to uncover possible relation between distance and species of the nearest trees and form factor of the sampled trees. 2. Materials and Methods Materijali i metode 2.1 Study area – Područje istraživanjaThe study area was in the central part of the Rhodope Mountains, which is under the management of the Forest Service of Xanthi, Greece. Data covered an area about 3100 ha (longitude 41º19’N and latitude 24º43’E), where altitude range from 1200 to 1500 m. (Figure 1). In the wider region, stands of Fagus sylvatica L. s.l., Pinus sylvestris – F. sylvatica, Abies borisii-regis – F. sylvatica – P. sylvestris, and F. sylvatica – A. borisii-regis and are mainly occurred (Milios 2000a, 2000b, 2004, Milios et al. 2008). Scots pine species occurs mainly in mixed stands with beech in three productivity sites. The age of Scots pine trees in several cases exceeds 120 years (Milios 2000a, 2000b). In the scots pine – beech stands, the basal area of scots pine ranges from 17.00 to 41.15 m ^{2}/ha and in beech ranges from 0.39 to 26.38 m^{2}/ha. In almost all cases scots pine appears mainly in the overstory. On the other hand, in a rather small totally area beech appears with many trees in the overstory (Milios 2000a, 2000b). 2.2 Data collection – UzorkovanjeRaw data were collected in the framework of a Master thesis prepared at the Department of Forestry and Management of the Environment and Natural Resources, of Democritus University of Thrace, in Greece (Lipiridis 2013). Sampled trees were selected applying Neyman’s random stratified sampling, with optimum distribution of sampled units to strata (Neyman 1934). Stratification was applied by distinguishing three site types (A, B, C) in the study area (Milios 2000a). Site type A represents the best sites (good site quality), B the intermediate sites (medium site quality) and C the worst sites (poor site quality). The distinction of site types was based on a combination of site attributes and the growth performance of predominant trees, using plots of 500 m ^{2}. The site distinction was referred mainly to F. sylvatica that is the main (abundant) late successional species |

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of the area (Milios 2000a). By applying Neyman’s method, which achieves minimum variation in the sample assuming that the cost is the same for each sampling unit (tree), 60 trees were selected randomly from the site type A, 53 from B, and 45 from C. Sampled trees were measured as follows: • Breast height diameter D (in meters with 2 decimals) was measured with a calliper• Total height H (in meters with 0.5m precision) was estimated with a Blume-Leiss altimeter• Form factor f was estimated with a Bitterlich´s Spiegel relaskop.Total volume v (m^{3}) of each tree was calculated using the formula (Van Laar and Akça 2007): . For each sampled tree, distance of the three nearest trees was measured and species of these trees was determined, in an attempt to relate nearest trees establishment to form factor. 2.3 Regression models – Modeli regresijeThe regression models that were tested for fitting to data are given in Table 1. These models were fitted for each site type separately and for the whole study area. In each case, approximately 80% of the data were used for fitting and the remaining 20% for validation (Ezekiel and Fox 1959, Marquardt and Snee 1975). Regression analysis was performed using the statistical package SPSS v.19.0 (Kitikidou 2005, IBM 2010). The criteria used for comparing the five regression models were (Table 2): 2.4 Nearest neighbor analysis – Analiza metodom najbližih susjedaNearest neighbor analysis is a method for classifying cases based on their similarity to other cases. In machine learning, it was developed as a way to recognize patterns of data without requiring an exact match to any stored patterns, or cases. Similar cases are near each other and dissimilar cases are distant from each other. Cases that are near each other are called “neighbors” (Weber et al. 1998). In our study, nearest neighbor analysis was performed using the statistical package SPSS v.19.0 (IBM 2010), using the Euclidean metric for distance transformation. The number of nearest neighbors k was set equal to 3, i.e. for each sampled tree (case) the three nearest trees were examined. Three new (theoretical) cases were used as focal identifiers, corresponding to three trees with mean v, D, H and f for each site type. |

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3. Results Rezultati 3.1 Exploratory data analysis – Preliminarna analiza podatakaDescriptive statistics of the sampled trees, for each site type and for the study area as a whole, are given in Table 3. Mean volume was statistically significantly different between site types, ( F = 28.214, p = 0.000), justifying the development of volume estimation models for each site type separately.Summary statistics for the nearest neighbors to the sampled trees (distances and species) are given to tables 4 and 5, respectively. 3.2 Selection of the best regression model and validation for site type A – Odabir najpovoljnijeg modela regresije za lokaciju ABased on the results of Table 6, for site type A, model 2 should be rejected, because, although is adequately fitted, has negative R^{2} for validation data. Also, models 4 and 5 should be rejected, because, although they have fairly good values for comparison criteria, both for fitting and validation data, some of their regression coefficients are not statistically significant at the level p<0.05 (Table 7). Moreover, Model 1 is inappropriate, because regression coefficients are not statistically significant at the level p<0.05, for validation data (Table 7). Regression coefficients and their 95% confidence intervals are given in Table 7. Therefore, the selected model is:3. Combined variable One should note that R^{2} for validation data is quite small, which means that, by taking a new sample, regression coefficients of the selected model might be different.3.3 Selection of the best regression model and validation for site type B – Odabir najpovoljnijeg modela regresije za lokaciju BValues for tested models gave satisfactory values for comparison criteria, both for fitting and validation data (Table 8). However, we should reject models 1, 4 and 5, in which |

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some regression coefficients do not differ significantly from zero, both for fitting and validation data, and model 3, for which regression coefficients do not differ significantly from zero, for validation data (Table 7). Therefore, the selected model is: 2. Constant form factor 3.4 Selection of the best regression model and validation for site type C – Odabir najpovoljnijeg modela regresije za lokaciju CAs for site type C, all models have negative values for R^{2}, either for fitting or validation data, so we cannot choose one.3.5 Selection of the best regression model and validation for the study area as a whole – Odabir najpovoljnijeg modela regresije za sve tri lokacije zajednoAnalysis of data as a whole, i.e. without distinguishing site types, gave highly satisfactory results, both for fitting and validation data (Table 9). After rejecting models 4 and 5, because some of their regression coefficients for fitting data are not statistically significant at the level p<0.05 (Table 7) and models 1, 3, 4 and 5, because their regression coefficients for validation data are not statistically significant at the level p<0.05 (Table 7), the following model was selected: 2. Constant form factor 3.6 Nearest neighbour analysis – Analiza najbližih susjedaSampled trees of site type C had the most distant neighbours (Table 4), while the majority of their neighbours were Pinus sylvestris trees (Table 5). |

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4. Discussion Rasprava At least thirty four volume models are reported in Europe for Scots pine, from which more than half were developed for Scandinavian countries (Zianis et al. 2005). Comparing our models with the ones developed by Näslund (1947) (breast height diameter ranges between 5 and 49.9 cm, and total tree height between 3 and 32.9 m), we can demonstrate that volume - dimensions ( D, H) relationship of the forest studied in the present research and of the forest studied in Sweden are comparable. Näslund’s models are:vˆ = 0.1028D^{2}0.02705D^{2}H + 0.005215DH^{2 } (1)vˆ = 0.1072D^{2} + 0.02427D^{2}H + 0.007315DH^{2 }(2)where total volume vˆ is in dm^{3}, breast height diameter D in cm and total tree height H in m.For the common D and H ranges of both studies (Näslund’s and the present): m and m, volume is m^{3} for model (1), for model (2), for site type A of the central part of the Rhodope Mountains, for site type B and for the studied area as a whole. The central part of Rhodope and the Swedish forest appear to have similar volumes for the same tree dimensions (D, H).In an attempt to examine possible effects of distance between trees on form factor, we applied nearest neighbor analysis, a method used in forestry to assess animal damage to trees (Pepper 1998) and cavity tree abundance (Temesgen et al. 2008). Form factor is related to stand density (competition between neighbor trees) (Philip 1994) Nearest neighbor analysis revealed that trees of site type C are more isolated, compared with trees of site types A and B; based on the analysis, neighbor trees of the sampled trees were more distant than those of the site types A and B. This fact did no led to a lower form factor in the sampled trees of site type C compared with the trees of site type A, where a lower form factor and smaller distances between sampled trees and their neighbors were observed. This happened because the nearest trees to the sampled trees in site type A were beech trees with small dimensions. In most cases, in the mixed P. sylvestris – F. sylvatica stands of the study area, beech appears in the understory and in the middle story as a small tree. As a result, the competition imposed to pine trees was not significant, as well as the influence of beeches on the form factor of pines. The main influence on the form |

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factor of pine trees is induced by overstory pine trees. According to Milios (2000a), the density of overstory pines in the development stages where beech trees have been established under the shade of pines (and grow in the understory and middle story) is the lowest in site type A (143 trees/ha) and seems to be the highest in site type B (290 trees/ha in the first development stage and 640 trees/ha in the second). In site type C the density of overstory trees is 335 trees/ha. These data explain the values of form factors of sampled pine trees in the different site types; 0.41 for site type A, 0.47 for site type B and 0.45 for site type C (Table 3). In conclusion, from the central part of the Rhodope Mountains, selecting 158 Pinus sylvestris trees from 3 site types, by applying Neyman’s random stratified sampling, we developed volume estimation models for each site type and for the whole study area. Selected models were:For site type Α: , R^{2} = 0.7653, standard error = 0.3096For site type B: , R^{2} = 0.8146, standard error = 0.3379For the total area: , R^{2} = 0.8377, standard error = 0.3039.For site type C none of the tested models was selected. There is not a clear effect of the distance of the nearest trees on the form factor of sampled trees since the species and dimensions of the nearest trees have different influence in the form of trees. As for site types A and B and for the study area as a whole, they seem to be analogous regarding volume – dimensions ( D, H) relationship with a similar study in Sweden. References Literatura Burkhart, H., 1977: Cubic-foot volume of Loblolly pine to any merchantable top limit. Southern Journal of Applied Forestry 1: 7-9. Draper, N., Smith, H., 1997: Applied regression analysis. 3rd edition. Whiley and Sons, USA. 736 p. Everitt, B., Skrondal, A., 2010: Cambridge Dictionary of Statistics. 4 ^{th} edition. University Press, Cambridge UK. 478 p. Ezekiel, M., Fox, K., 1959: Methods of correlation and regression analysis. John Wiley and Sons, New York. 548 p. Farjon, A., 2005: Pines: Drawings and Descriptions of the Genus Pinus. 2^{nd} edition. Brill Academic Pub., the Netherlands. 236 p.Gevorkiantz, S., Olsen, L., 1955: Composite volume tables for timber and their application in the Lake States. U.S. Dep. Agric. Tech. Bull. 1104. Google Earth, 2013: http://www.google.com/earth/index.html IBM, 2010: SPSS Regression 19. 51 p. Janssen, P., Heuberger, P., 1995: Calibration of process-oriented models. Ecological Modelling 83: 55-66. Kitikidou, K., 2005: Applied statistics using the statistical package SPSS. Tziola publications, Thessaloniki, Greece. Lipiridis, I., 2013: Volume tables for the Scots pine ( Pinus sylvestris L.) in the central part of the Rhodope mountains. MSc thesis. Department of Forestry and Management of the Environment and Natural Resources, Democritus University of Thrace, Greece. 25 p.Marquardt, D., Snee, R., 1975: Ridge regression in practice. The American Statistician 29(1): 3–20. Mathews, J., 1987: Numerical methods for computer science, engineering and mathematics. Prentice-Hall, Englewood Cliffs, New Jersey. 507 p. Mayer, D., Butler, D., 1993: Statistical validation. Ecological Modelling 68: 21-32. Milios, E., 2000a: Dynamic development and evaluation of mixed stands in Rhodope, prefecture of Xanthi, Greece. PhD thesis. Department of Forestry and Natural Resources, Thessaloniki, Greece. 345 p. Milios, E., 2000b: Dynamics and development patterns of Pinus sylvestris L. - Fagus sylvatica L. stands in central Rhodope. Silva Gandavensis 65: 154–172.Milios, E., 2004: The influence of stand development process on the height and volume growth of dominant Fagus sylvatica L. s.l. trees in the central Rhodope Mountains of north- eastern Greece. Forestry 77: 17–26.Milios, E., Pipinis, E., Smiris, P., Aslanidou, M., 2008: The influence of overhead shade on the shade mortality of Abies x borisii – regis Mattf. seedlings and saplings in the central Rhodope mountains of North-eastern Greece. Plant Biosystems 142: 219–227.Mirov, N., 1967: The Genus Pinus. Ronald Press, New York. 602 p.Näslund, M., 1947: Funktioner och tabeller för kubering av stående träd. Meddelanden från Statens skogsforskningsinstitutet 36(3): 1–81. Newnham, R., 1967: A modification to the combined-variable formula for computing tree volumes. Journal of Forestry 65: 719-720. Neyman, J., 1934: On the two different aspects of the representative method: The method of stratified sampling and the method of purposive selection. Journal of the Royal Statistical Society 97(4): 557–625. Pepper, H., 1998: Nearest neighbour method for quantifying wildlife damage to trees in woodland. Forestry Commission Practice Note no1, Edinburgh, UK. Philip, M., 1994: Measuring trees and Forests, second edition. CAB International, Cambridge. 310 p. Romancier, R., 1961: Weight and volume of plantation-grown loblolly pine. USDA For. Serv. Southeast. For. Exp. Stn. Res. Note 161. Schumacher, F., Hall, F., 1933: Logarithmic expression of timber-tree volume. Journal of Agricultural Research 47: 719–734. Spurr, S., 1952: Forest inventory. Ronald Press, New York. 476 p. Temesgen, H., Barrett, T., Latta, G., 2008: Estimating cavity tree abundance using Nearest Neighbor Imputation methods for western Oregon and Washington forests. Silva Fennica 42(3): 337–354. Van Laar, A., Akça, A., 1997: Forest Mensuration. Cuvillier Verlag, Göttingen, Germany. 418 p. |

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Wackerly, D., Mendenhall, W., Scheaffer, R., 2008: Mathematical statistics with applications. 7 ^{th} edition. Duxbury Press. Belmont. 944 p.Weber, R., Schek, H., Blott, S., 1998: A quantitative analysis and performance study for similarity-search methods in high-dimensional spaces. Proceedings of the 24 ^{th} VLDB Conference, New York, USA, pp.194-205.Zianis, D., Muukkonen, P., Raisa Mäkipää, R., Mencuccini, M., 2005: Biomass and stem volume equations for tree species in Europe. Silva Fennica Monographs 4. 63 p. Sažetak Obični bor ( Pinus sylvestris L.) euroazijska je vrsta drveća, ekonomski važna radi vrijednosti i iskoristivosti drva. Cilja istraživanja bio je razviti modele procjene volumena drva stabala običnog bora u mješovitim borovo-bukovim sastojinama u središnjem masivu Rodopa (sjeveroistočna Grčka). Primijenjeni regresijski modeli koriste prsni promjer i ukupnu visinu stabala običnog bora kao predikcijske varijable. Za svako uzorkovano stablo te njegova tri neposredna susjedna stabla analizirani su strukturni odnosi primjenom metode najbližih susjeda. Nadalje, metoda najbližih susjeda primijenjena je kako bi se analizirao učinak udaljenosti između stabala i pripadnosti vrsti drveća na njihov oblik. Istraživanje je provedeno na tri stanišna tipa, “A”, “B” i “C” (dobri, srednji i slabi stanišni uvjeti). Za stanište “C” nije bilo moguće izvesti model procjene volumena. Na preostala dva staništa odabrani modeli bili su kako slijedi: na staništu “Α“:, R^{2} = 0.7653, standardna pogreška = 0.3096, na staništu “B”: , R^{2} = 0.8146, standardna pogreška= 0.3379, te sveukupno, za sva tri staništa , R^{2} = 0.8377, standardna pogreška= 0.3039. Nije utvrđen utjecaj udaljenosti među susjednim stablima na oblik analiziranih stabala. Istraživanje je pridonijelo razvoju volumnih prediskcijskih modela na staništima “A” i “B” kao i na sva tri staništa zbirno. Analiza sastojinskih strukturnih odnosa metodom najbližih susjeda ukazala je da vrsta drveća i udaljenost među stablima imaju različit utjecaj na oblik stabala.Ključne riječi: Pinus sylvestris, Grčka, modeli procjene volumena, metoda najbližih susjeda. |