Allometric biomass equations for young trees of four broadleaved species in Albania Erion Istrefi1*, Elvin Toromani2, Nehat Çollaku2 and Bashkim Thaçi3 1 Ministry of Tourism and Environment, Environmental Services Project, Blv Zhan D’Ark, Tirana, Albania. 2 Agricultural University of Tirana, Faculty of Forestry Sciences,1029 Koder-Kamez, Tirana, Albania. 3University of Applied Sciences in Ferizaj. Rr.Universiteti, Ferizaj, Kosovo. *Corresponding author: erion.istrefi@yahoo.com (Received for publication 5 April 2019; accepted in revised form 6 May 2019) Abstract Background: Biomass assessment of young forest stands is important because of their role in the carbon cycling. The aim of this study was to develop biomass equations for young broadleaved species growing in natural conditions in Albania. Methods: Five forest stands were investigated using circular sample plots. Diameter at breast height (DBH) and height (H) from 58 sampled trees ranging in age from 4 to 34 years old of Turkey oak (Quercus cerris L.), sweet chestnut (Castanea sativa Mill.), European hornbeam (Carpinus betulus L.) and manna ash (Fraxinus ornus L.) were measured in situ. Logarithmic regression equations were used and tested for their performance to estimate aboveground and tree-components biomass for each species using DBH, H and their combination DBH2 x H as predictors. Results: We found that DBH was a reliable predictor for estimation of aboveground and components biomass for young trees but the inclusion of height in biomass allometry did not improve the biomass estimation. We observed differences in scale (β0) and exponent (β1) coefficients of biomass models, not only between broadleaved species, but also among tree- components within species. Both coefficients were strongly species-specific and their values reflect differences in biomass stocking rate due to different growth strategies of each species in early development phases. Conclusions: Allometric equations to estimate aboveground and tree-component biomass appeared to be species-specific, meaning that such models are applicable for species growing at sites with similar ecological conditions. From the tree variables used, DBH was the most reliable predictor of aboveground and individual components biomass, whereas height proved to be a promising predictor for stand biomass. These allometric equations developed for young trees will improve the accuracy of current estimates of forest carbon stock in Albania. New Zealand Journal of Forestry Science Istrefi et al. New Zealand Journal of Forestry Science (2019) 49:8 https://doi.org/10.33494/nzjfs492019x51x E-ISSN: 1179-5395 published on-line: 22 July 2019 © The Author(s). 2019 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Research Article Open Access equations. Such allometric models are commonly used to estimate biomass in mature forests, but these are missing for young forests. They are adequate tools to express biomass in terms of dry mass on the basis of easily measured variables. Most of these equations in the Albanian and international literature use diameter at breast height (DBH at 1.3 m from the ground) and tree height (H) to estimate aboveground biomass (AGB) or tree-components biomass. Other variables such as wood density, crown length, height-to-diameter ratio, or tree Introduction During the last decades, the area of young forests in Albania has been expanding due to intensive management and damage incurred by forest fires. Since young forest stands play a critical role in the forest carbon cycling due to their capacity in dioxide carbon uptake in early growth phases, we urgently need to develop and improve techniques for accurate prediction of their biomass (Lehtonen 2005). One of the most efficient ways to achieve this goal is to use allometric Keywords: biomass model performance, Carpinus betulus, Castanea sativa, Fraxinus ornus, Quercus cerris, tree biomass Istrefi et al. New Zealand Journal of Forestry Science (2019) 49:8 Page 2 age are also used to improve the accuracy of allometric equations in biomass prediction. The information on biomass of forest stands is required to assess the amount of carbon stocked in Albanian forests and to estimate changes in carbon stocks to meet reporting requirements of Albania to the United Nations Framework Convention on Climate Change (UNFCCC). For that reason, the development of biomass functions in each country has become an important issue and it is encouraged to be done for most relevant tree species (IPCC 2003). Despite recent developments in remote sensing techniques, biomass allometric models are fundamental to estimating biomass at the tree or stand level. Few studies on biomass and biomass expansion factors (BEFs) have been reported for forest species in Albania. The first results regarding biomass estimation at country level were provided in the framework of the National Forest Inventory (ANFI 2004). Biomass was calculated using inventory data on stand volume per hectare and biomass expansion factors (BEFs) from other countries with similar site conditions. Omuri (2006) generated allometric equations and determined BEFs for Austrian pine (Pinus nigra Arn.), beech (Fagus sylvatica L.) and birch (Betula pendula L.) ≤50 years old in the Shishtavec area, northern-east Albania. Toromani et al. (2011) developed allometric equations for young poplar plantations growing in eastern Albania, in the region of Pogradeci, based on several tree variables. Istrefi et al. (2018) conducted research in several areas in eastern and central Albania to assess aboveground and tree components biomass of Turkey oak (Quercus cerris L.) ≤0 years by using linear and non-linear allometric models. Several studies on allometry have been conducted worldwide, where 279 equations have been developed for different tree species and ecological regions (Zianis et al. 2005; Zianis and Mencuccini 2004). These biomass equations were developed for young trees with a threshold of DBH ≥10 cm omitting trees with a smaller diameter. Based on our review of the literature, we noted that most biomass equations were developed for mature stands (Wirth et al. 2004; Joosten et al. 2004; Zianis et al. 2005) and only few for young stands (Dutca et al. 2010). Despite the limited number of published equations, for many other forest species growing in Albania the availability of allometric equations is still limited. Therefore, there is still a need for improving existing biomass models and developing new ones for other forest species such as Turkey oak, sweet chestnut (Castanea sativa Mill.), European hornbeam (Carpinus betulus L.), manna ash (Fraxinus ornus L.) and others. From the review in the GlobAllomeTree platform (http://globallometree.org, Henry et al. 2013), the only available allometric equations for young trees were for Cas. sativa, and Car. betulus. Due to the lack of biomass equations for young broadleaved species in Albania, the development of allometric models for biomass estimates remains a challenge for researchers in Albania. The main objective of this study was to develop species-specific allometric equations for predicting aboveground and tree-components biomass (i.e. stem, branches, and foliage) using several tree variables and to test their accuracy and precision for biomass prediction. Methods Study area Forests in Albania cover an area of 941957 ha (ANFI 2004) distributed over the whole territory. Within project “Assisted Natural Regeneration of Degraded Lands in Albania”, the project area was stratified in four ecological zones based on climate, soil, elevation and geology (UNFCCC 2009). The first ecological zone comprises forest areas of Mediterranean shrubs and gariga, while the second ecological zone includes mixed oak forest stands (Quercus spp.) with hornbeam (Carpinus betulus L.) and other species. The third ecological zone includes European box (Buxus sempervirens L.) with common juniper (Juniperus communis L.), while the fourth ecological zone comprises alpine vegetation areas with dwarf juniper (Juniperus nana Miquel.). Our study was focused on the second ecological zone dominated by pure and mix oak forest stands (Fig. 1). A systematic 1 x 1 km geo-referenced grid using ArcGis program was established, where 19 intersections of this grid were located in the second ecological zone. Eight out of 19 intersections located in young natural forest stands were selected randomly from north-east to central part of Albania. The main species at the research sites were: Turkey oak (Quercus cerris), sweet chestnut (Cas. sativa), European hornbeam (Car. betulus) and manna ash (Fraxinus ornus). The study areas have a distinct Mediterranean climate; the mean annual temperatures vary across sites ranging from 8.8°C to 14.4°C (Table 1), with extreme minimum and maximum temperatures of -14°C to 6.2°C and 23.7°C to 30°C, respectively (Harris et al. 2014; www.climexp.knmi.nl). The rainfall time series indicated the presence of spatial and temporal variability in annual and seasonal precipitation sums at all sampling sites. Cinnamon and dark mountain forest soils, the most common in the sampling sites, are deep with moderate fertility as well as high clay content and strong alkalinity (FAO 2015). Sampling methodology and procedure Starting from the main grid (1 x 1 km), biomass sampling plots were established at the intersections of a 200 x 200 m grid. Five sample plots were randomly selected and trees inside circular sample plots (400 m2) were measured. Before conducting the destructive sampling, the diameter at breast height [DBH (cm)] of trees was measured by calliper with ±1 mm accuracy in two perpendicular directions. Tree heights [H (m)], were measured by ultrasonic hypsometer Vertex III (Haglöf, Sweden). The position of each tree in relation to the plot centre was recorded by measuring the distance from the centre and tree azimuth. In total, three to five trees per sample plot were selected and felled at ground level during the period from June 2016 to October 2017. Fifty-eight sampled trees were partitioned into the three main components (stem, branches and foliage), whereas plant roots were not investigated. The fresh weight of the stem, branches and leaves was weighed in the field using a precision scale with 50 kg capacity and accuracy ±1%. The same procedure of destructive analysis was followed at all research sites. Three to five subsamples from each tree-component were stored in sealed plastic bags and then sent to the laboratory of the Faculty of Forestry Sciences in Tirana. Masses of stem discs (2–3 cm thick), branches and foliage samples were weighed. Subsequently, all samples were dried at 70°C temperature, until a constant weight was achieved. Tree- components biomass was assessed on the basis of fresh to oven-dry weight ratio (Eq. 1) of subsamples collected from sampled trees. c = DWsubsample/GWsubsample (1) In those cases where the stem could not be weighed in the field, the diameter over bark was measured at 1-metre intervals from the stem base to the top to determine the log volumes using Newton–Riecke’s equation (Van Laar & Akça 1997). The total AGB of each tree was estimated by the sum of stem-wood, branches and foliage weights. Development of biomass equations So far, researchers have used a variety of regression models for estimating tree and tree-components biomass. Biomass data exhibit heteroscedasticity because the variance differs across observations and for that reason the power function is considered an appropriate model in our study. We transformed the observed data using logarithmic transformation which is commonly used in dimension analysis studies to fit appropriate allometric equations. The following models with this form were fitted to the sampled tree data: Model 1: ln DW=ln β0+β1× ln DBH (2) Model 2: ln DW=ln β0+β1 × ln H (3) Model 3: ln DW=ln β0+β1× ln DBH 2 × ln H (4) Model 4: ln DW=ln β0+β1ln DBH+β2 ln H (5) where DW is the aboveground dry biomass, or any of three components (stem, branches, foliage); DBH the diameter at breast height (cm); H the total tree height (m); and β0, β1 and β2 are the regression coefficients. In the biomass models 2, 3 and 4, β0 represents the scaling coefficient, while β1 is the scaling exponent. The natural logarithm transformation linearises the allometric relationships, equalises the variance over the entire range of the dataset and provides comparability with results of previous studies (Zianis et al. 2005; Niklas 2006). However, the transformation introduces a systematic bias into the calculation, therefore to eliminate the bias, the final result is usually multiplied Istrefi et al. New Zealand Journal of Forestry Science (2019) 49:8 Page 3 FIGURE 1: Location of the research sites and sampled species by a correction factor (CF) calculated from the standard error of the estimate (SEE) of the regression (Sprugel 1983): CF=exp×(SEE2/2) (6) Models were fitted using the regression procedure within the SPSS software (version 24) for Windows (IBM 2006) to relate aboveground tree mass to different measures of felled tree variables including diameter at breast height (DBH), tree height (H), and their combination (DBH2 × H). Biomass model fitting and evaluation Model fitting was carried out in two phases. First, we eliminated non-significant models (P>0.05) and those with low values of coefficients of determination (R2 <0.5). Secondly, in order to select the best equations for each species, several goodness-of-fit statistics were examined: the coefficient of determination (R2), the root mean squared error (RMSE), the root mean squared prediction error (RMSPE) and the mean error (ME). The coefficient of determination (R2) indicates the proportion of the total variance explained by the model, whereas the other fitting statistics analyse the accuracy of the biomass estimates. The smaller their values, the better is the biomass model prediction performance (Zeng & Tang 2011). We also applied the reduced major axis (RMA) regression, because the observed data are subject to errors. RMA is more appropriate than standard ordinary least squares (OLS) regression when the independent variable is measured with error (Sokal & Rohlf 2012). The tree variables (DBH or H) used to predict aboveground biomass are subject to natural variation and measurement errors (especially H) and this fact cannot be neglected (Niklas 2006; Kaitaniemi 2004). The scaling exponent of the RMA regression analysis was estimated using the equation 7: bRMA=β1/ryx (7) where bRMA is the scaling exponent based on the RMA model, β1 is the scaling exponent estimated by the least Istrefi et al. New Zealand Journal of Forestry Science (2019) 49:8 Page 4 square model regression (OLS) applied to Eqs. (2–4), and ryx is the correlation coefficient determined from the least square regression (Henry & Aarssen 1999). Uncertainty of biomass models Uncertainty is defined as the lack of knowledge of the true value which can be described as a probability density function characterising the range and likelihood of possible values of aboveground or tree-components biomass. It depends on the quality and quantity of applicable data as well as on the predictive ability of allometric equation to estimate biomass. We evaluated the reliability of the biomass models in terms of differences between the estimates obtained from allometric equation and the true value. For that reason, the biomass models developed for each species were used to predict the aboveground and tree- components biomass using sampled tree variables as predictors. Since the biomass equations were directly applied to sampled tree data of the investigated forest species, the components of the errors accounted for are the sampling and biomass model errors (assumed to be small). The key approach is that uncertainty in biomass estimates can be propagated from uncertainties in the biomass data and allometric equation prediction accuracy and its estimation is based on the error propagation equation (Bevington and Robinson 1992). Using this interpretation, a simple equation is used for the uncertainty of the sum, expressed in percentage terms: (8) where: U is the percentage uncertainty of aboveground biomass in the sum of the quantities (half the 95 percent confidence interval divided by the total (i.e., mean) and expressed as a percentage), DWst, DWbr, DWf are the uncertain quantities of stem, branches and foliage dry weight (kg) predicted by allometric equations, and Ust, Ubr, and Uf are the percentage uncertainties associated with biomass estimates of tree-components (i.e., stem, branches, foliage). Site Long (°E) Lat (°N) Elevation (m) MAT (°C) MAPS (mm) Sllove 20°24’’16’’ 41°45’35’’ 750 9.6 959 Bushtrice 20°25’02’’ 41°53’34’’ 780 9.7 1010 Maqellare 20°28’03’’ 41°39’17’’ 850 9.3 1000 Zerqan 20°22’’04’’ 41°30’48’’ 715 9.8 1008 Paper 19°57’42’’ 41°04’43’’ 160 14.4 1133 Tomin 20°25’’20’’ 41°41’18’’ 647 9.8 1030 Rrape 19°57’02’’ 42°02’45’ 805 10.1 1000 Qafe-Mali 20°06’28’’ 42°08’03’ 1160 8.8 1157 *source: www.climexp.knmi.nl TABLE 1. Site description including location, longitude (long), latitude (lat), elevation above sea level, mean annual temperature (MAT)* and mean annual precipitation sum (MAPS)*. 𝑈𝑈 = √(𝑈𝑈𝑠𝑠𝑠𝑠 ∙ 𝐷𝐷𝐷𝐷𝑠𝑠𝑠𝑠 )2 + (𝑈𝑈𝑏𝑏𝑏𝑏 ∙ 𝐷𝐷𝐷𝐷𝑏𝑏𝑏𝑏 )2 + (𝑈𝑈𝑓𝑓 ∙ 𝐷𝐷𝐷𝐷𝑓𝑓 )2 (𝐷𝐷𝐷𝐷𝑠𝑠𝑠𝑠 + 𝐷𝐷𝐷𝐷𝑏𝑏𝑏𝑏 + 𝐷𝐷𝐷𝐷𝑓𝑓 ) This error propagation equation is applicable for estimation of the overall uncertainty derived by the summed quantities of tree-components biomass estimates by allometric models. Results Sampled tree information The basic characteristics of sampled trees are shown in Table 2. The sampled trees ranged in age from 6 to 34 years, in DBH from 2 to 16 cm and in height from 1.90 to 9.83 m. A total of 58 sampled trees were analysed in this study. The aboveground and tree-components biomass was computed for the four species (Table 3). For Q. cerris the total tree biomass ranged between 1.07 and 56.34 kg, stem biomass from 0.84 to 34.65 kg, branch biomass from 0.19-17.84 kg, and foliage biomass between 0.04 and 3.84 kg. The relative contribution of stem biomass to AGB in Q. cerris increased from 62% for large diameter classes to 78% for small diameter classes (Fig. 2). The proportion of branch biomass for this species increased from 18% for the small diameter class to 32% for the large diameter class. The ratio of foliage biomass versus AGB increased proportionally with DBH from 4% to7%, indicating that leaf mass gives a marginal contribution in aboveground biomass. For Car. betulus, the AGB ranged from 0.72 to 21.80 kg, stem biomass from 0.40 to 13.12 kg, branch biomass from 0.23 to 6.25 kg, and foliage biomass from 0.09 to 2.43 kg. For this species, the proportion of stem increased from 55% for the small diameter classes to 60% for large diameter classes, while the contribution of branch biomass declined from 32% for the small diameter classes to 29% for large diameter classes. Regardless of the DBH values of Car. betulus trees, the relative contribution of foliage biomass was increased from 11.0 to 12.5%. For F. ornus, the AGB per tree ranged from 1.83 to 12.09 kg, stem biomass from 0.96 to 7.20 kg, branch biomass Istrefi et al. New Zealand Journal of Forestry Science (2019) 49:8 Page 5 Tree species Number of trees Age (years) DBH (cm) H (m) Quercus cerris 18 8–27 2.00–15.00 2.75–9.83 Carpinus betulus 17 6–34 2.00–16.00 2.30–9.10 Fraxinus ornus 16 6–26 2.20–7.50 1.90–8.00 Castanea sativa 7 7-15 3.20–12.00 2.75–9.60 Tree variable Species Number of trees Values DBH H DWst DWbr DWf AGB Q. cerris 18 Min 2.00 2.75 0.84 0.19 0.04 1.07 Max 15.00 9.83 34.65 17.84 3.84 56.34 Mean 6.51 4.43 7.97 3.46 0.74 12.16 SD 3.40 1.77 9.24 4.25 0.92 14.23 Car. betulus 17 Min 2.00 2.30 0.40 0.23 0.09 0.72 Max 16.00 9.10 13.12 6.25 2.43 21.80 Mean 6.94 5.28 3.85 3.31 1.23 8.40 SD 4.67 2.25 2.82 2.90 1.08 6.71 F. ornus 16 Min 2.20 1.90 0.96 0.65 0.12 1.83 Max 7.50 8.00 7.20 4.23 1.94 12.09 Mean 4.48 4.55 3.24 2.23 0.61 6.07 SD 1.85 1.69 1.86 1.09 0.53 3.38 Cas. sativa 7 Min 3.20 2.74 1.10 0.46 0.30 1.85 Max 12.00 9.60 16.72 9.22 5.15 31.09 Mean 7.74 6.20 9.65 5.68 2.82 18.15 SD 2.76 2.07 4.90 2.89 1.59 9.30 TABLE 3. Summary statistics of aboveground and tree-components biomass of felled trees (DBH, diameter at breast height (cm), H, total tree height (m), DWst, stem dry weight (kg), DWbr branch dry weight (kg), DWf, foliage dry weight (kg), AGB, aboveground tree biomass (kg)) TABLE 2. Summary of information of sampled trees used to develop the biomass functions from 0.65 to 4.23 kg, and foliage biomass from 0.12 to 1.94 kg. For F. ornus, the proportion of stem biomass increased proportionally with DBH from 53% to 60%, while the branch and foliage biomass proportions were inversely related to sampled tree DBH. The proportion of branch and foliage biomass in small diameter classes were 41.3 % and 7.4%, whereas in large diameter classes they were 33.2 % and 16.1 % respectively. For Cas. sativa, the aboveground biomass per tree ranged from 1.85 to 31.09 kg, stem biomass from 1.10 to 16.72 kg, branch biomass from 0.46 to 9.22 kg and foliage biomass from 0.30 to 5.15 kg. For Cas. sativa, the proportion of stem biomass was 54 % and 59 % for small and large diameter classes, respectively. The relative proportion of branch biomass increased proportionally with DBH from 25% to 30%, but the proportion of foliage biomass was equal (16% of the AGB) for small and large diameter classes. Istrefi et al. New Zealand Journal of Forestry Science (2019) 49:8 Page 6 FIGURE 2: Box plots of biomass components (in percentages) by forest species estimated by field destructive sampling by DBH (1.3 m from the ground) and tree height (H) classes. Frequency distribution of sampled tree variables All species exhibited different frequency distributions of diameter at breast height, where the biggest tree number occurred in the 2, 4 and 6 cm diameter classes (Fig. 3). The sampled Car. betulus trees had DBH values across the full range of diameter classes, whereas the frequency distribution of other species was noticeably concentrated in the smallest DBH classes which ranged from 2 to 10 cm. Fifty-three trees comprising 94% of the total number of sampled trees in all species had a DBH ≤6 cm. Regarding tree height, similar patterns in frequency distribution were observed for all species. A greater proportion of trees occurred in the mid-height range and a regular frequency decline of trees and a flattening of the curves towards the largest height classes was observed. We found a strong relationship between DBH and tree height (H) for all species (Table 4). The R2 values of the applied linear models were always significant Istrefi et al. New Zealand Journal of Forestry Science (2019) 49:8 Page 7 (P<0.05), with a lower value in F. ornus, probably due to the characteristics of this species in young development phases. For all studied species, age distributions were produced using 10-year age classes (Fig. 3c). In Q. cerris, Car. betulus and F. ornus we noticed a unimodal pattern in age distributions, typical for even-aged forest stands with few trees in young and old age classes. By contrast, in Cas. sativa, was observed the lack of a typical age distribution as well as the absence of mature trees in the forest stand. Relationship between AGB and tree variables Visual examination of the biomass data (Fig. 4) revealed the existence of a strong relationship between DBH (and/or DBH2 × H) and AGB on the logarithmic scale. The values of the correlation coefficient (r) between AGB and DBH varied between 0.92 (P<0.05) for F. ornus and 0.96 (P<0.05) for the other species. In addition, correlation between AGB and DBH2 × H ranged from r = 0.89 (P<0.05) for F. ornus to r = 0.97 (P<0.05) for Car. betulus and remained in the same level for the two other species. The relationship between AGB and tree height was clearly weaker for all species, where the values of the correlation coefficient varied from 0.78 (P<0.05) for F. ornus to 0.92 (P<0.05) for Cas. sativa. There was also evidence of changing variance in AGB values among species associated with an increasing value from Cas. sativa to F. ornus. Biomass model evaluation The coefficient estimates and goodness-of-fit- statistics (i.e. R2, RMSE, RMSPE, ME) of all biomass models for the four species (after applying the logarithmic transformation) are shown in Table 5. These statistics were significant at P<0.05 level, indicating that the fitted biomass equations performed well. The most reliable model fitting was obtained for aboveground and stem biomass, while the model fitting for foliage and branch biomass was less reliable with relatively lower R2, RMSE and high ME. In Model 1, which uses DBH as predictor, the values of the coefficient of determination (R2) indicated that the fitted model explained between 75% and 97% of the observed biomass variance. We noted that R2 values were different between biomass models, tree-components and across species. The lowest values of the coefficient of determination (R2) were observed in Model 3, which uses the product of squared DBH with tree height as predictors, whereas the highest values occurred in Model 1 and Model 4. The R2 values indicated that fitted models explained between 62% and 95% of the biomass variance per tree-component for all studied species with mean values of 75%, 79% and 82% of variance in foliage, branch and stem biomass, respectively, whereas the AGB equation explained on average 84% of the total observed variance. The inclusion of tree height (H) as independent variable in the Model 2, did not improve the goodness-of-fit- statistics for biomass prediction of tree-components in Q. cerris, F. ornus and Cas. sativa. The values of root mean square error (RMSE) varied among species and ranged between 0.18 and 4.46. All -a- -b- -c- -a- -b- -c- -a- -b- -c- FIGURE 3: Log-transformed frequency distribution (number per ha) of diameter at breast height (a), height (b) and age (c) of all sampled trees. The x-axis values are the central values of each class. a b c biomass models used in this study produced the most reliable estimates for AGB and stem wood biomass, whereas the least accurate estimates were derived for branch and leaves biomass. Most of the mean error (ME) values obtained from all biomass models were close to zero, indicating that all allometric equations except Model 2 provided accurate prediction of biomass. The values of this statistic obtained from biomass model 2 were far from zero, implying that allometric equations using tree height as a predictor performed the poorest. The dominance of positive values of ME indicated that the biomass models provided an underestimate of the aboveground or tree-component biomass, whereas in those cases when this statistic was negative, the biomass was overestimated. In this study we found differences between species in bRMA values for relationships between AGB versus DBH, H and their combination (DBH2 × H) (Table 6). In the case of DBH, two out of four values for Q. cerris and Cas. sativa were significantly different from the others. In the allometric models using tree height (H) as biomass predictor, the bRMA values decreased from Q. cerris to F. ornus. The lowest values of the scaling exponent of RMA regression were found in Model 3, which uses the predictor variable (DBH2 × H) for biomass estimate, whereas the highest values were obtained by Model 2, where total height was the only biomass predictor. In contrast to the bRMA values, correction factor scores (CF) showed less variability across tree-components and species. The largest differences in CF values were found between foliage biomass and DBH in Model 1 (Table 6). When tree height was the predictor, we observed less variation in CF values compared to DBH TABLE 2: Confusion matrix and a wider range of CF values in stem (1.010–1.070) and AGB (1.010–1.060). The largest values of CF were obtained when DBH2 and H were used as predictors in the allometric Model 3, whereas the largest values at species level were found in F. ornus and Cas. sativa. Uncertainty of biomass models In order to assess the bias of allometric equations in biomass prediction, the quantitative estimates of uncertainty were applied. The uncertainty estimates of the biomass models developed in this study ranged from 1 to 24.6%, depending on the species and tree- components (Table 7). The highest bias was found for biomass Model 4, while the best model based on uncertainty values was the allometric Model 3, where DBH2 x H was the predictor variable. When considering the bias values of biomass models by forest species, the highest values were found in Cas. sativa, and the lowest values in Q. cerris. The uncertainty of biomass models increased from foliage to stem biomass indicating that stem biomass was estimated more accurately. Discussion Allometric equations Four regression models developed to predict aboveground and tree-components biomass were evaluated for their performance and accuracy of the estimates. The multiple regression models which used DBH and total tree height (H) were the most accurate. The logarithmically transformed model using DBH alone as an independent variable performed better meeting the criteria of accuracy and biomass prediction Istrefi et al. New Zealand Journal of Forestry Science (2019) 49:8 Page 8 Species Dependent variable Independent variable R2 Regression coefficients ln β0 β1 Q. cerris DBH H 0.802 0.326 0.467 Car. betulus DBH H 0.970 0.689 0.474 F. ornus DBH H 0.752 0.018 0.788 Cas. sativa DBH H 0.823 -0.091 0.683 TABLE 4. Relationship between DBH and H, R2 and values of parameters lnβ0 and β1 FIGURE 4: Relationship between aboveground biomass (AGB) and diameter at breast height (DBH), tree height (H) and DBH2 × H on a logarithmic scale for all studied species. Istrefi et al. New Zealand Journal of Forestry Science (2019) 49:8 Page 9 Species F. ornus Cas. sativa Model coefficients Goodness-of-fit statistics Model coefficients Goodness-of-fit statistics ln β0 β1 β2 R² RMSE RMSPE ME ln β0 β1 β2 R² RMSE RMSPE ME 1 Stem 0.983 1.418 - 0.88 1.02 0.99 1.00 -1.600 2.153 - 0.96 1.37 1.36 1.43 Branch 0.013 1.405 - 0.83 1.02 1.00 1.00 -0.693 2.066 - 0.94 2.03 2.00 1.82 Foliage -0.073 1.231 - 0.79 3.47 3.39 2.39 -1.131 2.328 - 0.87 0.81 2.21 2.18 AGB -1.610 2.748 - 0.92 3.06 2.42 1.36 -1.253 2.143 - 0.97 0.23 0.18 0.00 2 Stem 1.523 1.281 - 0.62 0.65 0.59 0.50 -0.262 2.253 - 0.81 1.24 1.20 1.54 Branch -0.248 1.234 - 0.48 4.46 4.43 2.40 -0.588 2.164 - 0.72 1.83 1.78 1.80 Foliage 1.539 2.459 - 0.43 3.27 3.12 3.10 -1.030 2.423 - 0.79 2.10 2.07 2.10 AGB -1.540 2.459 - 0.66 3.46 2.84 1.34 -1.163 2.271 - 0.80 1.11 1.06 1.12 3 Stem 0.285 0.031 - 0.70 0.78 0.72 0.58 0.920 0.021 - 0.60 1.31 1.29 0.97 Branch 0.004 0.029 - 0.75 0.86 0.68 0.63 0.255 0.023 - 0.54 1.37 1.44 0.99 Foliage -2.511 0.061 - 0.53 0.87 1.65 0.65 -0.412 0.023 - 0.61 1.29 1.35 0.94 AGB 0.899 0.032 - 0.73 1.80 0.74 1.23 1.502 0.022 - 0.62 1.24 1.34 0.91 4 Stem -0.948 1.503 -0.123 0.91 0.18 0.16 0.00 -3.516 1.517 0.732 0.94 0.19 0.16 0.01 Branch -1.156 1.027 0.256 0.89 1.16 1.15 -1.15 -3.176 1.939 0.456 0.91 0.74 0.73 0.64 Foliage -4.976 2.809 -0.078 0.67 0.76 0.63 0.00 -2.089 1.629 0.512 0.91 0.24 0.22 0.58 AGB -0.376 1.413 0.006 0.91 0.18 0.15 0.00 -1.643 1.709 0.519 0.93 0.21 0.17 -0.04 TABLE 5. The coefficients estimate and goodness-of-fit-statistics of log-transformed biomass equations (R2, coefficient of determination, RMSE, root mean squared error, RMSPE, root mean squared prediction error, ME, mean error) for Models 1–4. Species Q. cerris Car. betulus Model coefficients Goodness-of-fit statistics Model coefficients Goodness-of-fit statistics ln β0 β1 β2 R² RMSE RMSPE ME ln β0 β1 β2 R² RMSE RMSPE ME 1 Stem -0.303 1.901 - 0.85 1.26 1.22 1.22 -0.474 1.371 - 0.96 0.94 0.88 1.67 Branch -0.599 1.918 - 0.82 1.69 1.65 1.26 -0.060 1.158 - 0.93 1.45 1.39 0.81 Foliage -0.959 1.895 - 0.75 2.74 2.72 0.77 -0.773 1.636 - 0.93 2.05 2.00 0.54 AGB -1.420 1.886 - 0.93 1.09 1.05 1.06 -1.148 1.633 - 0.97 0.33 0.26 0.34 2 Stem -0.587 2.628 - 0.68 1.56 2.28 1.45 -0.617 2.263 - 0.95 1.33 1.31 1.31 Branch -0.819 2.650 - 0.72 2.02 1.93 1.93 -0.696 1.927 - 0.92 1.80 0.57 3.71 Foliage -1.113 2.615 - 0.71 3.13 3.07 1.12 -1.288 1.527 - 0.92 3.09 3.08 1.60 AGB -1.525 2.618 - 0.72 1.34 1.23 1.21 -1.527 2.688 - 0.96 1.25 1.23 1.20 3 Stem 0.610 0.027 - 0.65 1.33 1.06 0.76 0.217 0.017 - 0.74 1.59 0.95 1.03 Branch -0.204 0.026 - 0.61 1.34 1.13 0.77 -0.499 0.024 - 0.71 1.15 1.36 0.75 Foliage -1.751 0.026 - 0.62 1.34 1.12 0.77 -1.487 0.024 - 0.71 1.32 1.94 0.87 AGB 1.056 0.026 - 0.65 1.32 1.08 0.76 0.767 0.020 - 0.75 2.29 1.11 -1.94 4 Stem -1.933 1.798 0.224 0.93 0.72 0.64 0.64 -2.190 -0.084 2.162 0.90 0.26 0.18 -0.43 Branch -2.715 1.781 0.213 0.88 0.38 0.36 0.00 -3.471 0.195 2.386 0.92 0.36 0.29 0.01 Foliage -4.270 1.743 0.267 0.88 0.38 0.35 0.00 -4.433 0.216 2.346 0.91 0.36 0.29 0.00 AGB -1.467 1.760 0.227 0.93 0.28 0.24 0.04 -1.787 0.084 2.130 0.95 0.22 0.18 0.00 Biomass Com- ponent Biomass Com- ponent quality. As suggested by other studies, DBH is more accurately measured and therefore, is relatively more reliable when is used as single independent variable to develop biomass equation (Chave et al. 2005; Pastor et al. 1984; Mosseler et al. 2014) than other tree variables such as tree height (Hosoda & Lehara 2010; Hunter et al. 2013). We observed that inclusion of tree height as single predictor variable did not improve the biomass model accuracy and this finding is consistent with that reported by Johansson (1999). In contrast, other Istrefi et al. New Zealand Journal of Forestry Science (2019) 49:8 Page 10 Model Biomass component Q. cerris Car. betulus F. ornus Cas. sativa bRMA CF bRMA CF bRMA CF bRMA CF 1 Stem 1.971 1.280 1.392 1.020 1.478 1.170 2.197 1.056 Branch 1.270 1.040 1.240 1.071 Foliage 1.432 1.040 1.140 1.060 AGB 1.030 1.030 1.210 1.060 2 Stem 3.097 1.070 2.310 1.020 1.577 1.010 2.535 1.051 Branch 1.060 1.040 1.030 1.065 Foliage 1.060 1.040 1.050 1.057 AGB 1.060 1.040 1.010 1.056 3 Stem 1.194 1.255 0.860 1.295 0.733 1.063 1.140 1.215 Branch 1.298 1.286 1.041 1.337 Foliage 1.285 1.284 1.636 1.233 AGB 1.243 1.159 1.060 1.247 4 Stem 1.052 1.058 1.020 1.038 Branch 1.093 1.081 1.020 1.070 Foliage 1.089 1.082 1.424 1.060 AGB 1.050 1.029 1.021 1.046 TABLE 6. Values of the scaling exponent (bRMA) of reduced major axis regression and the biomass correction factor (CF) by spe- cies and allometric models used in the study TABLE 7. Uncertainty estimates of biomass models by forest species and tree-components Model Biomass component Uncertainty (%) of biomass models by species and tree components Q. cerris Car. betulus F. ornus Cas. sativa 1 Stem 3.70 2.70 2.40 5.00 Branch 4.00 3.00 3.40 6.00 Foliage 4.50 3.50 3.50 6.60 AGB 2.33 1.75 1.73 3.51 2 Stem 2.95 3.95 2.80 5.25 Branch 3.24 4.25 3.40 5.70 Foliage 4.15 4.70 3.70 6.80 AGB 1.95 2.75 3.14 3.74 3 Stem 1.00 1.40 2.30 1.50 Branch 1.30 2.80 3.40 2.70 Foliage 1.70 3.20 3.50 5.40 AGB 1.26 1.24 3.03 3.41 4 Stem 4.30 9.00 6.10 6.50 Branch 6.10 17.00 7.80 10.30 Foliage 9.00 17.36 22.80 24.60 AGB 3.44 11.85 6.54 12.72 authors have found a significant improvement in model accuracy statistics when tree height was used as biomass predictor (Reed & Tome 1998), but this variable might be more useful for stand biomass estimates than for individual tree (Wang et al. 2013). In general, allometric models were more robust for stem and aboveground biomass than for branch and foliage biomass. Stem and aboveground biomass showed less variation than other tree components, and this may be related to the variation of local conditions, tree position in the canopy and sunlight availability. The coefficients of log-transformed allometric biomass equations differed between species. We found that the scaling exponent (bRMA) in regression equation varied among species and tree variables used as predictors, indicating that such models are species-specific and that the use of a common scaling coefficient for different species would lead to bias in biomass prediction. Our values of bRMA (2.05 for DBH and 2.38 for tree height) differed from that used by West et al. (1999). These authors suggested that AGB should be scaled with DBH according to a universal value of scaling exponent (bRMA = 8/3, i.e. 2.67), which depends on the tree architecture. West et al. (1999) assumed that using a universal value of b is not acceptable, especially when trees are growing under different environmental conditions. Although our sampled trees were growing under similar site conditions, the bRMA value in allometric models developed in this study were different from those reported earlier by Zianis and Mencuccini (2004). Therefore, we conclude that the scaling exponent value is probably mainly affected by species traits and their growth during the juvenile period (Poorter et al. 2015). Pilli et al. (2006) reported three different scaling exponent values for juvenile (b = 2.08), adult (b = 2.66) and mature (b = 2.51) trees, whereas Niklas (2004) reported scaling exponents close to 1.0 in the case of young plants, while for large plants the exponents declined to below 0.75. In contrast, we found that tree age is associated with a decrease of b from 2.2 (age class 1–10 years) to 2.0 (age class 11–20 years). Moreover, we observed that the variability of the scaling exponent was lower for stem biomass than for branch and foliage biomass. The scaling exponent values varied across species and were different from those reported in a previous study. Thus, Blujdea et al. (2012) reported for the same allometric model a higher value for F. excelsior (b = 3.04) and a lower value for Quercus species (b = 1.22). The most reliable fitted model for estimation of aboveground biomass was the multiple regression function (Model 4). Based on the goodness- of-fit-statistics (R2; RMSE; RMSPE), all our biomass models produced the most reliable estimates for AGB and stem biomass and the least accurate estimates for branch and foliage biomass. Most of the mean error (ME) values obtained from the biomass models were close to zero, indicating that all allometric equations except Model 2 could provide accurate estimates. In Albania, as in other European countries, biomass estimates based on allometric equations and BEFs have been applied without any quantitative estimates of uncertainty. Therefore, information on the overall error occurring with the use of biomass models is missing. The uncertainty estimates of the biomass ranged from 1.0 to 24.6%, depending on the species, tree components and biomass model applied. The uncertainty in the biomass estimates of Cas. sativa was high because the number of sampled trees used to generate allometric equations was low. By contrast, the lowest values of error were found in Q. cerris where the number of trees used to develop the biomass models was the highest. The uncertainty results indicate that the applicability of biomass models needs to be carefully evaluated, especially for the presence of bias, before using these in other geographic areas or in other countries. Contribution of tree-components to total AGB For all species studied, stem wood was the main contributor to the total AGB, followed by branches and foliage. The fact that the highest proportion of the AGB is allocated in the stem has been documented in previous studies, with proportions ranging from 50% to 92% for different species (Fonseca et al. 2011). Our results are within the same range varying from 52% (Car. betulus) to 65% (Q. cerris). The proportions of biomass of each tree component relative to AGB are consistent with those reported by Blujdea et al. (2012) for several broadleaved species growing in Romania. As expected, the proportion of biomass allocated to stems increased with tree size. As trees grow, age and size-related changes in tree shape and form alter the contribution of stem to whole-tree biomass increment (Bartelink 1998). In contrast, the relative contribution of branches and foliage to AGB decreased. We found that the biomass allocation to each tree-component differed among species, suggesting that their proportion relative to AGB depends on tree species in a mixed stand and stem density. Allometric equation comparison with previous models The literature and GlobAllomeTree repository (http:// globallometree.org, Henry et al. 2013) contain numerous allometric equations for different trees species from the Mediterranean basin and other regions. Such allometric equations to estimate tree biomass have been developed for various species growing under different site conditions. We noticed that information about biomass equations for Q. cerris and F. ornus is missing in the GlobAllomeTree web platform (Table 8), and the equations developed in this study can enrich the database. The allometric equations we developed used variables from 58 sampled trees growing in specific sites representing a small region. Some authors suggest that biomass regression equations developed for a site or region can be used to predict tree biomass in other places (Wirth et al. 2004). To verify that, we compared the results provided by Model 3 developed in our study with allometric models found in the GlobAllomeTree platform for Car. betulus and Cas. sativa. We could not do the same comparison for other species because our models differed from those found in this platform. The average values of AGB estimates from each allometric equation were compared using one-way ANOVAs. Means Istrefi et al. New Zealand Journal of Forestry Science (2019) 49:8 Page 11 were separated using Tukey HSD post-hoc test. In the case of Car. betulus we found that the mean values of biomass estimated from each model were significantly different (F=7.162; P=0.002), whereas in the case of Cas. sativa this difference was not significant (F=1.739; P=0.204). The results of the post-hoc test revealed significant differences in the mean AGB values estimated by our model for Car. betulus and those of Hoellinger (1987) (i.e. model 3 (P=0.002) and model 4 (P=0.022) in Table 8). In contrast, the results of the post-hoc test for Cas. sativa indicated no significant difference between the AGB estimated by our model and those of Hoellinger (1987) (i.e. models 5 (P=0.212) and 6 (P=0.352) in Table 8).This suggests that the use of allometric equations needs to consider factors such as species characteristics, age, soil fertility and climate (Madgwick & Satoo 1975). Another limitation in the use of biomass equations is the range of values of independent variables. Extrapolation below or above these ranges could lead to substantial differences between the true and predicted values (Zianis & Mencuccini 2003). Since allometric relationships between biomass and tree variables vary across species, tree size and age, the use of such models in other geographic areas is not suggested because this may lead to incorrect estimations (Harding & Grigal 1986; Wang et al. 2002; Zianis & Mencuccini 2003; Zabek & Prescott 2006). Finally, the biomass equations were developed on a relatively narrow DBH and H range and their application to large trees outside these ranges may be associated with larger errors in biomass prediction. Conclusions The dataset from 58 young trees representing four broadleaved species were used to develop allometric equations to estimate aboveground and tree- components biomass. The intention is to use these equations in biomass estimation for respective species in the framework of the National Forest Inventory. Stem and AGB biomass by DBH were the most accurately predicted, whereas the use of tree height as biomass predictor was associated with a decrease in prediction accuracy. The possibility of estimating young tree biomass by forest yield tables or forest inventory data is limited due to the lack of biomass expansion factors. Since few biomass equations exist and there is a need for their development, further investigations in other ecological zones and other species should be conducted in Albania. List of abbreviations AGB, aboveground biomass; BEFs, biomass expansion factors; CF, correction factor; DBH, diameter at breast height; H, tree height; IPCC, Intergovernmental Panel on Climate Change; ME, mean error; RMSE, root mean squared error; RMSPE, root mean squared prediction error; UNFCCC, United Nations Framework Convention on Climate Change. Competing interests The authors declare that they have no competing interests. Authors’ contributions NÇ and BTH undertook the fieldwork and data collection, ET did the data processing, statistical analysis, and EI wrote the manuscript. All authors read and approved the manuscript. Acknowledgements This research was conducted in the framework of PhD studies. We acknowledge the help of Ing. Saimir Beqo and Ing. Albert Buzali with sample preparation and Ing. Edmir Novaku with biomass data sampling. The authors thank the editor and two anonymous reviewers for their comments which helped to improve the quality and clarity of the manuscript. References ANFI. (2004). Albanian National Inventory Final Report. Tirana, Albania: Agrotec Consortium, 140 pp. Bevington, P. R., & Robinson, D. K. (1992). Data Reduction and Error Analysis for the Physical Sciences. New York: McGraw-Hill. Bartelink, H. H. (1998). A model of dry matter partitioning in trees. Tree Physiology, 18(2), 91–101. TABLE 8. Allometric equations found in the GlobAllomeTree platform for species included in this study Nr Allometric equation Number of trees R2 Location Source Quercus spp. 1 Log Biomass = - 0.883 + 2.14·Log (DBH) 33 n.a. 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