BIOMASS OF Eucalyptus globulus IN YOUNG PLANTATIONS IN URUGUAY

In four areas of the western coast of the Oriental Republic of Uruguay (Algorta, Bequeló, Quebracho and Tres Bocas) the aerial biomass of Eucalyptus globulus plantations was quantified with ages between 3 and 9 years. In 20 circular plots of 300 m, 616 trees were measured, selecting 132 for quantification. In each tree, the biomass of five components was calculated: leaves, green branches, dry branches, stem and total aerial, the latter obtained by adding the previous components. Four allometric functions were adjusted in three scenarios: by location, for total locations and for total locations, but identified by dummy variables. The functions by location presented minimal difference from Akaike information criterion (AIC), so that in all cases this type of function was selected. The average annual increase in biomass was obtained, with average values for all the localities of 1.18 ± 0.45, 1.08 ± 0.18, 0.58 ± 0.22, 11.24 ± 1.86 y 14.20 ± 2.50 Mg ha year for leaves, green branches, dry branches, stem and total aerial, respectively. An analysis of variance by component identified statistically significant differences in the average annual increase in biomass between locations. The localities with the highest increase were Bequeló and Tres Bocas, followed by Quebracho and Algorta. The analysis of variance incorporated planting density as a covariate, proving to be significant for the components of greater dimensions.


INTRODUCTION
In Uruguay 64% of wood production is used for energy purposes, with Eucalyptus globulus being the species with the largest forested area (DGF-MGAP, 2012). The estimation of aerial biomass from these plantations will serve to better characterize this resource, since the measurement units for these products are usually associated with biomass.
Tree biomass is often determined using destructive sampling (PÉREZ-CRUZADO and RODRÍGUEZ-SOALLEIRO, 2011), which according to Gibbs et al. (2007) is summarized in three steps, (i) obtaining the green mass of each component, (ii) taking a sample of the components and determining their green and dry mass, and (iii) obtaining the dry mass of each component using proportions (Dry mass = Green mass * Dry mass sample / Green mass sample).
In general, biomass functions are adjusted by location for each of the considered components, or for the set of locations. In general, the functions for the whole have a lower performance than the functions by location (van BREUGEL et al., 2011;PAUL et al., 2013;VALLEJOS-BARRA et al.; and in some cases have variable results since in some locations there is little error, while in others the errors can be significant. (CHAVE et al., 2005).
Another alternative is to consider the set of localities but identifying each one of them by means of Dummy variables. This increases the degrees of freedom for the estimation of population parameters and therefore improves the relative precision of the estimates, which could not be verified by Vallejos-Barra et al. (2014); However, António et al. (2007) and Zeng et al. (2011) report that biomass estimation was improved by incorporating a Dummy variable identifying the origin of the stands.
Akaike Information Criterion (AIC) was used to select functions, since it is a powerful tool for comparing functions (SNIPES and TAYLOR, 2014). Burnham and Anderson (2002) describe it as: = (̂2) + 2 Where AIC is the Akaike Information Criterion, n is the amount of data used in the adjustment, ̂2 = ∑( −̂) 2 ⁄ and k is the total of estimated parameters, including the intercept and ̂2.
The AIC value measures loss of information by a given function (MAZEROLLE, 2006), but by itself its value is not relevant. The important thing is to obtain the difference of the AIC between each adjusted function and the function with the lowest value (BURNHAM and ANDERSON, 2002); so the best function will have a difference equal to zero; with a difference up to 2, the function could be equally satisfactory. A difference between 4 and 7 reduces the significance of the function, while a difference greater than 10 rules out the use of the function.
The hypothesis is that it is possible to model the biomass of different components of E. globulus by means of allometric functions, it is also hypothesized that there should be no difference in the average annual increase between the sampled localities. The aim of this study was to select biomass functions for the leaves, green branches, dry branches, stem and total aerial, of E. globulus trees growing in the western coast of the Oriental Republic of Uruguay in South America, in order to estimate the average annual increase of the aerial biomass (Mg ha -1 year -1 ) of each of the components and to observe if there are significant differences between the four locations sampled.

MATERIALS AND METHODS
In the sedimentary basin of the west coast of the Oriental Republic of Uruguay, the company EUFORES has unmanaged plantations of Eucalyptus globulus L. According to the Köppen-Geiger climate classification, the region is characterized by a temperate and humid climate with hot summers (Cfa) (INIA, 2011). Cruz et al. (2000) characterize this zone with an average annual rainfall of 1,174 mm and average monthly temperatures ranging from 10.5 to 22.5 ºC. The relief is of high and medium plains with soft, sometimes flattened hills and strong hills, which are no higher than one hundred meters above sea level.
The measurements were taken on 20 circular plots of 300 m 2 in 4 geographical locations (6 in Algorta, 6 in Bequeló, 6 in Quebracho and 2 in Tres Bocas) where EUFORES has young plantations. The planting density varied between 733 and 1267 trees ha -1 with ages between 3 and 9 years. The plots were representative of the average growth of trees in each locality, based on data from permanent plots of the owner company.
In the plots the diameter at breast height (DBH) of all trees was recorded (616 in total), with a calliper of parallel arms, graduated to the millimeter. A total of 132 trees representative of the measured diameter classes were upturned (40 in Algorta, 42 in Bequeló, 36 in Quebracho and 14 in Tres Bocas). The height of the trees was obtained by measuring the length of each one of them, once they were turned over, using a distance measuring device, graduated to the millimeter. Determining height in this way is common in some studies (ÁLVAREZ et al., 2012;KUYAH et al., 2013). Each tree was divided into four components: green branches, dry branches, leaves and stem. The branches were separated from the stem with an axe or pruning shears when their size allowed. The FLORESTA, Curitiba, PR, v. 50, n. 4, p. 1798-1807 leaves were manually separated from the branches and the stem was cut into two-meter-long logs. Additionally, the diameters of each of the logs were recorded, in order to calculate the volume of the stem, by adding the Smalian volume of each of the logs.
In the field, the green mass of the components was obtained using a Thunderbird field balance with an accuracy of 200 g. A sample of each component was sent to the laboratory recording the green mass with a My Weigh KD 600 electronic balance with an accuracy of 1 g. Later, when the samples reached a constant mass in a Venticell oven at 65 ºC, their dry mass was obtained. The dry mass of each tree component was calculated by multiplying the ratio between the dry and green mass of the sample obtained in the laboratory by the green mass recorded in the field. The fifth component, the total aerial dry mass of the tree, resulted from the addition of the dry mass of the components recorded in the field. The basic density of the stem wood was obtained by dividing the dry mass of the stem by the volume of the latter.
The entire statistical analysis was performed with the free statistical program R version 3.4.0. Four nonlinear functions ([1] to [4]) were adjusted for each component in each of the locations. The non-linear adjustment method (nls), which uses the Gauss-Newton method, was used for regression adjustment.
Where B is the biomass of each component (kg), d is the diameter at breast height (cm), h is the total height (m),  is the basic density of the stem (kg m -3 ), b0 is the regression constant and bi are the regression coefficients (i = 1 and 2).
A total of 120 function settings were made: 80 function settings per location (5 components * 4 locations * 4 functions per location) and 40 global settings (5 components * (4 global functions + 4 global dummy functions). In order to make the adjustments of the various functions comparable, the Akaike information criterion (AIC) was calculated by component and for each location, then the differences were obtained in relation to the lowest AIC, as recommended by Burnham and Anderson (2002) and Burnham et al. (2011); selecting those functions with the minimum values of this difference. As some of the selected functions incorporated the height of the trees, functions ([9] to [11]) were adjusted to estimate this variable in those trees where it was not measured. An adjustment was made for each location and another for all locations, so that a total of 15 function adjustments were made.
The regression adjustment for stem density was not significant so the probability density function that best represented the basic stem density was determined, with the intention of giving readers the inverse integral to estimate the density at a certain probability. With the selected functions, the biomass of each of the plots was estimated and the existence of statistically significant differences in the increase of biomass per hectare between FLORESTA, Curitiba, PR, v. 50, n. 4, p. 1798-1807 the localities was determined using an analysis of parametric variance. The analyzed variable was the average annual increase of biomass per hectare (MAI Mg B ha -1 ) and as there was variation in planting density, the number of trees ha -1 from each plot was included as a covariate. The assumptions of this analysis were verified with the Shapiro-Wilk and Levene tests. When there were statistically significant differences between the sources of variation these were identified with Duncan's multiple comparison test.

RESULTS
The mean annual increment (MAI) in diameter at breast height and height was used to characterize each locality (Table 1). Both increases diminished as the age of the plots increased. Over 5 years of age, regardless of location and planting density, the MAI in d and height did not exceed 2.50 cm year -1 and 2.73 m year -1 , respectively. The largest increases were obtained in Bequeló up to 5 years of age. The increase was equal to or greater than 3.37 cm year -1 and 3.02 m year -1 , for the diameter at breast height and the height, respectively. These increases are associated with lower planting densities ( 1034 trees ha -1 ). No clear trend was observed in the decrease or increase of the MAI in diameter at breast height and height with fluctuation in the number of trees ha -1 .  Table 2). The number of AICs (300) exceeded the number of adjustments (120), since the AIC was obtained by location, function and component (240 AIC) and also by function and component for all locations (60 AIC).
It is observed that the differences equal to zero are only found in the functions adjusted for each of the locations. Both adjustments for the total number of locations, in their great majority, were not significant since the differences were greater than 10.
The selected functions, those with a difference equal to zero, are presented in (    Where b0 is the regression constant, b1 and b2 are the regression coefficients, Sbi is the standard error of the regression constant if i = 0 and of the regression coefficients if i = 1 or 2, EEE is the standard error of estimation in kilograms, R 2 A is the adjusted coefficient of determination and AIC is Akaike information criterion. Where b0 is the regression constant, b1 is the regression coefficient, Sbi is the standard error of the regression constant, if i = 0 and of the regression coefficient if i = 1, EEE is the standard error of estimation in meters, R 2 A is the adjusted coefficient of determination and AIC is the Akaike information criterion. The biomass functions [2] and [4] require the estimation of the stem density, but this variable did not present a connection with the recorded variables, so it was decided to select the probability density function that FLORESTA, Curitiba, PR, v. 50, n. 4, p. 1798-1807 represented this variable. Of the thirty functions tested, the Logistics function [12] was selected, which obtained a Kolmogorov-Smirnov test statistic of 0.044, with a probability of 0.96. To obtain the basic density of the stem at a specific probability [14], the inverse density function was calculated, clearing the basic density of the distribution function [13], which is the integral of function [12]. The values estimate for µ and  were 525.83 and 29.15 respectively. The quantification of the aerial biomass of each component on the 20 plots (   The validity of the analysis of parametric variance in the MAI for aerial biomass was checked, since both the assumption of normality (W-statistician of the Shapiro-Wilk test) and the assumption of homocedasticity (Zstatistician of the Levene test) were not statistically significant (Table 7). This analysis identified significant differences between the means of the locations in each of the components. Where (*) indicates significant statistical differences (probability < 0.05), (**) indicates highly significant statistical differences (probability < 0.01), (ns) reveals that there are no significant differences (probability  0.05). W is Shapiro-Wilk's statistician and Z is Levene's statistician. F corresponds to Snedecor's F-test statistician and (***) indicates that there are no statistically significant differences between locations with the same sub-index letter in the vertical (probability  0.05).

DISCUSSION
The increases presented in Table 1 are consistent with those reported by Resquin et al. (2012) for locations close to the geographical area of this research, so that the growth observed corresponds to the normal development of a plantation in these locations.
In Figure 1 total biomass and stem biomass are observed according to location. With this distribution of data, it would have been simpler to estimate the biomass of these components if the selected functions had considered the total of localities, since with one function the component under analysis would have been estimated. However, both adjustments for the total number of locations did not prove to be significant since the differences in the AIC, in most cases, were greater than 10 ( FLORESTA, Curitiba, PR, v. 50, n. 4, p. 1798-1807 Table 2) and as indicated by Burnham and Anderson (2002) the use of these functions should be ruled out.
In all components differences equal to zero were only found in the functions adjusted for each of the locations ( FLORESTA, Curitiba, PR, v. 50, n. 4, p. 1798-1807 Table 2). This result coincides with that informed by Vallejos- Barra et al. (2014) in the estimation of absorbed carbon for the species and agrees with that expressed by van Breugel et al. (2011) and Paul et al. (2013). 75% of the adjustments presented an adjusted R 2 greater than 0.7, showing a close relationship between the biomass and the explanatory variables considered. The contribution of the height variable was important since 60% of the selected functions incorporated this explanatory variable, which contradicts what was indicated by Montagu et al. (2005) and reinforces the points made by António et al. (2007). At the same time, the density of the wood was presented in 75% of the selected functions, in accordance with what was expressed by Kuyah et al. (2012); nevertheless, it was not possible to relate the density of the wood to the DBH, using a probability density function representing this variable.
The values of the universal exponent were lower than the theoretical value (8/3) in 70% of the selected functions, as was the case for Zianis and Mencuccini (2004), Pilli et al. (2006) and Kuyah et al. (2013).  (Table 6), the influence of the number of trees per hectare on the quantification of the aerial biomass of the stem and total is highlighted, due to the fact that the greatest increases are achieved with higher planting densities. On the other hand, in the remaining components, the greatest increases are frequently found in the lower planting densities.
The estimation of each component (Table 6) and its subsequent addition differs slightly from the estimates of the total by an average of 0.9% with a range that fluctuates between 0.1 and 2.4%, confirming the consistency among the selected functions.
The recorded increases in the total aerial count coincide with those reported by Zewdie et al. (2009), not so in the remaining components, which evidences a differentiated distribution of biomass among the components between the two studies. Peréz-Cruzado and Rodriguez-Soalleiro (2011) obtained an increase in total biomass that fluctuated between 13.9 y 14.6 Mg ha -1 año -1 , which indicates some similarity with the results of this research.
The plantation density used as a covariate in the analysis of variance was highly significant for the total aerial and stem component, indicating that this covariate has direct implications for determining the increase in biomass for these components. In the remaining components there was no statistical significance, therefore, the number of trees per hectare considered in this research, did not significantly affect the increase in biomass of leaves, green branches and dry branches.

CONCLUSIONS
The analyzes carried out allow us to conclude that: • The functions selected corresponded to those adjusted by location, described in Table 3, since they presented the least difference from the AIC.