Study area

The study was carried out in three forest plantations of Cedrela odorata species (Figure 1): 1) Experimental Site Costa de Jalisco La Huerta, municipality, Jalisco (19°31'15" N and 104°32'00" W; 298 masl), with a predominance of medium-textured haplic Phaeozem soils, and the climate corresponds to the Aw₁(w) type with annual rainfall of 1 012 mm; 2) El Molino farm, Casimiro Castillo municipality, Jalisco (19º32'05'' N and 104º26'20" W; 412 masl); the soils are of the distric Cambisol type, with a medium texture; the climate is Aw₂(w) with an average annual rainfall of 1 496 mm; and 3) Tecomán Experimental Station, Tecomán municipality, Colima (18°58'01" N and 103°50'32" W; 60 masl); the soil is classified as a medium-textured salic Calcisol, and the prevalent climate is BS1(h')w(w), with 790 mm of mean annual precipitation (^{Ruiz et al., 2012}; ^{INEGI, 2016}). The predominant natural vegetation type in the area of influence of the properties corresponds to medium subdeciduous forest (VSa/SMS and VSA/SMS, i.e. SDTF and MSDF secondary arboreal vegetation).

Figure 1 Location of the three Cedrela odorata L. forest plantations. 

Sample tree selection

In the selection of the individuals that made up the sample, only those trees marked to be felled in the thinnings that are part of the management of the plantations were considered. The selective process began with the classification of the trees by 5 cm diameter classes. Since it was not a sampling exercise, healthy individuals without deformities were identified, from which 27 trees were selected (randomly), covering, proportionally, the range of diameter classes present in the three plantations (^{Ruiz-Aquino et al., 2014}). With the trees still standing, the normal diameter (ND in cm) was measured with a diametric tape (Forestry Suppliers, 5 m). The individual trees were directionally felled with a chainsaw. In order to obtain its total height (TH, in m), the height of the stump was determined with a flexometer (Pretul, metalic metric tape, 5 m), and the tree was measured lengthwise with a longimeter (Truper^®, 30 m fiberglass tape), from the base of the trunk to the apex of the crown, and the height of the clean trunk and its total length were also recorded.

Aerial biomass sampling

The methodology used to sample the aboveground biomass was that described by Díaz et al. and ^{Figueroa-Navarro et al. (2010)}. In order to facilitate their use and management after felling, the aerial components of the tree (trunk, branches and foliage) were separated and sectioned as follows:1) logs 1.5 to 2.5 m long (base of stem and stump); 2) boles 1.0 to 1.25 m long (upper part of the stem and thick branches); 3) 1.0 m long firewood (thin branches and shaft tip); and 4) lower, middle and upper canopy foliage (leaves, fine twigs, flowers and fruits).

The wet weight of the structural components was recorded in the field and separately by component; for logs and noles, the weight of each section was obtained, from which a sample (5 cm wide slice) was taken; The firewood was arranged and weighed by loads, from each load two to six samples (10 cm long segments) were randomly extracted; while for the foliage, the collected material was weighed in three portions (lower, middle and upper part of the canopy), from which a sample (0.1 to 1.0 kg) was obtained at random. The sections were weighed with an electronic scale (Torrey CRS-500) with a capacity of 500 kg ± 0.1 kg; an electronic scale (Torrey PCR-20) with a capacity of 20 kg ± 0.01 kg was used to weigh the samples. The wet weight of the stump was estimated as follows: its volume was calculated with the cylinder formula, and a green density equal to that present in the first log was assumed.

Determination of aerial biomass

Once the wet weight was obtained in the field, the collected material was transferred to the laboratory for dehydration to constant weight in an electronic oven (Felisa, Fe-291ad); wood samples were dried at 70 °C (12-15 days), and foliage samples, at 35-40 °C (5 days); the dry weight was recorded with an accuracy of 1.0 g. The dry weight of each section was estimated by multiplying its wet weight by the factor resulting from the dry weight ratio: wet weight of the respective sample. The total aerial biomass of the tree and its structural components was calculated by adding the dry weight of its corresponding sections (^{Acosta-Mireles et al., 2002}; ^{Díaz et al., 2007}; ^{Lim et al., 2013}; ^{Cutini et al., 2013}; ^{Rueda et al., 2014}).

Determination of carbon concentration

After the dry weight determination, component samples were taken from five randomly selected trees; a 100 g subsample was extracted from each one, ground and sent to the laboratory to determine their carbon concentration in a LECO TruSpec Micro equipment, which uses a combination of a continuous-flow carrier gas system and an infrared light system. With the results of the analysis, a biomass-to-carbon conversion factor (CF) was obtained for each component. The carbon concentration of the components was estimated as follows:

Where:

CCC _i = Carbon concentration of component i (logs, logs, bolls, firewood and foliage; in kg)

BC _i = Biomass of component i (kg)

FC _i = Conversion factor of component i

The total carbon concentration of each tree is the sum of the carbon concentration of its components.

Model adjustment

Allometric models estimate biomass based exclusively on the normal diameter (^{Návar et al., 2004}; ^{Avendaño et al., 2009}). However, several authors recommend including height, since it reduces the standard error, avoids overestimations and improves the fit of the models (^{Figueroa-Navarro et al., 2010}; ^{Ruiz et al., 2011}; ^{Rodríguez et al., 2012})

Linear and nonlinear models cited in the specialized literature were tested to relate aboveground biomass (BA) to the variables normal diameter (ND) and total height (TH) or both (ND·TH; ND ² ·TH). According to the analysis performed, the best fit was obtained with the potential model expressed in its normal form as:

Where:

AB = Aerial biomass (kg)

ND = Normal diameter (cm)

β ₀ and β ₁ = Estimated parameters of the function

This model is one of the most widely used to determine aboveground biomass (^{Acosta-Mireles et al., 2002}; ^{Díaz et al., 2007}; ^{Gayoso et al., 2002}). This preference is because it expresses a proportionality of the relative increases between two tree dimensions and is broadly consistent for different growth forms (^{Gayoso et al., 2002}).

In addition to obtaining the equation to determine the total aerial biomass of the tree, an equation for the biomass of its structural components was adjusted. In order to estimate the concentration of carbon in the aerial biomass of the tree using the same model, an equation was fitted that correlates the carbon concentration with the normal diameter of the tree.

The equations were fitted, statistically analyzed and diagnosed using the MODEL and NLIN procedures in SAS software (^{SAS Institute Inc., 2011}). The criteria for rating the goodness-of-fit of the system that best explain the variability of the biomass data are based on a numerical and graphical analysis of the residuals (^{Gómez-Díaz et al, 2011}). In the numerical case, statistics frequently used in biometrics were used, such as the adjusted coefficient of determination (R ² _a ), the root mean square of the error (RMSE), the coefficient of variation (CV) and the significance of the parameters of each equation (^{Álvarez et al., 2005}; ^{Rojo et al., 2005}). In addition, to validate the reliability of the results of the selected equation, the regression assumptions were verified analytically: normality (Shaphiro-Wilk, Kolmogorov-Smirnov, Cramer-von Mises and Anderson-Darling tests), independence (Durbin-Watson d test) and homoscedasticity (White and Breusch-Pagan tests) of the data (^{Fonseca et al., 2011}).

Estimation of tree biomass

The normal diameter of the sampled trees ranged from 4.0 to 28.0 cm; their aboveground biomass ranged from 2.42 to 275.53 kg, with a mean of 41.06 kg and standard deviation of 53.68 kg. The distribution of the aerial biomass of the tree is shown in Table 1; it can be seen that the highest average proportion corresponded to the trunk (logs and boles), with 71.37 %, followed by branches (firewood) and foliage with 21.96 and 6.67 %, respectively. The average percentage of logs (trunks), where the greatest proportion of biomass is concentrated, was similar to that cited for hardwood trees (49.1 %) (^{Soriano, 2014}; ^{Soriano-Luna et al., 2015}).

The equation determined to estimate the aerial biomass of C. odorata was expressed as follows:

Where:

AB = Aerial biomass (kg)

ND = Normal diameter (cm)

The exponential trend of the equation coincides with what has been documented for Pinus hartwegii Lindl. (^{Carrillo et al., 2016}). The equation analysis showed the following statistical indicators: adjusted coefficient of determination, R ² _a =0.9787; coefficient of variation, CV=390.449; and root mean square error, RMSE=7.487. Figure 2 shows the scatter plot and the relationship between the variables ND and AB of the trees.

Biomasa aérea total = Total aerial biomass; Diámetro normal = Normal diameter.

Figure 2 Scatter plot and relationship between the normal diameter and the total aerial biomass of Cedrela odorata L. trees. 

The different tests used for the analytical diagnosis of the model showed that the regression assumptions are verified, which validates the statistical analyses performed. Table 2 shows the values of the statistics.

In reference to the assumption of normality, the four tests indicated that the residuals have a normal distribution (p-value > 0.05); for that of independence, the Durbin-Watson d test (d _U < 1.6996 < 4-d _U ) showed that the residuals are not correlated; and for homoscedasticity, both the White test (Chi ² > 3.91; p-value > 0.05) and the Breusch-Pagan test (Chi² > 2.49; p-value > 0.05) showed that there are no heteroscedasticity issues. The same model was fitted and an equation was generated for each component, whose parameters and regression estimators are summarized in Table 3.

Figure 3 illustrates the scatter plots and the relationship of normal diameter with biomass by component of Cedrela odorata; the best fit of the model corresponded to the stem (biomass of logs and boles), with an R ² _a =0.9918. However, total biomass values were approximately one third of those reported for species such as Alnus acuminata Kunth (^{Díaz-Ríos et al., 2016}) and Abies religiosa (Kunth) Schltdl. et Cham. (^{Avendaño et al., 2009}). On the other hand, the total biomass coincides with that cited for Pinus hartwegii (^{Carrillo et al., 2016}).

Diámetro normal = Normal diameter; Biomasa en fuste = Stem biomass;Biomasa en leñas = Firewood biomass; Biomasa en follaje = Foliage biomass; Biomasa en árbol = Tree biomass.BAtotal = Total biomass estimated with model 1; BAft = Stem biomass; BArm = Branch biomass; BAfj = Foliage biomass; BAtotal = Total aerial biomass calculated by means of the sum of the biomass estimated for each of its components.

Figure 3 Relationship between normal diameter and aerial biomass by structural component. 

The graphs in Figure 3, plot not only the trend line obtained by fitting the potential model for the biomass of each component (solid line) but also the trend line resulting from the biomass partitioning (dotted line). The graph corresponding to the biomass of the stem, as in the case of the foliage, does not show significant differences in the behavior of both trends, while for the branches the differences are more evident, which could be due to the problems of normality in the data of this component.

Likewise, in the graph corresponding to total aboveground biomass, both the biomass estimated with Equation 1 and that calculated by adding the biomass of its components show very similar trend lines. This reflects a biological logic in the distribution of the data, since the greatest proportion of the tree biomass is concentrated in the wood of the trunk and this exerts a greater influence on the model, both in the variability and in the normality of the data. Specifically, the trend defined for foliage is similar to that reported for Abies religiosa, although in this case, the model defined is polynomial (^{Flores-Nieves et al., 2011}).

Regarding the relationship between stem biomass and normal diameter, the trend is similar to that presented by ^{Flores-Nieves et al. (2011)} and even fits an exponential model. However, it is important to consider that, in some cases, the biomass correlation is better defined by the tree height (^{Chou and Gutiérrez-Espeleta, 2013}).

Estimation of carbon concentration

According to the analysis of the five sampled trees, whose carbon concentration by component is shown in Table 4, the biomass to carbon conversion factor (CF) is as follows= for the stem sCF=0.4688, branches bCF=0.4791, foliage lCF=0.4335 and for the tree tCF=0.4686. These values are slightly lower than those recorded for other species such as Pinus hartwegii Lindl. (^{Carrillo et al., 2016}). However, they coincide with the carbon concentration of 7-year old pine and second vegetation forests (^{Figueroa-Navarro et al., 2005}).

In order to calculate more accurately the carbon concentration of the trees, the specific conversion factor for the biomass per component was used, and, with the sum of these values, the carbon concentration of each sampled tree was obtained. The average carbon distribution was 71.33 % for the stems, 22.49 % for the branches and 6.18 % for the foliage. By fitting the same model used for aerial biomass, the equation determined for estimating the carbon concentration of C. odorata was expressed as follows:

Where:

CC = Carbon concentration (kg)

ND = Normal diameter (cm)

The equation analysis showed the following statistical indicators: adjusted coefficient of determination, R ² _a =0.9783; coefficient of variation, CV=391.503 and root mean square error, RMSE=3.7115. Figure 4 shows the scatter plot and the relationship between the variables ND and CC concentration of the trees.

Concentración de carbono = Carbon concentration; Diámetro normal = Normal diameter; CC observado = Observed CC; CC estimado= Estimated CC.

Figure 4 Scatter plot and relationship between normal diameter and carbon concentration in Cedrela odorata L. trees.