Study Area

The research was carried out in plantations aged 22 years, located in two ejidos of Saltillo, Coahuila. The first one, called Cuauhtémoc, is located at the coordinates 25°16'45.60" N and 100°59'20.49" W and an altitude of 2 162 m; and the second, named El Recreo, located at the coordinates of 25°14'43.94" N and 101°04'26.47" W and an altitude of 1 982 m. In the area there are pine forests, microphyllous and rosetophyllous desert shrubs; the climate is arid semi-warm (BS_ohw) and semi-arid temperate (BS₁kw), with summer rains, a mean annual precipitation of 125 to 400 mm, a mean annual temperature of 14 to 18 °C, and Lithosol and Calcic Xerosol soils (^{García, 1998}).

Indirect method for estimating the biomass

The Adelaide method (^{Foroughbakhch et al., 1996}) was utilized. An average tree in terms of diameter and height was selected from the plantation and divided into three sections, and the (Adelaide) method was applied to each section. A representative branch was cut only once. Later, the number of times that the representative branch of each section could be contained in its respective section of the tree was calculated. 50 healthy trees that were considered representative of the categories of normal diameter and height were sampled for each species. In each individual, the normal diameter (cm) and the smallest and largest diameter of each section (cm) were measured with a Forestry Suppliers Metric Fabric Diameter Tape Model 283D/5M, and the heights of each section (m) were measured with a Truper FH-5ME measuring tape.

The representative branch was carried to the laboratory and placed in a Blue M. drying oven at a temperature of 105 °C until it reached its constant weight (^{Schlegel et al., 2000}); after drying, the dry weight was obtained with a Torrey Pizza Controller PZC-5 scale, with a capacity for 5 kg and a 1 g accuracy. Once the value of the dry weight of each representative branch had been calculated, it was multiplied by the estimated number of branches of the corresponding section; the three sections were added to obtain the dry weight of the leaves-branches of each tree. The dry weight of the stem was obtained by multiplying the volume by the basic density. The stem volume was determined using the Smalian formula (1), and the basal area (g), using the second formula (2).

Where:

g = Basal area (m²)

g ₁ = Smallest basal area of the section (m²)

g ₂ = Largest basal area of the section (m²)

L = Log length of the section (m)

D = Diameter (m)

The basic density in P. cembroides is 450 kg m^-3 (^{Ordoñez et al., 2015}) and 494 kg m^-3 in P. halepensis (^{Ruano et al., 2012}). The total dry weight of the tree was calculated by adding the dry weight of leaves-branches and the dry weight of the stem (kg).

Allometric model adjustment and selection

The estimation of the biomass by component (leaves-stem, branches and total) was carried out using logarithmic regression models (Table 1), which were adjusted in accordance with the method of least squares, using the R Project statistical package (^{R Core Team, 2017}). The logarithmic transformation is of great utility, since it corrects the heterogeneity of the variance of the independent variable with respect to the data of the dependent variable (^{Brown et al., 1989}). It is necessary to make the transformation, because the variance is highly unstable in arithmetic units, and the logarithmic transformation rectifies the problem (^{Baskerville, 1972}). Six models were evaluated using the following statistics: adjusted coefficient of determination (_adjR²), standard error (Syx) and significance of the regression parameters (P < 0.05).

Parameters of the adjusted models

Only models 4 and 6 showed no significance (P > 0.05) in the estimation parameters for BLB and TB; the estimation parameters for SB were also not significant in models 3, 5 and 6. Using the same independent variable -normal diameter-, but different models for the total biomass, ^{Díaz et al. (2007)} and ^{Rodríguez-Ortiz et al. (2012)} cite smaller parameters than the ones in this study (P. cembroides), of β₀= 0.035 and 0.001 and β₁ = 2.691 and 1.980, respectively, in P. patula Schiede ex Schltdl. & Cham. (Table 3).

In Pinus halepensis, models 1 and 2 produced parameters with significant differences (P < 0.05), compared to the rest of the models, for BLB and TB; as for the SB, the parameters of models 1, 2 and 6 exhibited significant differences (P < 0.05), unlike models 3, 4 and 5. Model 2 presented some similarity in the parameters of (β₁,) 0.444 for BLB, (β₁,) 0.633 for SB, and (β₁,) 0.540 for TB (Table 4).

^{Méndez-González et al. (2011)} used the same independent variables (ND² × H) to predict the TB; their parameters were different from β₀= 4.660, β₄= 0.006 for the biomass of leaves and branches, β₀,= 6.183, β₁,= 0.009 for stem biomass, and β₀ = 10.843, β1= 0.014 for total biomass in P. devoniana. ^{López (2012)} pointed out the similarity of the negative values in the origins of ordinate, and positive values in the slopes of BLB and SB in the species that is also the object of the present study (P. halepensis); however, the opposite is true for the TB, as both the origin of ordinate and the slope proved to be positive in this study (P. halepensis).

Biomass by component in Pinus cembroides and P. halepensis

Of the six tested models, in the case of P. cembroides model 3 was selected because it presented the best statistics for BLB and TB, with an adjusted coefficient of determination (_adjR²) above 0.90; on the other hand, the model selected for SB was No. 4 (_adjR² of 0.75), with a mean _adjR² of 0.86 for BLB, SB and TB. However, in the case of P. halepensis, model 2 was selected for BLB, SB and TB, with a mean _adjR² of 0.79 (Table 5).

Based on the same model (3) ^{Álvarez (2008)} estimated an _adjR² of less than 0.93, as well as an error of 0.67 kg in TB for Centrolobium tomentosum Guill. ex Benth. Other studies have cited the same _adjR² of 0.94 for TB, as well as a lower error of 0.33 kg (^{Schlegel, 2001}; ^{Aguirre-Calderón and Jiménez-Pérez, 2011}). Using the normal diameter as the independent variable, ^{Xiao and Ceulemans (2004)} obtained a better fit and larger error for P. sylvestris L. (_adjR² of 0.97, with an error of 2.61 kg), compared to the P. cembroides of this study. ^{Méndez-González et al. (2011)} document a mean R² of 0.87 in P. pseudostrobus, a value similar to that estimated in this study (for P. cembroides).

In the same species (P. halepensis) ^{Domingo et al. (2016)} and ^{López (2012)} cite better adjustments, with a higher R², of 0.77, 0.94 and 0.89 in BLB, SB and TB, and errors of more than 12.59 kg. Conversely, ^{Návar (2011)} documents a lower adjustment of 0.60 and 0.81 for BLB and TB, and a higher adjustment for SB (R² 0.87), as well as errors of over 9.4 kg, in the species of this study, P. halepensis. However, ^{Rodríguez-Ortiz et al. (2012)} found an error of less than 5.0 kg and an adjustment of more than 0.87 in the TB of P. patula. ^{Montero et al. (2005)} registered a mean _adjR² of 0.85, which represents a higher adjustment than that obtained for P. halepensis, with an error of < 0.92 kg.

Figures 1A - 1F show the adjustment curves. Among the SB components there was a larger dispersion of estimated values with respect to those observed in P. cembroides, due to their variation coefficient (VC) of 11.94 %. While in P. halepensis the larger dispersion occurred in the component of BLB, with a VC of 21.81 %. In addition, both species had a lower dispersion in the values for TB.

Biomasa hojas-ramas = Biomass of leaves and branches; Biomasa fuste = Stem biomass; Biomasa total = Total biomass; Dn = DN; Observados = Observed; Esperados = Estimated

Figure 1 Observed and estimated biomass of leaves and branches, stem biomass and total biomass in trees from a Pinus cembroides Zucc. (A - C) and Pinus halepensis Mill (D - F) plantation. 

Model 3 registered a higher error in the 10 cm category for BLB (Figure 2A), unlike in the 5 cm category for TB (Figure 2C). As for the SB, (Figure 2B) Model 4 had the highest error in the 5 cm category. However, for P. halepensis, model 2 obtained a lower error in category 15 of the stem component (Figure 2E) than in the rest of categories. For BLB (Figure 2D) and TB (Figure 2F), the model had lower errors in the 10 cm categories.

Bhr = BLB; Bf = SB; Bt= TB; Biomasa hojas-ramas = Biomass of leaves and branches; Biomasa fuste = Stem biomass; Biomasa total = Total biomass; Categoría diamétrica = Diameter category; est = Estimated; obs = Observed P. cembroides: BLB and TB = Biomass estimated with Model 3; SB = Biomass estimated with Model 4; P. halepensis: BLB, SB and TB = Biomass estimated using model 2.

Figure 2 Percentage error of estimation of the biomass per component in each diameter category of Pinus cembroides Zucc. (A - C) and P. halepensis Mill (D - F).