Study area

The study area is located in the northwestern part of the state of Oaxaca, in the Sierra Norte region. Pinus ayacahuite is between 96° 27'31.278" north latitude and 17° 24' 01.286" west longitude in the community of Ixtlan de Juarez, Oaxaca. Its distribution includes 1 137 ha in altitudes of 2 680-2 960 m and is associated with P. patula Schl. et Cham, P. pseudostrobus Lindl and Quercus sp.

In 2013 12 circular sites (400 m²) randomly established and directed a density stands of trees and different forestry methods throughout the study area. In the sample units woodland inventory was performed to obtain the diameter and height structure, which served to distribute the sample trees to break down in proportion to the relative frequency.

Biomass sample

The obtaining biomass of each air compartment it was carried out following the methodology proposed by ^{Rodríguez-Ortiz et al. (2012)}. The destructive sample consisted of 30 trees, without deformities, representative of the categories in diameter and height; in each tree several variables inventory were measured (normal diameter (DN), total height (AT), length of clear bole (LFL), length of live crown (LCV), crown diameter (DC) and diameter of stump (DT ). The diameter was obtained with diameter tape (model 283D/20F, Jackson, MS, USA), lengths with longímetro® and height with electronic inclinometer (Haglóf EC II, Sweden). The trees were felled, sliced and separated by components (branches, foliage and wood with bark), using chainsaw (Husqvarna® 50 cm).

Estimating biomass of branches and leaves

The nine samples per tree were taken (three in each section of the cup), in which leaves and branches were separated by placing them in paper bags properly identified with progressive tree and branch numbers; was obtained green weight (PV, in g) of both components using a model Dhaus CS scale with capacity of 5 000 g.

The samples of leaves and branches dried in an oven model MemmertBeschichung/Loading-Moll 100-800 at an average temperature of 75 °C until the constant weight. With DHAUS CS model scale with capacity of 5 000 g dry weight it was recorded (PS, in gr) corresponding constant of each sample of leaves and branches. In total 30 samples of each component they were obtained. The estimate of biomass of branches and leaves and tree branch level was obtained by adjusting nonlinear regression models using the Nlin Method= Dud procedure of SAS statistical package (^{SAS Institute Inc., 2004}).

Estimation of biomass wood with bark

After removing branches and leaves of trees felled 30, each stem is sectioned into commercial logs of 2.57 and 1.25 m in length depending on the quality of each product. Before measuring each commercial trozathree slices of10 cm average thickness as a sample of each tree, which were identified and heavy instantly obtained for its green weight (PV, g). In each slice vernier measured with Scala mark to the nearest millimeter 222A®, thickness and diameter in different axes (cm) for fresh volume (VV, cm³). For their constant dry weight (PS, g) took to the drying oven at an average temperature of 105 °C. With these data the specific gravity (GE= PS/VV, g cm^-3), whose product with the volume of each log was obtained, generated stem biomass of each log and individual.

Estimating biomass component tree wood+bark level was performed using nonlinear regression models, using the same procedure and statistical package using variables easy field measurement.

Getting volume tables and biomass expansion factor

To obtain the volume table with and without bark, were adjusted regression models that helped predict the different volumes of trees, depending on variables easy field measurement (normal diameter, DN) and overall height, AT). The models were fitted using linear regression techniques using the GML procedure of SAS statistical package (^{SAS Institute Inc., 2004}); evaluated through their statistical values, coefficient of determination R², amount of residual mean square error (CME) and dispersion of waste. The biomass expansion factors were obtained by the ratio of total aboveground biomass and total tree bark.

Volume models with and without bark

The model volume with and without bark tree (VTcc and VTsc) for Pinus ayacahuite presented a good fit in their prediction parameters, with a coefficient of determination (R²) of 0.99 in both variabless, CME 0.034 in VTcc and 0.035 in VTsc and coefficient of variation of 13.7 and 15.9%, respectively. Both parameters of the equation showed significance of p≤ 0.0001. The relationship between volume and diameter of trees can be described by a quadratic linear function (Figure 1).

Figure 1 Relationship between normal diameter and volume with and without bark of Pinus ayacahuite of Ixtlan, Oaxaca. 

VT_CC= 0.0004670490 (DN²)+0.0000088023 (DN²xAT)

VT_SC= 0.000376587 (DN²) + 0.0000092893 (DN² x AT)

Where: VTCC, SC= total volume with bark and bark (m³), DN= normal diameter (cm), AT= total height (m).

The fit coefficients and other statistical models volume is substantially improved by involving, in addition to the DN, the AT generating highly reliable equations (R²= 0.99). The like P. ayacahuite, many species of cloud forest (^{Acosta et al, 2011)}, Pinus cooperi Blanco (^{Arroyo and Paredes, 2006)} and P. chiapensis (^{Chávez-Pascual et al, 2013)} have shown this improvement in their estimates.

Models to estimate biomass by air compartment

The regression model showed a good fit in different prediction parameters biomass branch level was the nonlinear model (1 and 2), with pseudo-R²= 0.81 in leaves and 0.74 in branches showing significance (p< 0.0001) in both models (Table 1).

Table 1 Nonlinear models for estimating biomass in Pinus ayacahuite branch level of Ixtlan, Oaxaca. 

BH= biomasa de hoja (kg); BR= biomasa en rama (kg); ABR= área basal de la rama (n/4xDB², cm²); DB= diámetro de base de la rama (cm); A= altura de inserción de la rama en el tallo (m); ß_0,1,2= coeficientes de regresión.

The estimate tree biomass level according to their compartments, according to the regression models showed high p-R² (0.91) in leaves and branches and 0.97 for biomass and aboveground stem (Table 2).

Table 2 Nonlinear models to estimate biomass components air a level tree Pinus chiapensis of Ixtlan, Oaxaca. 

BT= biomasa total aérea (kg); BH= biomasa en hojas (kg); BR= biomasa en ramas (kg) y BF= biomasa en tallo con corteza (kg). DC= diámetro de copa (m); AT= altura total (m); DN= diámetro normal (cm), ß_0,1,2= coeficientes de regresión.

The total biomass model that best fit the data was the considered the normal diameter and tree height as independent variables for this study. These match ^{Figueroa-Navarro et al. (2009)}, who indicate that both variables using statistical estimators inventory equations are improved.

Compartmental distribution of biomass and biomass expansion factors (FEB)

The average distribution of biomass by Pinus ayacahuite compartment for stem was 81%, 14% to branches and leaves 5%. The results show that a greater diameter greater accumulation of biomass in any of the compartments in question; however, small trees tend to allocate more to the compartments of leaves and branches.

The amount of air that total biomass was estimated to Pinus ayacahuite is in a range between 26.95 and 147.57 t ha¹, generated in the study area (1137 ha) between 30 644.49 and 167 788.36 tB. The largest proportion of biomass is on the stem (72.81 t ha^-1) and lowest in the foliage (3.3 t ha^-1) (Table 3).

Table 3 Estimated volume, biomass component and total air of Pinus chiapensis in Ixtlan, Oaxaca. 

^&Intervalos de confianza (95%) mediante la prueba t-Student, t_{α/2 (n-1)}.

The study shows that in the shaft is most (81%) of tree biomass, varied according to the size of the tree. ^{Diaz-Franco et al. (2007)} reported similar values (82% stem biomass) and ^{Figueroa-Navarro et al. (2009)}, found n range from 36 to 85% for Pinus patula Schl. et Cham. Some biomass values reported in other species such as Pinus pseudostrobus Lindl. (Commercial plantations), are in a range of 65.7 to 82%, depending on the location and age of the stand (^{Méndez-González et al., 2011}).

^{Jimenez (2010)} found an average of 65.31% stem biomass in P. hartwegii Lindl. and ^{Pacheco (2011)} reports similar values (63.25%). However, this distribution is low compared to other studies, for example; ^{Avendaño et al. (2007)} found that religious Abies religiosa Kunt Schltdl. et Cham, the average biomass of 81.27% shaft is, as ^{González (2008}) found 87.6% stem biomass 6 tree 67.2 cm diameter in P. maximinoi H. E. Moore, these reported values are Similar to P. ayacahuite under study.

The biomass sheets P. ayacahuite (species of interest) accounted for 5% of the total aboveground biomass with a constant behavior with respect to shaft diameter (about the diameter class 15 onwards). This value is different reporting ^{Rodríguez-Ortiz et al. (2012)} of 2.4% because the study was conducted in young stands.

The foliar biomass in trees younger ages reported 18% in Pinus patula (^{Díaz-Franco et al., 2007}). In Salto, Durango; ^{Pacheco et al. (2007)}, found 25% of foliar biomass plantation P. greggii Engelm of 6 years old. ^{González (2008)} reports a distribution of biomass in branches of 8.49% for P. maximinoi and 11.20% for P. oocarpa Shiede, these values are close or equal to P. ayacahuite (species under study). Other studies found high results, such ^{Jiménez (2010)} found 23.79% in P. hartwegii and ^{Pacheco (2011)} found 23.49% for P. patula.^{Gayoso et al. (2002)} note that the proportional distribution of biomass in the tree components, is associated with the characteristics of trees by species, the state of development and degree of silvicultural to exposed individuals interventions.

Aboveground biomass of the species of interest showed a range of 26.95 to 147.57 t ha^-1. Similar results 29.4 to 122.1 and average (39.36 57 t ha^-1) were reported for P. pseudostrobus Lindl. (^{Mendez-González et al, 2011}). In turn, ^{Gutiérrez and Lopera (2001)} estimated 87.2 and 446 tB ha^-1 in commercial plantations of P. patula of 6 and 29 years respectively. About ^{Rodríguez-Laguna et al. (2007)} found a ratio of546.90 kg biomass in trees normal diameter of 5 to 42 cm for P. pseudostrobus.

This variation between P. ayacahuite, P. patula and P. pseudostrobusoccurs under such values are of species, age, geographical location and different methodologies to those used for this study. This indicates that in commercial plantations of fast growing process biomass accumulation is faster than in natural forests. The increase in biomass depends mainly on soil and climatic conditions including the rate of return and depending on the responsiveness presenting the trees will grow and therefore their biomass in relation to carbon sequestration (^{Acosta et al., 2001}).

With the resulting model biomass expansion factor (FEB) it is possible to know the total biomass accumulated air from a tree, knowing is a function of the height and normal diameter. In this study the FEB presented a value of 470.9 kg m^-3 for an average normal diameter of 17.92 cm and a height of 16.2 m.

Where: FEB= biomass expansion factor (kg m^-3); AT=total height (m); DN = normal diameter (cm).

The biomass expansion factor (obtained in inventory), provided an estimate biomass aerial total of 470.9 kg per tree average tree in (17.92 cm diameter and total height 16.2 m) in the species of interest. These values agree with ^{Chávez-Pascual et al. (2013)} that determined 444.14 kg/ tree average size of 27.7 cm average diameter and total height of

23.3 m in P. chiapensis (Martínez) Andresen. On the other hand, ^{Silva-Arredondo and Návar-Cháidez (2010)} obtained from 0.55 to 0.98 t per tree in Pinus sp.