Study area

The research was carried out in 87 ha planted with P. chiapensis, established in El Campanario, located in the town of Chicuaco, Tlatlauquitepec municipality, Puebla (Figure 1). The information comes from 35 trees sampled and felled in 2014, systematically distributed in ages of 3 to 7 years. These plantations are located between 19°46’10.6’’ N and 97°28’34.6’’ W. The plants come from seeds of selected trees of the region, produced in three certified forest nurseries: Mazatepec (Tlatlauquitepec), Esperanza de la Mañana (Cuetzalan) and Atoluca (Teziutlán); they were placed on land that was previously used for fruit and coffee production (^{Fierros et al., 2018}).

Figure 1 Location of the study area. 

The plantation (PFC) was established at a density of 1 100 trees ha^-1, in real frame with a spacing of 4 m between rows and 2.25 m between plants. The climate is semi-warm humid with rain throughout the year, with an average annual temperature of 17 °C and average annual precipitation of 2 350 mm. The predominant soils in Tlatltauquitepec are Andosol with 68 %: Acrisol with 12 %; Phaeozem with 5.5 % and Leptosol with 2 % (^{Inegi, 2009}).

Biomass sampling by components

With the direct methodology, 35 trees of P. chiapensis of different ages (3, 5, 6 and 7 years old) were sampled in 2014, for which individuals without physical damage were selected and that covered all the categories of diameters and heights. The felling took place at 5 cm above ground level; subsequently, each tree was measured the following variables: total height (H in m measured with a 30 m Truper measuring tape) and normal diameter (D in cm measured with a 50 cm Haglof Mantax Blue caliper).

In the felled individuals the stem, the branches and the foliage were separated, then the bole was sectioned, the first log was cut to 1.20 m in length and the rest to 2.40 m until reaching the tip of the tree, the weight was recorded in green (kg), with a 120 kg Oken platform scale model K-1. For the first log, two slices were obtained (lower and upper) and for the others only the upper one, with an average of 5 cm in thickness, noting the diameter with bark (DCC, for its acronym in Spanish) and the weight in green (kg) with a scale Torrey^® electronics L-EQ-10 series, 10 kg. For the total green weight of the branches and foliage, random samples of 1 kg and 1/2 kg of branches and foliage were taken, respectively. In the laboratory the dry weight was determined by components, after being dried in a Sheldon model 1675-S kiln, at 75 °C, until constant dry weight was achieved.

Estimation of biomass by component

Biomass was estimated for stem (B_F), branches (B_R) and foliage (B_H), based on the methodology suggested by ^{Repola and Ulvcrona (2014)} as a function of the ratio estimator (r), in the dry weight ratio ( ps) and the green weight (pv) of the samples of the components. The estimator of r was used to convert the total green weight by components (PV_i) to biomass. B_F, B_R and B_H were calculated using equation (1):

Where:

B _i = Biomass per components

PV _i = Total green weight per components

r = Ratio estimator

Constant and variable biomass expansion factor

The total aerial biomass can be estimated by a constant or variable biomass expansion factor (FEB), by converting the volume (V in m³) to biomass (B_T in kg). Therefore, it is assumed that the V is a direct linear function of D² × H, this makes it possible to calculate the total aerial biomass as a direct ratio of the total volume of the plant multiplied by a constant FEB with the equation (2) (^{Hernández et al., 2017}):

Where:

B _T = Total aerial biomass (kg)

ϑ = Constant FEB

V = Total volume of the stem (m³) estimated with the ^{Schumacher and Hall type volume equation (1933)}, generated for the same species studied and plantation by ^{Martínez (2016)}

The V function presented an adjusted coefficient of determination value (Radj2) of 99.66 % and root mean square error (RMSE) of 0.0058. The V was estimated by equation (3):

Where:

V = Total volume of the stem (m³)

D = Normal diameter (cm)

H = Total height (m)

From the above reasoning, generating a variable FEB may be more realistic than a constant FEB, since the latter assumes, precisely, that the proportion of biomass remains constant, which is not completely true, because at different ages and site quality, the FEB presents a significant differential variation in a tree (^{Enes and Fonseca, 2014}). The variable FEB is a way to analyze how the biomass varies depending on the size (D and H) of the tree, and one way to generate it is from the relation of the equation (5) of total aerial biomass generated for the same species and plantation studied by ^{Martínez (2016)}, in which the function of total aerial biomass presented an adjusted coefficient of determination value (Radj2) of 98.44 % and root mean square error (RMSE) of 9.44 and equation (3), as expressed in the general equation (4) (^{Pajtík et al., 2008}).

Where:

α=α1α2

β=β1-β2

Where:

FEB = Variable biomass expansion factor

αi,  βi = Parameters of the B_T y V equations

B _T = Total aerial biomass (kg)

V = Total stem volume (m³)

The total aerial biomass is obtained by multiplying the constant and variable FEB by the estimated V for each tree measured in forest inventories, by means of equation (6) (^{Magalhães and Seifert, 2015}):

Where:

B _T = Total aerial biomass (kg)

FEB = Biomass expansion factor

V = Total stem volume (m³)

Aerial biomass distribution partition system

Although the estimation of the FEB allows estimating the total aerial biomass derived from a forest inventory (^{Magalhães and Seifert, 2015}), the distribution of the biomass by components of the individuals coming from a P. chiapensis plantation under management is still unknown. Therefore, an aerial biomass partition system was generated by the expression (7):

Where:

Bi = Biomass per components

λi = Biomass per components ratio in regard to B _T

B_T = Total aerial biomass (kg)

To know the distribution of the biomass in the tree components, a direct function of the total aerial biomass and a partition factor λi,was adjusted, as indicated in equation (8) (^{Aquino et al., 2015}):

Where:

Bi = Biomass per components

fi = Function that defines the biomass of the components

λi = Ratio of the biomass per components in regard to B _T

B_T = Total aerial biomass

ε = Random error

From which a system of equations is derived as follows:

Where:

B _F = Stem biomass

B _R = Branch biomass

B _H = Foliage biomass

B _T = Total aerial biomass

g(λ1,BT), h(λ2,BT), i(λ3,BT) = Functions that define the biomass of the components

Therefore, the additivity is guaranteed with the linear restrictions on the regression coefficients, in such a way that the sum of the biomass of the components is equal to the total aerial biomass, by means of equation (12) (^{Parresol, 2001}):

Fitting methods of the models

The fit of the variable expansion factor and the aerial biomass partition system were made with the SUR method or Seemingly Unrelated Regressions (^{SAS, 2011}). The SUR procedure homogenized and optimized the standard error of the parameters; with this, the complete compatibility in the aerial biomass partition system was obtained, and a lower variance was generated as well as efficient results in the predictions (^{Parresol, 2001}).

Characteristics of the forest attributes of Pinus chiapensis

The normal diameter of the sampled trees was recorded in a range of 3.20 to 26.50 cm, total height of 4.25 to 17.05 m and total aerial biomass 2.46 to 220.52 kg (Table 1). The stem was the component with a large increase in the proportion of biomass by increasing the diameter and total height. The validity of the factors of expansion of biomass and the system of participation of aerial biomass are restricted to the minimum and maximum values of the dasometric variables, this implies that they can only be applied for the species studied and for the same region.

Constant biomass expansion factor

The results of the constant FEB adjustment statistics showed a value of 97.51 % in the adjusted coefficient of determination (Radj2) and an average error of 10.9183 kg in the root of the mean square of the error (RMSE). The value of the estimator of the parameter θ showed high significance (p <0.0001). So the equation (2) to estimate the total aerial biomass as a function of a constant FEB (ϑ) is as follows:

Where:

B_T = Total aerial biomass

V = Total volume of the stem with bark (m³)

The estimated value of the parameter ϑ representing the constant FEB was 709.8016, which suggests that for each m³ there are 709 kg of total aerial biomass in P. chiapensis.

In conifers, dry stem biomass and stem volume have an approximately constant FEB of 500 kg m³; the difference of this value gives an idea of the proportion of branches and leaves. With the focus of this study, ^{Cruz (2007)} estimated, in managed forests of Zacualtipán, Hidalgo, a value of 623.2698 kg m³ for Pinus teocote Schltdl. & Cham; while, for hardwoods: Liquidambar macrophylla Oerst., Quercus spp, Clethra mexicana D.C., Prunus serotina Ehrh ssp. capuli (Cav.) Mc Vaugh, Alnus jorullensis Kunth subsp. lutea Furlow, Carpinus caroliniana Walter and Viburnum ciliatum Greenm., the estimated FEB was 905.1358 kg m³. The author reported a greater proportion of branch biomass with respect to stem biomass.

Something similar arises ^{Aquino (2014)} with FEB values of 1 358.5 and 998.56 kg m³ for the tropical species Cupania dentata DC., Alchornea latifolia Sw. and Inga punctata Willd, respectively. In the work done by ^{Chávez-Pascual et al. (2013)} reported an average FEB of 443.53 for P. chiapensis, in natural stands in the Sierra Norte de Oaxaca under forest exploitation. The authors point out that the branch and foliage biomass represented 7.5 % of the total aerial biomass, while in this study it was 31 % and an FEB of 709.9016.

Undoubtedly, variations in branch and foliage biomass are more influenced by young ages, physiological and morphological functions, and applied silvicultural practices (weed control and pruning) to P. chiapensis trees. The latter as those observed during the data recording: at ages 3 to 7, all trees were pruned and vegetation control measures were observed, which leads to the development of wide and well-shaped crowns. ^{Fierros-Mateo et al. (2017)} documented for the same plantation that silvicultural treatments such as pruning and weed control applied to the mass of P. chiapensis at an early age (first year after planting) give rise to high growth rates, and, consequently, a robust development of crowns that allow a greater photosynthetic efficiency for the transformation to aerial biomass.

Variable biomass expansion factor

The variable FEB expressed by equation (13) was obtained by substituting the values of the parameters of the total aerial biomass equation and the total stem volume by the expression (4):

With the equation (13) it is possible to observe how the variable FEB is modified according to the dimensions of the trees (Figure 2), which leads to more accurate biomass predictions (^{Chávez-Pascual et al., 2013}), since they reflect indirectly changes the proportion of the components.

Figure 2 Expansion factors of variable biomass by diametric categories and sampled heights, estimated from the equation 15. 

The variable FEB by diametric category refers to the changes in the balance of the stem biomass with respect to branch and foliage biomass. As the D and H increases the biomass increases, but the variable FEB tends to stabilize in diameter categories (CD) of 20 cm of D and H of 15 m, since the shaft of the tree begins to concentrate a greater biomass possibly in this stage, the level of contribution of the branch to the total biomass of the tree is stabilized and the percentage of foliage continues to decrease. It is likely that this is related to limited light resources under closed canopy conditions and as a consequence the limitations for foliage survival (^{Konôpka et al., 2015}). ^{Silva and Návar (2010)} and ^{Chávez-Pascual et al. (2013)} indicated the same variation, because variable FEBs are dependent on tree dimensions, such as D and H.

Such behavior is similar to that described by ^{Chávez et al. (2013)} for natural stands under management of P. chiapensis in the Sierra Norte de Oaxaca, and as recorded by ^{Hernández et al. (2017)} for Eucalyptus urophylla S. T. Blake in commercial forest plantations aged 1 to 7 years in Humanguillo, Tabasco.

^{Enes and Fonseca (2014)} recorded a similar tendency of variable FEB for natural stands of Pinus pinaster Ait in the North of Portugal. According to ^{Konôpka et al. (2015)}, the variable FEB decreases progressively as a contribution of tree components that changes with the increase in tree size (D and H), in which a significant change is observed for smaller individuals.

Undoubtedly, these changes obey the strategy of changing growth from early stages (where the first intention is to occupy enough space on the ground) to later ones (to compete with neighboring trees for light). ^{Pajtík et al. (2008)} mention that the amount of light captured by the canopy in the young trees is 100 % and the branches, therefore, represent more branch biomass, which explains a higher variable FEB. However, after the canopy closes, the proportion of branch biomass decreases significantly along with the amount of light that is intercepted by the canopy; in consequence, the variable FEB, because the stem begins to concentrate more biomass.

Figure 3 shows that the total aerial biomass calculated with the variable biomass expansion factor is more conservative, according to the trend of total aerial biomass observed.

Figure 3 Relation of the total aerial biomass predicted with the constant and variable FEB as a function of the observed total aerial biomass (kg). 

For future studies in the plantations it will be very difficult to directly obtain the total aerial biomass; therefore, it is suggested to use the variable biomass expansion factor since it provides greater reliability, with the purpose of estimating total aerial biomass indirectly for trees measured in forest inventories.

Biomass partition systems

Table 2 summarizes the goodness of fit statistics of the biomass partition system: root mean error square (RMSE), adjusted coefficient of determination (R² _adj.) and parameter estimators. The results indicated that the stem biomass showed the highest value in the R² _adj. with 99.56 %, followed by the foliage biomass with 97.28 % and finally the biomass of branches with 96.37 %.

The independent variables of D and H were well adjusted to the biomass data, explaining a variation greater than 96 % for the prediction of the biomass by components. While, the values in RMSE were 3.21, 2.76 and 1.02 for biomass of stem, branches and foliage, respectively. The γi parameters are highly significant in the hypothesis test, given that their associated probability is less than the 5 % level of significance (α = 0.05). The γi values represent the proportion of biomass per component, with respect to the total aerial biomass.

The values of γi indicate that the highest accumulation of biomass is concentrated in the stem with 69 %, followed by 21 % in branches and 10 % for the biomass of the foliage (Table 3). These results are similar to those of ^{Soriano et al. (2015)} with the biomass proportions for Pinus patula Schiede ex Schltdl. et Cham.: stem (68.2 %), branches (14.3 %), foliage (8.2 %) and bark (9.3 %), which is explained by the fact that both species have partial (rapid) growth rates and share mesophilous forest habitats.

^{Martínez et al. (2016)} determined 81 % for trunk, 14 % branches and 5 % foliage in P. ayacahuite var veitchii Shaw in natural stands of Ixtlán, Oaxaca. This distribution differs from the cited studies reported by ^{Rodríguez et al. (2012)} for a 14 years plantation of P. patula, whose proportion of stem biomass was 92.9 %, of branches of 4.7 % and foliage of 2.4 %. The above shows that the foliage proportion of P. patula has greater photosynthetic efficiency with respect to Pinus chiapensis. However, it can also be attributed to the thinnings made in the plantation, which generated more concentration in stem biomass. This agrees with the studies of ^{Chávez-Pascual et al. (2013)}, who registered distributions of stem biomass of 92.5 %, branches with 6.3 % and foliage with 1.2 % for stands of P. chiapensis under management.

The distribution of biomass from tropical climate species such as Cupania dentata DC., Alchornea latifolia Sw. and Inga punctata Willd. contrasts with conifers since they present, generally, a greater concentration of biomass of branches and foliage (54.32, 50.58, 59.26 %, respectively) than in stem biomass (40.69, 38.53, 33.65 %, respectively) (^{Aquino et al., 2015}).

A system of equations for individual trees was formed in the following way: equation (6) calculates the total aerial biomass at the tree level, which multiplies the variable biomass expansion factor (13) by the total stem volume (3).

Then, once the total aerial biomass is estimated, it is possible to know the proportion by components, by substituting the values γi estimated in the aerial biomass partition system, by means of expressions 9, 10 and 11. With this system the additivity is fulfilled (12), also allows to build a table of yield of total aerial biomass and by components, based on the D and H (Table 3).