Study area

The study was performed in the Iztaccíhuatl-Popocatépetl National Park, which is located at the Eje Neovolcánico Transversal, between 21°11’58’’ North and 53°60’14.83’’ West, whose average altitude is 3 770 m in a range between 3 000 and 5 480 m (^{Semarnat, 2013}). It comprises 39 819.086 ha divided into the states of Estado de México, with 28 307.48 ha (71.09 %); Puebla with 11 072.91 ha (27.81 %) and Morelos with 438.68 ha (1.10 %) (Figure 1).

Source: ^{Semarnat, 2013}.

Figure 1 Location of the Iztaccíhuatl Popocatépetl National Park Natural Protected Area. 

Its geoforms (mountain chains, volcanic cones and hillsides) have a volcanic origin, in which the basaltic rocks and andesites prevail. According to FAO’s classification (^{FAO, 2015}), the present soil units are: Lithosols, Regosols, Andosols, Cambisols and Fluvisols.

The average annual temperature fluctuates from 3 to 5 °C, with an annual variation less than 3 °C, but with enough daytime oscillation for frosts to occur throughout the year. The average annual rainfall is between 600 and 800 mm, and although a considerable percentage falls as snow, it does not remain for long periods on the ground. Sunlight and wind are intense, thus favoring a high evaporation (^{Rzedowski, 2006}).

The PN Izta-Popo Management Program (^{Semarnat, 2013}) is divided into three sub-zones: Restauration, Public Use and Conservation, among the present study was established, mainly on the first one (Figure 1).

Obtaining of biomass

The methodology that was used was similar to that proposed by several scientists (^{Acosta, 2003}; ^{Avendaño et al., 2009}; ^{Carrillo et al., 2014}; ^{Carrillo et al., 2016)}, but it was different since instead of using normal diameter (DN) as an independent variable, the base diameter, the hight up to the first branch and total height were used, as most of the seedlings had not fully developed a DN.

Based on the cost of its extraction, a sample size of 90 seedlings was used to obtain an allometric equation for biomass and carbon. The selection criterion was that seedlings had been planted through reforestation projects since 2008, and were 10 years-old as maximum age, in order to include most of the available categories to increase the range of variability.

Before the extraction of the seedlings from the root, the diameter at the base, total height and height at the first live branch were measured. Later, they were stored in bags with their respective identification number, after which they were transferred to the greenhouse of the Valle de México Experimental Field of Instituto Nacional de Investigaciones Forestales, Agrícolas y Pecuarias (INIFAP) in Coatlinchán, Texcoco de Mora, Estado de México. There they were kept inside the bags for five weeks so that they lost as much moisture as possible before putting them in a Blue M 0v-490A2 drying kiln.

The foliage, branches, stem and root were separated and weighed on a Tecnocor 20-CHIS digital scale, for minimum weights of 200 g and maximum weights of 30 kg to get the dry weight. Samples weighing less than 200 g were weighed on a Scout^®Pro precision scale. When the samples were weighed, aliquots were obtained to be introduced into the drying kiln for 48 h at 70 °C and obtain the 4-component dry weight per 90 seedlings, for a total of 360 samples. Once the moisture percentage after passing through the drying kiln was recorded, it was added to the fresh weight of each component, with which the total and section biomass were calculated.

With the biomass data, the predictive models were adjusted for each one of the variables of interest: the base diameter, total height and the height up to the first living branch. The equation in its potential form was used for the base diameter and total height:

For practical matters, DB was used for base diameter and h _T as total height.

The equation in its second degree polynomial linear form was used for the height to the first living branch:

Where:

B = Biomass (kg)

X’s = Independent variables

β’s = Adjustment coefficients

All the statistical analyses were performed in the free R software (^{The R Team, 2013}).

Categories of the variables of interest

Four diametric categories were defined for the base diameter and 10 for total height; both were used to construct a biomass table that allows predicting such variable by using these two measurements.

Carbon determination

For the calculation of the carbon contained in the saplings, 13 specimens were selected, in order to include the widest range of size intervals, with their respective components; some, subsamples were taken, and carried to the Soil Fertility and Environmental Chemistry Laboratory of the Colegio de Postgraduados, Montecillo campus. The dry combustion method was applied to them on the Shimadzu TOC 5050A carbon analyzer.

Once the results of the analysis were obtained, the coefficient of carbon content per component was applied to the 90 seedlings.

Fresh weight and dry weight

As the seedlings were small, it was not necessary to determine fresh weight directly at the field as suggested by several authors (^{Acosta, 2003}; ^{Avendaño et al., 2009}; Bonilla, 2009; ^{Carrillo et al., 2016}). The average numbers of moisture loss for each component were 8. 3% for leaves, 11.1 % for branches, 16.2 % for the stem and 15.6 % for the root.

Biomass distribution

The distribution of biomass in the seedlings was 30 % for foliage, 8 % for branches, 24 % for the stem and 37 % for the root. Several authors (^{Díaz et al., 2007}; ^{Avendaño et al., 2009}; ^{Carrillo et al., 2014}; ^{Carrillo et al., 2016}) suggest different distributions, even though they do not take into account the root. ^{Castañeda et al. (2012)} proposes between 15 and 20 % as a per cent of biomass of the root for adult trees, which is also far from the actual results of this study.

^{Chávez et al. (2016)} mention that age directly affects the distribution of biomass in trees. In the early stages of a stand, this distribution will be conditioned by the physiological functions required by the species. In Pinus, the first stages focus on the high demand for carbohydrates advocated to the stem that will provide support and can be maintained at a constant rate during its growth. The root must constantly supply water to the leaves, which, in turn, will need great physiological capacity by increasing the leaf area to capture and use solar energy, which will increase photosynthetic rates and biomass production. ^{Vose and Ryan (1994)}, ^{Van and Franklin (2000)}, ^{Wang et al. (2007)} and ^{Pretzsch (2014)} mention that the leaf biomass and crown structure of different forest species are crucial for tree growth and development.

Equation fit

For DB a coefficient of determination was obtained as R ²=0.9521 and a potential equation B=0.0092*DB ^2.7226. For h _T, R ²=0.8644 and the equation B=0.7546*h _T ^2.5819. For the height up to the first living branch, R ²=0.3203, making it unnecessary to show the equation as such coefficient was under what was considered a good fit. The DB graph is shown in Figure 2 and h _T in Figure 35.

Figure 2 Trend line of the biomass values related to the base diameter. 

Figure 3 Data dispersal and trend line of the biomass values related with total height. 

^{Brown et al. (1989)} believes that it is better not always to include the total height of the trees in the biomass estimation procedures due to the complexity of taking the height by closed canopies and because ecological inventories have not included these data in the case of tropical forests.

With the previous results, it was observed that height itself is a significant variable to estimate the biomass in seedlings because this type of vegetation does not have closed canopies, in addition to the fact that the distances between Pinus hartwegii trees are very wide (in some cases up to 15 or 20 m from tree to tree), probably from an innate characteristic of the species.

Biomass tables

Table 1 shows the biomass tables generated from the DB and h _T equations (with the highest coefficient of determination), with the categories defined for these variables.

The table above represents a tool that can facilitate in the field the calculation of biomass for a specific tree or set of trees, such as a stand, through the categories of base diameter or total height.

Obtaining of carbon content

Table 2 shows the results of carbon content by component of the seedlings.

The percentage of carbon found in the present study was similar (50 %) to that proposed by the International Panel for Climate Change (^{IPCC, 1996}) Some authors calculated percentages not so far for mild-temperate species. For example, ^{Carrillo et al. (2016)} obtained 48.5 % for Pinus hartwegii; ^{Avendaño et al. (2009)} 46.48 % for Abies religiosa (Kunth) Schltdl. et Cham., and ^{Carrillo et al. (2013)} 48 % for Quercus. For Pinus patula Schiede ex Schltdl. & Cham., ^{Carrillo et al. (2016)} determined 48.55 % and ^{Díaz et al. (2007)}, 50.31 % for the same species.

With the obtained coefficient, the carbon content was calculated by applying the value of 0.5081 to the total biomass or by component of each seedling.