Introduction

With the incorporation of Mexico to the General Agreement on Tariffs and Trade (GATT) in 1986 and the entry into force of the North American Free Trade Agreement (NAFTA) in 1994, the pressures on the country’s natural resources increased. Authors such as ^{Barton and Merino (2004)} speculate that these have been factors that contribute to the deterioration of forest resources. However, they are not exclusive of free trade; there are causes that go beyond commercial exchanges -e.g. poor forest management plans, the growing urban sprawl, the increase in agricultural land and pastures for livestock, and illegal logging.

Historically, the timber production in Mexico comes from natural forests (^{Álvarez et al., 2015}; ^{Luján et al., 2016}); on average, during the period of 1990 to 2014, 84 % of the production came from coniferous forests, 11 percent, from broadleaf forests, and 5 %, from tropical forests (^{Semarnat, 2014}). This is why special attention was given to the estimation of biological or technical shifts (^{Semarnat, 2010}).

In 1995, the establishment of commercial timber plantations (CTPs) was encouraged with the three-fold purpose of increasing the production and productivity of the raw materials subsector, reducing the pressure on the natural forest areas, and increasing the income of rural households (^{Luján et al., 2016}). Moreover, they emerged as a productive option to convert agricultural land that had lost its vegetation into forest land capable of producing raw materials to supply the forest industry and provide ecosystem services (^{Conafor, 2016}). ^{Andreoni and Bussoni (2014)} point out that the growing demand for timber products can be addressed by means of an adaptive strategy through genetic improvement in plantations.

On the other hand, with the implementation by CONAFOR of the National Strategy of Sustainable Forest Management to increase the production and productivity (Enaipros) 2013-2018 and of the National Strategy for REDD+ (Reducing Emissions from Deforestation and Forest Degradation), one of the greatest challenges is to increase the forest timber production and to reduce the emission of greenhouse gases; therefore, CTPs are considered to be a viable option for the achievement of these objectives (^{Geréz and Pineda, 2011}; ^{Conafor, 2016}).

The implementation of both strategies has promoted the establishment of CTPs of fast-growing tropical species such as Tectona grandis L. F., Gmelina arborea Roxb., Cedrela odorata L., and Eucalyptus grandis Hill ex Maiden (^{Conafor, 2016}). This brought about the need for viable forest shifts according to the current necessities (technical, economic shifts and economic-environmental).

The application of the theory of the economically optimal shift in CTPs has not been addressed with sufficient profusion by the forestry literature of Mexico. Authors such as ^{Medema and Lyon (1985)}, who wrote one of the first papers that dealt with the issue, applied Faustmann’s formulation and solution, proposed in 1849, using an iterative procedure for the calculation of the optimal age. ^{Tait (1986)}, ^{Chang (1998)}, and ^{Smart and Burgess (2000)} utilized the formulation with a generalized solution, using dynamic programming. As for the forest shifts, which incorporate as input the timber production and carbon capture, they have been cited since the 1990s (^{Hoen and Solberg, 1994}; ^{Van et al., 1995}; ^{Romero et al., 1998}).

Although, studies of forest shifts have been carried out at the international level, the basic issues of forest management and exploitation in Mexico revolve around the few efforts made to research appropriate shifts and, to a greater extent, for the State of Tabasco, despite its being one of the main entities with CTPs (^{Conafor, 2016}).

This research posed the following hypothesis: as environmental aspects are incorporated in the estimation of the economic shifts, the optimal felling age is greater, resulting in a lengthening in the number of years of the forest shift. The objective was to analyze the behavior and the relationship between three types of forest shifts in commercial plantations of Eucalyptus grandis Hill ex Maiden located in Balancán, Tabasco, Mexico, by calculating three shifts -technical, economic and environmental-economic-, as well as to provide elements that may contribute to decision-making in the forestry companies.

Materials and Methods

Study area

The study area is located in the municipality of Balancán in the Usumacinta region of Tabasco, Mexico. It is located at the coordinates 17°48' N and 91°32' W. It borders Campeche to the north, the municipalities Tenosique and Emiliano Zapata to the south, the state of Campeche and the Republic of Guatemala to the east, and the municipality of Emiliano Zapata and Campeche to the west (^{Municipios.mx, 2016}) (Figure 1).

Figure 1 Location of the study area. 

Results and Discussion

The Schumacher production function was formulated based on the results of this study.

The production function shows a high correlation coefficient (R² = 0.9989), which is indicative of an adjustment, as well as low levels of Sum of Squares of the Error (SCE = 0.00062).

Technical shifts. The Schumacher-type function has a horizontal asymptote, which implies that it does not decrease. To this end, we obtained an approximation by discriminating 10 % of the total production, since the marginal increases are minimal, as shown:

Where:

α = Percentage of production for discrimination (10 % in this study)

By solving this equation and replacing in the production function (Eq. 9), the Maximum Total Production (MTP) is shown to be attained at 97.20 years of age of the plantation. The Schumacher production function turned out to be an inappropriate model for the calculation of the MTP, whereas the adjusted model allows projecting it 25 % into the future, according to ^{Montgomery et al. (2007)}; i.e. it predicts acceptably up to the 19^th year (the information presented is indicative).

The Maximum Average Production (MAP) corresponds to 10.24 years of age of the plantation (Figure 2).

Volumen = Volume; Edad = Age

Figure 2 Marginal Production Curves (PMg) and Mean Product (PMe) for Eucalyptus grandis Hill ex Maiden, derived from the adjusted Schumacher function. 

Economic shifts. Once the economic values in the formulations of Hotelling and Faustmann had been replaced, the balance curves were calculated for each formulation, being of 11.32 years for Hotelling’s shift, and 10.82 years for Faustmann’s (Figure 3, Table 2).

VAN = CNV (Current Net Value); Edad = Age

Figure 3 Hotelling, Faustmann and Hartman equilibrium curves for Eucalyptus grandis Hill ex Maiden, derived from the adjusted Schumacher function. 

Environmental-economic shift. The balance function, whose shift is reached at 11.64 years of age, was calculated by integrating the economic and environmental values (Figure 3, Table 2).

The estimated forest shifts constitute a novel contribution to investors both in the CTPs of the municipality of Balancán, Tabasco, and in certain places with similar biophysical characteristics to those of the study area, since they may be used as a reference point in the forest management of the plantations.

According to ^{Frangi et al. (2016)} and ^{Santiago et al. (2015)}, Eucalyptus grandis has a rapid growth; for this reason, the forest shifts are short compared to those of other species destined for sawmilling. The following is a brief comparison and a description of the relationship between the five shifts considered.

A growing relationship was observed in the shift rotation with the incorporation of environmental and economic variables such as the carbon capture. In general terms, the rotation has diminished as a larger number of economic aspects (costs) are considered in its determination; conversely, it has increased with the inclusion of environmental and recreational aspects (income). The corresponding behavior was as follows: Maximum Average Production (10.24 years), Faustmann shift (10.82 years), Hotelling shift (11.32 years), Hartman shift (11.64) and Maximum Total Production (97.20 years).

In the analysis of shifts, the Hartman shift was observed to increase by 3.2 months compared to the Hotelling shift; in relation to the Faustmann shift, the increase was 9.8 months, and with regard to the MAP, it was 16.8 months.

Similar data were estimated in the state of Oaxaca for this species (^{Téllez et al., 2008}), after analyzing two scenarios -1) wood for cellulose and 2) wood for sawmilling and pulp- with an economic approach. In the first scenario, the shift was determined to range between 6.9 and 9.0 years, while for the second, it ranges between 9.0 and 13.5 years; when an income for carbon capture was incorporated into the calculation, the shift increased between 12 and 20, and 17 and 30 months, respectively. Certain authors consider that the forest shifts of Eucalyptus grandis in Colombia range between 6 and 8 years (^{Restrepo and Alviar, 2010}; ^{Gómez et al., 2012}).

It is worth mentioning that the extension of the forest shift is a consequence of the genesis (structure) of each model, and that it favors the generation of (larger quantities of) heartwood and the capture of carbon. ^{Dias et al. (2016)} points out that for the genus Eucalytus short shifts result in good growth rates but a poor quality as wood, as pulp for the manufacture of paper, and for the drying process. Therefore, an extension of the shift makes it possible to obtain timber with better anatomical features.

Conclusions

As economic-environmental aspects are incorporated into the estimation of the forest shifts for Eucalyptus grandis, the optimal felling age increases.

The estimation of forest shifts for E. grandis is shown to involve a maximum average production, a Faustmann shift, a Hotelling shift, a Hartman shift and a maximum total production.

The Hartman shift is suitable for sustainable forest harvesting, inasmuch as it incorporates aspects of the proposal of Faustmann as well as the value of the environmental and recreational services provided by the plantation.

The extension of the forest shifts increases the volume of biomass, with the possibility of harvesting larger quantities of heartwood for cellulose and capturing more carbon, whereby the social benefit is enhanced.