### African Journal ofAgricultural Research

• Abbreviation: Afr. J. Agric. Res.
• Language: English
• ISSN: 1991-637X
• DOI: 10.5897/AJAR
• Start Year: 2006
• Published Articles: 6396

## Effect of growth and yield modelling on forest regulation and earnings

##### Larissa Bitti Vescovi
• Larissa Bitti Vescovi
• Department of Forest Engineering, Universidade Federal de Viçosa, Av. Purdue, S/N, Campus Universitário, 36.570-900, Viçosa, Minas Gerais, Brazil.
##### Helio Garcia Leite
• Helio Garcia Leite
• Department of Forest Engineering, Universidade Federal de Viçosa, Av. Purdue, S/N, Campus Universitário, 36.570-900, Viçosa, Minas Gerais, Brazil.
##### Carlos Pedro Boechat Soares
• Carlos Pedro Boechat Soares
• Department of Forest Engineering, Universidade Federal de Viçosa, Av. Purdue, S/N, Campus Universitário, 36.570-900, Viçosa, Minas Gerais, Brazil.
##### Márcio Leles Romarco de Oliveira
• Márcio Leles Romarco de Oliveira
• Department of Forest Engineering, Universidade Federal do Vale do Jequitinhonha e Mucuri, Diamantina, Campus JK - MGT 367 - Km 583, nº 5000 Alto da Jacuba, 39100-000, Diamantina, Minas Gerais, Brazil.
##### Daniel H. B. Binoti
• Daniel H. B. Binoti
• Dap Florestal. Rua Papa João XXIII, n 9, Lourdes, 36.570-900, Viçosa, Minas Gerais, Brazil.
##### Leonardo Pereira Fardin
• Leonardo Pereira Fardin
• Department of Forest Engineering, Universidade Federal de Viçosa, Av. Purdue, S/N, Campus Universitário, 36.570-900, Viçosa, Minas Gerais, Brazil.
##### Gabriela Cristina Costa Silva
• Gabriela Cristina Costa Silva
• Department of Forest Engineering, Universidade Federal de Viçosa, Av. Purdue, S/N, Campus Universitário, 36.570-900, Viçosa, Minas Gerais, Brazil.
##### Lucas Sérgio de Sousa Lopes
• Lucas Sérgio de Sousa Lopes
• Department of Forest Engineering, Universidade Federal de Viçosa, Av. Purdue, S/N, Campus Universitário, 36.570-900, Viçosa, Minas Gerais, Brazil.
##### Rodrigo Vieira Leite
• Rodrigo Vieira Leite
• Department of Forest Engineering, Universidade Federal de Viçosa, Av. Purdue, S/N, Campus Universitário, 36.570-900, Viçosa, Minas Gerais, Brazil.
##### Ricardo Rodrigues de Oliveira Neto
• Ricardo Rodrigues de Oliveira Neto
• Department of Forest Engineering, Universidade Federal de Viçosa, Av. Purdue, S/N, Campus Universitário, 36.570-900, Viçosa, Minas Gerais, Brazil.
##### Simone Silva
• Simone Silva
• Department of Forest Engineering, Universidade Federal de Viçosa, Av. Purdue, S/N, Campus Universitário, 36.570-900, Viçosa, Minas Gerais, Brazil.

•  Accepted: 13 March 2020
•  Published: 31 July 2020

ABSTRACT

The elaboration of a forest schedule involves constructing and solving a forest regulation model. The regulated structure is not easy to obtain, considering the fluctuations in the effective planting area during the planning horizon, technological advances, and changes in annual demand. Nevertheless, the establishment and implementation of a regulation model often results in an improvement of the forest, in terms of the distribution of age classes. The successful use of regulation models and consequent definition of a forest management plan depends on the quality of data from forest inventory plots and prediction accuracy of stand wood stock. This study evaluated the effect of different alternatives of growth and yield modelling on the regulation of a eucalyptus even-aged forest. Each alternative was used to create yield tables, which were used as inputs in a linear programming model. In this model, restrictions of area, demand, and regulation were included, with the goal of maximising the total net present value. The most consistent forest schedule was obtained with a total stand model.

Key words: Forest management, forestry planning, scheduling, growth, yield models.

INTRODUCTION

Forest management is the application of analytical techniques in the selection of management alternatives to meet the objectives of a company or forestry organisation (Bettinger et al., 2017; Araujo et al., 2018). The best choice among these alternatives depends on the accuracy of information on forest resources (both data and models used to estimate and predict population variables, like wood volume), (Carvalho et al., 2016) and the intensity of interventions during the planning horizon (Clutter et al., 1983; Duvemo and Lämas, 2006). Due to the substantial investments required for management of timber production, highly accurate models of tree attributes and stand development are required (Burkhart and Tomé, 2012).

To develop a management plan for an even forest requires knowledge of the three essential elements of management: land classification, establishment of prescriptions, and prediction or projection of growth and harvest stock. According to Campos and Leite (2017), modelling growth and stand production is related to the first and third of these elements.

Data from inventory can be used to construct site index curves and map stand production capacity. This information together with the forest historic and physiographic maps of soils and roads, results in a detailed description of each forest compartment and growth and production models can be adjusted and employed to examine forestry and logging options, to determine sustainable production, to examine the impacts of management options and guide forest policy (Davis and Johnson, 1987).

Growth and yield models looking for describe precisely how a forest population grows, providing information for decision making (Peng, 2000; Fahlvik et al., 2014), help managers to exploit forest resources in a sustainable way (Vanclay, 1994) and can be used as input for models to regulate the forest production (Casas et al., 2018). Choosing the appropriate approach for growth and yield modelling depends on the management’s purpose, the stratification of the forest, and on the size, quality, and representativeness of the data from the permanent plots or stem analysis (Campos and Leite, 2017). These models can be divided according to the level of detailed: total stand, diameter distribution and trees (Palahí et al., 2003; Castro et al., 2013).

Considering the competitiveness of the increasingly forest-based market, regulating a forest also means maintaining a sustainable production that meets fluctuating market specifications and demand and satisfies capital and operational constraints. It also ensures regular employment (Bachmatiuk et al., 2015; Troncoso et al., 2011) and presents minimum costs and maximum returns within a planning horizon (Heinonen, 2007; Mäkinen et al., 2012; Pereira et al., 2015; Martin et al., 2016).

The regulation of forest production consists of obtaining continually forest products of the same volume, size, and quality. To regulate a forest, managers must determine where, how, and when to sustainably produce goods and services from the forest, to better achieve the objectives of the owner (Pukkala, 2002; Heinonen, 2007; Bouchard et al., 2007). Forestry regulation can ensure continuous production of various products and use of forests regarding sustainability.

The two main models used for the forest production regulation are known as Models I and II (Johnson and Scheurman, 1977). In this classical approach, each management unit should be assigned to one prescription. The basis for this formulation is  the  initial  subdivision  of the forest into homogeneous age classes, prescribing a set of requirements for each class (Carvalho et al., 2015). The difference between these two models is that in Model I, the prescriptions assigned to a management unit remained in place until the end of the planning horizon (Buongiorno and Gilles, 2003).

The influence of the growth and yield model on the forest schedule is straightforward because this model generates future information on the expected harvest (Siipilehto and Rajala, 2019). Managers usually select the best model based on its statistical performance, without considering its effect on the management plan (Castro et al., 2016).

The objective of this study is demonstrating the effect of the growth and yield models on the regulation of a eucalyptus even-aged stand.

MATERIALS AND METHODS

Data

For the regulation models, we built yield tables using five growth and yield models. These models were adjusted using data from a continuous forest inventory of a eucalyptus stand located in northern Minas Gerais, Brazil in an area of about 17,000 ha. The area is used for producing wood for charcoal and contains 13 different clones of Eucalyptus spp in a 3.0 x 3.0 m spatial arrangement. 2700 permanent plots of 600 m2 were installed in the stand and the trees had their height and diameter at the breast height (dbh) measured in four different years (2005 thru 2008). Tables 1 and 2 show the statistics information of all measurement.

The data was used to adjust the whole-stand and the diameter-distribution models. When possible, we adjusted the models after arranging the data according to genetical material (clone) stratrum. The plots were grouped in bigger groups, called management units (m.u.), by having the same genetic material, age class and productivity capacity.

Site index

To determine the productive capacity of the stands, we defined site indexes using the guide-curve method (Clutter et al., 1983) with an index age of 60 months. The guide-curve method was adjusted for each genetic material using the logistic model (Draper and Smith, 1998):

where Hd denotes the dominant height, in meters; Age denotes the age in months; β0, β1 e β2 are the model parameters, and is the random error

Yield tables and costs

The yield tables used in this study were built using five growth and yield modelling alternatives: four whole-stand (Models 1 to 4) and one  diameter-distribution  model  (Model 5)  as  shown  in  Table 3.

V: volume in m³ha-1; A: age, in years; S: site index (m) in the index age of 60 months, B: basal area, m²ha-1; ΔB: basal area increase, m²ha-1 per year; c: constant of relative approximation on the sum of the maximum and minimum rates of basal area growth; γ: shape parameter of Weibull function, β: scale parameter of Weibull function; dbh: diameter at 1.3 m height (in cm); dmax: maximum diameter in cm; dmin: minimum diameter in cm, N: number of trees per hectare; Δdbh: diameter increment, cm per year; BAL: competition index measured by the sum of sectional area of trees with diameter greater than the evaluated tree, m², H: total height in m; Hd: dominant height in m; Ddom: the diameter of the dominant tree in cm, D: Square root of the diameter in cm, Ln: Napierian logarithm; β0, β1, β2, β3e θ0: model parameters.

The models were adjusted for each genetic material stratum, except those that contained insufficient data to fit a specific model; in this case, the models were fitted using all the data without stratification. The yield tables for each management unit were constructed using the results from the last inventory as the input. Five yield tables were obtained for each of the 341 management units using the fitted models. Productive capacity was used as an input in alternatives 2 and 4. The simulated costs were based on Melido (2012) study and timber price was set as €25.00/m3. Brazilian currency (R$) values were converted to euros (€) using the conversion factor of 2.436 (€1.00 = R$ 2.436), as on 1 August, 2008 (European Central Bank, 2019), the last year that the plots were measured.

Projection errors

We used the correlation coefficients to evaluate the models’ goodness of fit, bias, relative bias (bias%), and error variance to assess the estimation precision of timber stocks (Islam et al., 2009):

where   are the estimated and observed production values and n is the number of permanent plots.

The models were categorised into four groups according to the magnitude and variance of relative bias (Figure 1). The groups are named: LBLV (low bias % and low variance), LBHV (low bias % and high variance), HBLV (high bias % and low variance), and HBHV (high bias % and high variance) (Islam et al., 2009).

Forest production regulation

For the yield tables, cost worksheet, price of wood, and definition of regulatory rotation (6 years), planning horizon (18 years), and management prescriptions, we formulated the forest regulation model using linear programming (LP) model I (Leuschner, 1984; Dykstra, 1984), so named by Johnson and Scheurman (1977). The only difference between the five management plans was the yield table employed. We used the 12% annual interest rate. The management prescription was clear cut with 6 years followed by replanting. We consider that the genetic materials and yield of a plot does not change from one cutting cycle to another.

The objective function defined to maximise the total net present value (NPV) of the stand is as follows:

where,

Cij denotes the NPV of management unit i assigned to prescription j;

Xij denotes the area (ha) of management unit i assigned to prescription j;

M denotes the number of management units, M = 341; and

N denotes the number of alternative prescriptions.

The net present value (NPV) is calculated as Equation 3:

where,

Cij denotes the NPV management unit i assigned to prescription;

Rk denotes revenue at the end of period k, k = 0, 1, ..., 17;

Ck denotes final cost in period k, k = 0, 1, ..., 17;

w denotes interest rate = 0.12;

n denotes the max(k) = the horizon planning (18); and

k denotes period in years.

The area (4), production (5 and  6),  and  regulatory  constraints  (7) are shown below:

where,

Ai = Area of the ith management unit (i = 1, 2, ..., 341);

Vijk = Volume (m3) of management unit i assigned to prescription j at year k;

Dmin and Dmax = Minimum and maximum demand for timber in year k;

Xij = area of the ith management unit in the jth prescription;

Xijt = area of the ith management unit in the jth prescription, where trees have t years during the final period of the planning horizon; and

r = number of age class, equal to 6 years (regulatory rotation).

Five different management plans  were  generated  using  the  yield tables resulted from the five growth and yield models tested. The results from the LP problems were compared in terms of their prognosis errors to detect their effect on the prescribed management plan. Additionally, the standard deviations of the costs and harvesting were considered to verify their uniformity during the planning horizon. The LP models were solved using Lindo Systems Inc. (http://www.lindo.com).

RESULTS

All models had satisfactory results, with correlation coefficients above 0.7. The whole-stand models better describe the volume yield, especially the Clutter et al. (1983) model, for the different clone strata with correlation coefficients from 0.87 to 0.98, indicating that the independent variables contributed effectively to explain the production variations. The results for each model are presented in Tables 4 and 5.

The categories defined for bias and variance values show that Model 3 is both most accurate and precise. From a comparison of the prognosis errors (bias), we verified that there is a direct relationship between the error categories and the total NPV from the optimization (Table 6). That is, the models with lower biases and variances yield a higher overall NPV. The obtained NPV has high amplitude, ranging from about € 50 (Model 5) to € 94 million (46.5% difference) (Model 3).

The complete formulation of the LP problem for yield regulation resulted in 16,401 decision variables (Xij), with 341 area constraints. As only one restriction is required for  each  management  unit, 18 demand constraints, one for each year of the planning horizon, and six regulatory restrictions were defined by the regulating age. For all five management plans, restrictions were met, but with differences in overall NPV, annual costs, and annual cutting area during the planning horizon (Table 7 and Figure 2).

In this study, the best model was a whole-stand model (Model 3) for both the overall NPV and evenness of harvested areas within the planning horizon. This model had the lowest standard deviation for annual harvested areas. Although Model 5 had the lowest standard deviation for annual costs, followed by Models 1, 4, and 3 (Table 7), it performed poorly on forest regulation and had the lowest NPV.

The differences in costs between  Model  3  and Models 4, 5, 2, and 1 were -41.3, -7, 5, -6.2, and -5.0%, respectively. Conversely, the corresponding percentage differences in the total NPV were -35.3, 46.5, 37.9 and -8.0%, respectively. Therefore, even with fluctuating costs over the years, the profitability was at least 8% greater in Model 3.

By adopting the second-best modelling alternative (Model 1), based on the measures of precision, accuracy, the forest manager would have a reduction in the updated cost for the zero year of 5%. However, there would be an 8% reduction in return on investment (NPV). This and the results in Table 7 show the consequences of using inefficient modelling alternatives.

The use of a poor modelling alternative, such as alternative  4,  would result in great chances of not reaching the objectives established when formulating the regulation model. Alternative 4 had resulted in a strong bias, with underestimation of production. Thus, the use of this alternative would result in a great chance of not meeting the management objectives over the planning horizon.

DISCUSSION

The Clutter et al. (1983) model was the most representative for the volume data used in this study. Whole-stand models are explicit, less complex, require less information and, therefore, have fewer errors (Soares et al., 2004; Oliveira et al.,  2009;  Scolforo  et al., 2019). In relation to the  other whole-stand models, the Clutter et al. (1983) model uses more explanatory variables other than age and site-index, making it more precise. Usually, models that consider only age as an independent variable do not explain yield variations properly (Silva et al., 2003; Nascimento et al., 2015; Novaes et al., 2017) and need maximum data classification. In this study, we have stratified data by genetic material, making these models specific and efficient for volume estimation. However,  we  would  not  recommend using this model for areas with no stratification.

The differences in NPV are associated with the predicted volume in each model. In some cases, the future volume of a stand is underestimated resulting in significant losses. In this study, the best model is a whole-stand model (Model 3) based on the yielded NPV. The same result may not be the same in different types of forests, especially if they do not have homogeneity in even-aged eucalyptus forests (Härkönen et al., 2010; McCullagh et al., 2017).

The lowest standard deviations for harvest and cost were obtained in Models 3 and 5, respectively. This is important because one of the benefits of regulation is maintaining regular employment, and lower standard deviations indicate a greater possibility of achieving this goal. For managers, less variation in annual harvest and annual costs facilitates the planting, harvesting, and replanting activities and workforce and equipment scheduling to perform those activities during the planning horizon (Rode et  al., 2014; Oliveira Neto et al., 2020).

These   results   demonstrate   the   consequences    of inefficient modelling alternatives. Poor modelling, as shown in  Model  4,  results  to  differences  in  cost,  total NPV, and annual harvesting areas, with similar results found in Silva et al. (2003). Since Model 4 resulted in a strong bias with a yield underestimation, using it would result in a higher probability of failing to meet management objectives during the planning horizon, with a possibility of producing excess wood in the annual cutting.

CONCLUSIONS

Choosing an inefficient modelling alternative, results in profound changes and uncertainties in the forest management plan. That is, the successful implementation of a management plan is dependent on the quality of the yield tables used. In this study, the management plan is more consistent when using the Clutter et al. (1983) model, fitted using the genetic material strata.

CONFLICT OF INTERESTS

The authors have not declared any conflict of interests.

REFERENCES