Original article

Preliminary evaluation of the efficacy of the variable probability method in Miombo woodland

Marisela Frías Tamayo^{1  *} 
http://orcid.org/0000-0002-3854-5888

Nheza Filomena Pereira Jay¹ 
http://orcid.org/0000-0003-3421-7833

Edilio Aldana Pereira¹ 
http://orcid.org/0000-0002-3218-3302

¹Universidad de Pinar del Río "Hermanos Saíz Montes de Oca". Pinar del Río, Cuba.

ABSTRACT

In the research, three factors of basal area were analyzed according to the theoretical basis of sampling with variable probability, with the objective of preliminarily evaluating the effectiveness of Bitterlich's variable probability method for the estimation of basal area in forests of the Miombo formation. By means of systematic sampling, 11 temporary circular plots of fixed area of 500 m² were established. In the center of each of these plots, measurement points were established with a mirror relascope, where the basal area factors (FAB) 1, 2 and 4 were used. The fixed area plots were taken as references and the results were compared for which the analysis was performed with the statistical package SPSS for Windows Version 19.0. There were no significant differences in the results of basal areas obtained between the different factors of basal area 1, 2 and 4, with respect to those obtained in the plots of fixed areas. In the time analysis, basal area factor number four was the best with the least number of minutes during the measurement of the sampling unit.

Keywords: Horizontal point sampling; Basal area; Systematic sampling; Miombo.

INTRODUCTION

In the Upper Central Plan of Angola, where Huambo province is located, forest resources are exploited without adequate management. This area is constituted by an ecosystem called Miombo, which is distributed by several African countries, with an approximate extension of 270 million hectares ^{(Campbell, 1996)}.

One of the main causes of deforestation in the Miombo is the exploitation of wood for conversion into charcoal, since the lack of economic alternatives often makes this resource the only source of income for rural communities.

The proper management of forest resources requires, for its planning and execution, quantitative and qualitative information obtained through the forest inventory, which is based on sampling and statistics, to obtain estimators of the variables of interest (Druszcz, 2008).

Traditionally, inventories are carried out using plots of fixed dimensions and various forms, temporary or permanent, and although the use of the variable probability method has spread throughout the world, fixed area plots are still the most widely used. Despite the wide application of this method, in forest inventories, there are some disadvantages regarding the time of establishment and measurement of trees in the plots, compared to variable probability methods ^{(Vastaranta et al., 2015)}; (Fiorentin et al., 2015).

Currently, for the evaluation of forest resources, there is a tendency to use variable probability sampling points, based on the theoretical foundation of Dr. Grosenbaugh's method and implemented by Walter Bitterlich when constructing the mirror relascope ^{(Aldana, 2010)}.

The sampling method using the horizontal point type allows obtaining the basal area per hectare of the forest mass where the observation is made; complemented with some additional observations and measurements, information on the quantification of volumes per unit area and other characteristics linearly associated with the basal area can be obtained.

Tropical native forests require effective and direct methods for the estimation of dendrometric and dasometric attributes, which facilitate information for the management of this resource in a reliable and accurate manner.

Little is known about dasometric studies in the Miombo formation, specifically in the area of this research in the Cuima community of Huambo province in Angola.

The mirror relascope (Bitterlich) allows estimating the basal area per hectare, which is a very important variable, since it is an indicator of the occupation of the growing space. With the morphic coefficient and the height of the average basal area tree, an estimate of the volume of the forest mass is quickly obtained.

Considering the low cost and easy to operate in the field the variable probability method is used in forest inventory ^{(Mulyana et al., 2018)}.

The objective of this paper is to preliminarily evaluate the effectiveness of Bitterlich's variable probability method for basal area estimation in forests of the Miombo formation.

MATERIALS AND METHODS

The Miombo open forest occupies about 45.2 % of the total forest area of Angola, scattered over vast areas of the country and presents innumerable dominant associations, where the most frequent is constituted by the genera Isoberlínea, Brachystegia and Julbernardia; Brachystyergia speciformis, Brachystegia tamarindoides, Brachystyergia floribunda, Brachystegia boehmii, Brachystegia utilis, Julbernardia paniculata and Ficus sansibarica.

The Miombo formation is of medium productivity in terms of commercial timber, but has a high social value in terms of woody fuel, construction materials, food products and medicinal plants (Caetano, 2012).

The forest area covered by this study covers an area of 308 hectares and consists entirely of natural forests of the Miombo formation in the village of Calombo in the province of Huambo, located between the geographical coordinates: 13° 14' 40'' South and 15° 38' 29" East (Figure 1).

Fig. 1. - Location of the Miombo formation in Calombo village in Cuima, Huambo 

Eight plots were pre-sampled and used as the basis for calculating the final sample size using the formula (Equation 1).

For a finite population, this resulted in a final sample size of 11 circular plots of 500 m². The location of the plots was done by systematic sampling, where the slope of the terrain was taken into account to determine the radius of the plots, which were distributed throughout the area. The first plot was located randomly.

For the establishment of the variable probability plots with each of the basal area factors, the midpoint of the fixed area circular plots was taken as the center.

The Bitterlich mirror relascope with three basal area factors (FAB = 1 m²ha^-1, FAB = 2 m²ha^-1 and FAB = 4 m²ha^-1) was used for the survey.

Fixed area sampling plots

All the diameters at 1.30 m from the ground of all the trees included in each plot were measured with a forcepod. The basal area (G) was obtained by the diameters at 1.30 m height of the trees within the sampling unit and converted to cross-sectional areas (g), summed for the trees measured (m) and multiplied by the proportionality factor (F), to convert it to values per hectare using the following formula (Equation 2).

Bitterlich variable-probability sampling points

For the variable probability sampling points, all trees were counted whose diameters were greater than or equal to a given angle projected at a height of 1.30 m of the stem from the ground, known as the critical angle or basal area factor. The basal area by this method is easily obtained as follows (Equation 3).

Where:

m	= number of trees included in the sampling point;
FAB	= basal area factor (m^2ha^-1)

The SPSS program (Statistica) was used to compare the results obtained by the methods studied. The results were evaluated by analysis of variance (ANOVA) and the comparison means by means of Tukey's test for a p≤0,05.

RESULTS AND DISCUSSION

Evaluation of basal areas per hectare

The variable probability method is not known to be used in Miombo woodlands. However, ^{Couto et al., (1990)} used it to measure the height of dominant trees and number of trees per hectare in stands of Eucalyptus saligna; ^{Monteiro and Santos (2012)} used it in plantations of Eucalyptus grandis and ^{Peña (2000)} used the Bitterlich mirror relascope in the cubication of trees.

Taking into account that all the trees were measured in the fixed area plots, they were used as a standard to evaluate the effectiveness of the different basal area factors (FAB) corresponding to the Bitterlich variable probability method.

The dasometric variable to be evaluated is the mean basal area per hectare (m² ha^-1) as shown in Table 1 where the mean values per hectare of basal area in each of the 11 plots of fixed area and those obtained with the basal area factors (FAB) 1, 2 and 4) respectively (Table 1).

Table 1. - Mean basal areas in m² ha^-1 in the fixed area plots and with the variable probability method with FAB 1, 2 and 4 

Table 1 shows that, with respect to the fixed area plots, there is an underestimation of the basal area with the three FABs of Bitterlich's variable probability method, with a difference of 4.1 m²h^-1 with respect to FAB 1, 4.5 m²h^-1 with respect to FAB 2 and 3.5 m²h^-1 with respect to FAB 4. However, between the basal areas obtained with the three FAB 1, 2 and 4, there is practically no difference.

With the three FABs researched, error limits above ±10 % were obtained. The reason for these results regarding the high values of the relative error lies in the fact that the necessary number of sampling points with the different factors of basal areas was not raised, because as shown at the end of the table, it was necessary to establish 22, 13 and 16 points for FAB 1, 2 and 4 respectively and only 11 sampling points were established, since they were made to coincide with the number of plots of variable area.

^{Carneiro et al., (2015)} in a Tectona grandis plantation, to determine the basal area and volume per hectare obtained that the best method was the Bitterlich variable probability method, as well as the relative efficiency for the estimation of all the variables studied.

Figure 2 shows the distribution of basal areas, where it is observed that except in plots 2 and 10 in the fixed area method, the estimated basal areas are higher than those obtained with the three FABs of Bitterlich, there is practically no difference between the three FABs (Figure 2).

Fig. 2. - Distribution of basal areas in the sampling units, where FAB = fixed area and FAB 1, FAB 2 and FAB 4 are equivalent to Basal area factors 1, 2 and 4 respectively 

Looking at the distribution of Gha^-1 in Figure 2, it is not possible to select the best FAB to estimate the basal areas in Miombo.

Therefore, an ANOVA and multiple comparisons of means were performed for the dependent variable G ha^-1 with the three factors of basal areas.

Table 2 shows the analysis of variance where it is shown that there is a significant inter-group and intra-group difference (Table 2).

Table 2. - ANOVA for G ha^-1 

Table 3 shows the multiple comparisons of the basal area means obtained with the Bitterlich method and with the fixed area plot method (Table 3).

Table 3. - Multiple comparisons of means for the dependent variable G ha^-1 

It can be seen in Table 3 that for the estimation of basal areas with Bitterlich's variable probability method, FAB 1 or FAB 2 can be used, with a significance of 0.998, and the use of FAB 4 is rejected. However, when comparing the mean differences of the fixed area plot method with Bitterlich's variable probability method; it is observed that FAB 4 is the best, with a significance of 0.967.

Table 4 shows the time in minutes taken to measure all the trees in each of the fixed area plots and each of the trees that fell in the count with the respective FAB 1, 2 and 4.

As shown in Table 4, the time consumed in the survey with each of the FABs is much less than that consumed in the fixed area plots due to the reduction in the number of trees to be measured, decreasing this number from FAB 1 to FAB 4, registering in the latter the least time since very few trees were counted (Table 4).

Table 4.  - Average time consumed in the survey of the fixed area plots and in each of the FAB 1, 2 and 4 

Table 5 shows the multiple comparisons of means for the dependent variable of time and an analysis of variance is presented where there is no significant intragroup or intergroup difference (Table 5).

Table 5. - ANOVA for the time consumed in the survey of the plots 

In Table 6, it is observed that the difference of the mean of the fixed area plot with the three basal area factors of the Bitterlich variable probability method is significant at the 0.05 level. However, there are no differences in the means between the three basal area factors FAB 1, FAB 2 and FAB 4 (Table 6).

In the comparison of the means of the different FABs, there is a high correlation of 0.997 between FAB 1 and FAB 2, 0.987 between FAB 1 and FAB 4 and 0.999 between FAB 2 and FAB 4.

^{Silva et al., (2016)} point out that they found no statistically significant difference for the estimation of basal area and volume per hectare between the fixed-area and Bitterlich methods, independent of the basal area factor used in Eucalyptus grandis stands.

Table 6. - Multiple comparisons of the means of time as the dependent variable 

From the results of the time analysis it can be concluded that the Bitterlich variable probability method saves working time with respect to FAB 1 and 2 and more with respect to the fixed area plot method.

CONCLUSIONS

The application of Bitterlich's variable probability method for the assessment of basal area in the Miombo forest formation is feasible, provided that the sample to be taken is representative of the forest stand.

For the estimation of basal areas with Bitterlich's variable probability method in the Miombo, FAB 4 was better with a significance of 0.967 with respect to the fixed area plot method that was used as a comparison standard, being also the most economical in terms of time and with practically the same estimation of the mean basal area as FAB 1 and 2.

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Received: July 17, 2020; Accepted: May 06, 2021