*Cuban Journal of Forest Sciences. 2021; May-August 9(2):193-204*

*Translated from the original in spanish*

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

**Evaluación preliminar de la eficacia del método con probabilidad
variable en bosque de Miombo**

**Avaliação preliminar da eficácia do método da probabilidade variável na floresta de Miombo**

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

**Nheza Filomena Pereira Jay ^{1} **https://orcid.org/0000-0003-3421-7833

**Edilio Aldana Pereira ^{1}** https://orcid.org/0000-0002-3218-3302

^{1}University of Pinar del Río "Hermanos Saíz Montes de Oca". Pinar del Río, Cuba.

^{*}Corresponding author: mfrias@upr.edu.cu

**Received**: 07/17/2020.

**Approved**: 06/05/2021.

**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 m^{2} 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.

**RESUMEN**

En la investigación, se analizaron tres factores de área basal conforme el fundamento teórico
del muestreo con probabilidad variable, con el objetivo de evaluar preliminarmente la efectividad
del método de probabilidad variable de Bitterlich para la estimación del área basal en bosques de
la formación de Miombo. Mediante un muestreo
sistemático se establecieron 11 parcelas
temporales circulares de área fija de 500
m^{2}. En el centro de cada una de estas parcelas, se establecieron
los puntos de medición con relascopio de espejos, donde se utilizaron los factores de área
basal (FAB) 1, 2 y 4. Se tomaron como referencias las parcelas de área fija y se compararon
los resultados para lo cual se realizó el análisis con el paquete estadístico SPSS para Windows
Versión 19.0. No se presentaron diferencias significativas de los resultados de áreas basales
obtenidos entre los diferentes factores de área basal 1, 2 y 4, con respecto a los obtenidos en las
parcelas de áreas fijas. En el análisis del tiempo, el factor de área basal número cuatro resultó el
mejor con la menor cantidad de minutos durante la medición de la unidad de muestreo.

**Palabras clave: **Muestreo puntual horizontal; Área basal; Muestreo sistemático; Miombo.

**RESUMO**

Nesta investigação, foram analisados três factors de área basal de acordo com a base teórica da amostragem de probabilidade variável, a fim de avaliar preliminarmente a eficácia do método de probabilidade variável de Bitterlich para a estimativa da área basal nas florestas de formação de Miombo. Onze parcelas circulares temporárias de área fixa de 500 m2 foram estabelecidas por meio de amostragem sistemática. No centro de cada uma destas parcelas, os pontos de medição foram estabelecidos com um relascópio espelho, onde foram utilizados os fatores de área basal (FAB) 1, 2 e 4. As parcelas de área fixa foram tomadas como referência e os resultados foram comparados para os quais a análise foi realizada com o pacote estatístico SPSS para Windows Versão 19.0. Não houve diferenças significativas nos resultados das áreas basais obtidos entre os diferentes fatores de área basal 1, 2 e 4, em relação aos obtidos nas parcelas de áreas fixas. Na análise temporal, o factor de área basal número quatro foi o melhor com a menor quantidade de minutos durante a medição da unidade de amostragem.

**Palavras-chave:** Amostragem pontual horizontal; Área basal; Amostragem sistemática; 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).

**Figure 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
m^{2}. 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
m^{2}ha^{-1}, FAB = 2
m^{2}ha^{-1} and FAB = 4
m^{2}ha^{-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^{2}ha^{-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
(m^{2} 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 m^{2}
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
m^{2}h^{-1 }with respect to FAB 1, 4.5
m^{2}h^{-1} with respect to FAB 2 and 3.5
m^{2}h^{-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).

**Figure 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.

**REFERENCES **

ALDANA PEREIRA, E., 2010. *Medición
forestal* [en línea]. S.l.: Félix Varela. ISBN
978-959-07-1321-7. Disponible en: https://books.google.com.cu/books/about/Medici%C3%B3n_forestal.html?id=Pv6OswEACAAJ&re dir_esc=y.

CAMPBELL, B.M., 1996. *The Miombo in Transition: Woodlands and Welfare in
Africa* [en línea]. S.l.: CIFOR. ISBN 978-979-8764-07-3. Disponible en: https://books.google.com.cu/books/about/The_Miombo_in_Transition.html?id=rpildJJVdU4C&redir_esc=y.

CARNEIRO MIRANDA, D.L., FRANCIO, J., SANTOS, J. de P., SANQUETTA, C.R. y CORTE,
A.P.D., 2015. Precisão e eficiência relativa de métodos de amostragem em teca. *Pesquisa Florestal Brasileira* [en línea], vol. 35, no. 83, pp. 247-254. [Consulta: 2 septiembre 2020]. ISSN 1983-2605.
DOI 10.4336/2015.pfb.35.83.638. Disponible en: https://pfb.cnpf.embrapa.br/pfb/index.php/pfb/article/view/638.

COUTO, H.T.Z. do, BASTOS, N.L.M. y LACERDA, J.L., 1990. A amostragem por pontos na
estimativa da altura de árvores dominantes e número de árvores por hectares em povoamentos de
Eucalyptus saligna. *Scientia Forestalis* [en línea], vol. 44-43, pp. 50-53. ISSN 1413-9324. Disponible
en: https://www.ipef.br/publicacoes/scientia/nr43-44/cap06.pdf.

LÓPEZ PEÑA, C., 2000.
Utilización del Relascopio de Bitterlich para la cubicación de
árboles. *Forestalia* [en línea], vol. 2. [Consulta: 2 septiembre 2020]. Disponible en: https://docplayer.es/36256105-Utilizacion-del-relascopio-de-bitterlich-para-la-cubicacion-de-arboles.html.

MONTEIRO, J. y SILVA SANTOS, J., 2012. *Avaliação do método de amostragem de Bitterlich
em plantio de Eucalyptus grandis* [en línea]. Brasil: Universidade Federal do Espírito Santo.
Disponible en: http://www.florestaemadeira.ufes.br/sites/florestaemadeira.ufes.br/files/field/anexo /tcc_jeangelis_silva_santos.pdf.

MULYANA, B., ROHMAN, R. y PURWANTO, R.H., 2018. Application of point sampling method
in estimation of stand basal area in community forest. *Journal of Sylva Indonesiana* [en línea],
vol. 1, no. 01, pp. 45-54. [Consulta: 2 septiembre 2020]. ISSN 2622-5158. DOI 10.32734/jsi.v1i1.426. Disponible en: https://talenta.usu.ac.id/Jsi/article/view/426.

SILVA SANTOS, J., RIBEIRO DE MENDONCA, A., FERNANDES DA SILVA, G. y VIEIRA FRAGA
FILHO, C., 2016. Método de amostragem de Bitterlich: uma alternativa de inventário florestal para
pequenas propriedades rurais fomentadas. *Revista Brasileira de Ciências
Agrárias* [en línea], vol. 11, no.
1, pp. 46-52. Disponible en: https://www.redalyc.org/pdf/1190/119045655008.pdf.

VASTARANTA, M., GONZÁLEZ LATORR, E., LUOMA, V., SAARINEN, N., HOLOPAINEN, M. y
HYYPP, J., 2015. Evaluation of a smartphone app for forest sample plot measurements. *Forest* [en línea], vol. 6, pp. 1179-1194. [Consulta: 2 septiembre 2020]. ISSN 1999-4907. DOI 10.3390/f6041179. Disponible en: https://www.researchgate.net/publication/275259702_Evaluation_of_a_Smartphone_App_for_Forest_Sample_Plot_Measurements.

**Conflict of interests:**

The authors declare not to have any interest conflicts.

**Authors' contribution: **

**Marisela Frías Tamayo:** Conception of the idea, literature search and review, instrument making, instrument application, compilation of information resulting from the instruments applied, statistic análisis, preparation of tables, graphs and images, general advice on the topic addressed, drafting of the original (first version), review and final version of the article, article correction, authorship coordinator, translation of terms or information obtained, review of the application of the applied bibliographic standard.

**Nheza Filomena Pereira Jay: **Conception of the idea, literature search and review, instrument application, compilation of information resulting from the instruments applied, statistic análisis,
preparation of tables, graphs and images, drafting of the original (first version), review of the application of the applied bibliographic standard.

**Edilio Aldana Pereira:** Conception of the idea, mpilation of information resulting from the instruments applied, statistic análisis,
review and final version of the article, article correction, authorship coordinator, translation of terms or information obtained, review of the application of the applied bibliographic standard.

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0
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Copyright (c) 2021 Marisela Frías Tamayo, Nheza Filomena Pereira Jay, Edilio Aldana Pereira