Technical feasibility of forest management: a case study in a cerrado
sensu stricto
Legal
Reserve in
northern Minas Gerais, Brazil
Patrícia Noscilene Silva Campos
1
, Natielle Gomes Cordeiro
2
*, Kelly Marianne Guimarães Pereira
3
, Adriana
Leandra Assis
4
,
Carlos Alberto Araújo Júnior
5
, Christian Dias Cabacinha
6
DOI: https://doi.org/10.35699/2447-6218.2020.20601
Abstract
The Cerrado domain is considered as one of the global hotspots, although studies upon management in this vegetation
type have
many gaps in the forest literature. Thus, it’s important to propose viable alternatives to its use. This study aimed to evaluate
the technical feasibility of forest management in a legal reserve of cerrado sensu stricto in Minas Gerais state, as support to
the local increased demand for firewood. A forest inventory was applied from systematic samplings of 10 plots, based on the
diameter criteria at 0.30 m above ground (DAG) ≥ than 5 cm. The Shannon di- versity index (H’) and Pielou’s equability (J)
were used. Furthermore, diametric distribution models and the diameter classes were evaluated by De Liocourt quotient. We
observed that the Shannon diversity was 2.61 nats.ind-¹ and the Pielou (J) equability was 0.74. The De Liocourt quotient
showed a non-constant mean value of 1.97 between the diameter classes. None of the fitted models showed results likewise
the frequency observed in the study. The total wood volume estimated was 2,189.6765 m3. The study area possibly suffered
anthropic interventions, resulting both low volumetric yield and species diversity. Thus, the forest management to the legal
reserve area was considered unfeasible, as it does not present technical sustainability.
Keywords:
Sustainable management. Forest structure. Firewood demand. Brazilian savanna.
Viabilidade técnica de manejo florestal: um estudo de caso em uma reserva legal de
cerrado
sensu
stricto
no norte de Minas Gerais, Brasil
Resumo
O Cerrado é considerado como um dos hotspots mundiais, no entanto, estudos em manejo sustentável nesse domínio são
escassos na literatura florestal. Assim, é importante propor alternativas viáveis para a utilização de seus recursos. Esse estudo
objetivou avaliar a viabilidade técnica de manejo florestal em uma reserva legal de cerrado sensu stricto em Minas Gerais,
como suporte a demanda de lenha para a comunidade rural. Realizou-se o inventário florestal a partir da amostragem
sistemática de 10 parcelas, utilizando o critério de inclusão diâmetro à 0,30 m do solo (DAS)
≥ de 5 cm. Calculou-se o índice de diversidade de Shannon (H’) e equabilidade de Pielou (J). Realizou-se o ajuste de modelos de
distribuição diamétrica e verificou o balanceamento a partir do quociente de De Liocourt. A diversidade
1Forest engineer. São João da Ponte, MG. Brazil.
http://orcid.org/0000-0002-2084-0563
2Federal University of Lavras. Department of Forest Sciences. Lavras, MG. Brazil.
http://orcid.org/0000-0001-8460-4589
3Federal University of Lavras. Departament of Ecology and Conservation. Lavras, MG. Brazil.
https://orcid.org/0000-0003-2886-8795
4Federal University of Minas Gerais. Institute of Agrarian Science. Montes Claros, MG. Brazil.
https://orcid.org/0000-0002-0723-6935
5Federal University of Minas Gerais. Institute of Agrarian Science. Montes Claros, MG. Brazil.
https://orcid.org/0000-0003-0909-8633
6Federal University of Minas Gerais. Institute of Agrarian Science. Montes Claros, MG. Brazil.
http://orcid.org/0000-0002-8148-083X
*Corresponding author: natiellegcordeiro@gmail.com
Received may, 13, 2020. Accepted: august, 06, 2020.
e-ISSN: 2447-6218 / ISSN: 2447-6218. Atribuição CC BY.
CADERNO DE CIÊNCIAS AGRÁRIAS
Agrarian Sciences Journal
2
Campos, P. N. S. et al.
de Shannon (H’) foi 2,61 nats.ind-1 e a equabilidade de Pielou (J) de 0,74. O quociente de De Liocourt apresentou um valor
médio não constante entre as classes de 1,97. Nenhum dos modelos ajustados se aderiu à frequência observada no estudo. O
volume de madeira estimado foi de 2.189,6765 m³. A área de estudo possivelmente sofreu intervenções antrópicas, resultando
em um baixo rendimento volumétrico e diversidade de espécies. A implementação do manejo florestal para a área de reserva
legal foi considerada inviável, pois não apresenta sustentabilidade técnica.
Palavras-chave:
Manejo sustentável. Estrutura florestal. Demanda de madeira. Cerrado.
Introduction
The Cerrado (Brazilian savanna) covers more
than
2 million km², around 22% of the Brazilian territory and is
known for its high fauna and flora diversity, as well
as large
amount of endemic species (Strassburg et al.,
2017). Among
its main phytophysiognomies, the Cerrado
domain include
riparian forest, grasslands, woodlands and rupestrian
grasslands, being considered as one of the world hotspots for
conservation (Myers et al., 2000). Also, it harbors a diversity
of woody, medicinal and fruit species, which together with
its fauna, contribute to the environmental balance. Moreover,
the domain has great importance to water resources
conservation (Durigan et al., 2011; Ferreira et al., 2016;
Oliveira-Filho, 2009).
establishment of guideline and consistent techniques
(Froufe and Seoane 2011; Oliveira and Wolski, 2012).
The natural resources provided by native forests
subsidize the rural communities demand that live in their
surroundings. In this way, the timber and non-tim- ber
products are sources of income for the population.
However, in most cases these resources are used in a
predatory practice, without a professional assistance,
management plan and environmental permits (Costa
and
Mitja, 2010; Pereira et al., 2012). Besides that, there
is a lack
of information in the literature on the Cerrado
management,
especially regarding the technical feasibility
of sustainable
wood harvesting.
The devastation of Cerrado areas for economic
purposes, due to the constant and growing demand for
timber and non-timber products, implies in the need to
propose viable alternatives to natural resources in a
long-
term use (Paparelli and Henkes, 2012; Pereira et al.,
2012).
Hence, sustainable forest management plan has
been
considered as the main alternative to ensure an ade- quate
exploration, ensuring the biodiversity conservation
and
preservation (Scarano et al., 2014). In other words,
the
management plan enables the use of available resour-
ces in the
native forests through mitigating alternatives which may
imply in a low-impact generation, as well as achieving
economic, social and environmental success.
Therefore,
protected areas such as the Legal Reserve can
be used to
timber and non-timber products extraction, as long as it is
based on a sustainable management plan approved by the
competent authority (Brasil 2012; Braz et al., 2012;
Kanashiro, 2014; Minas Gerais, 2013).
In this sense, the decision-making regarding forest
resources requires knowledge about the forest structure and
composition, thus performing technical analyses from the
floristic, phytosociology, horizontal,
vertical, parametric and
diametric structures of the forest
community (Calegari et al.,
2010; Chaves et al., 2013; Klauberg et al., 2010). Thus, the
study aimed to evalua- te the implementation of sustainable
management to a legal reserve with cerrado sensu stricto
vegetation, as support to the energy demand of a rural
community in the municipality of Montes Claros, Minas
Gerais state, Brazil.
Materials and methods
The data of this study is from a Legal Reserve area
with cerrado sensu stricto vegetation, which has an extension
of 27.4 hectares, and is located at a rural area called Camelas.
Nowadays, about 70 families live in the community.
Therefore, there is a demand of approxima- tely 10.67
m³.month-1 of firewood and a representative
amount is
removed from the nearby native vegetation. The
firewood is
used to supply energy to the manufacturing process of
“rapadura”, a kind of Brazilian dessert.
The Legal Reserve area (LR) was instituted in
national level by the Forest Code, being regulated Federal
Law
12651/2012 and, for Minas Gerais state, by State
Law
20922/2013. The LR is considered a legally protected
area that
aims to maintain biodiversity and ensure the
environment
balance (Brasil, 2012; Minas Gerais, 2013).
Considering
properties with Cerrado vegetation which are not in the
Legal Amazon, the area destined to the Legal Reserve must
be equal to or greater than 20% of the property total area
(Brasil, 2012; Borges and Rezen- de, 2011). Further, the
Legal Reserve has specifications
regarding its exploitation, in
which clearcutting and land
use for non-conservation purpose
are prohibited. Howe- ver, it is possible to manage the LR
sustainably, as long as authorized by the competent
authority considering
The Camelas community, which has agriculture as
predominant activity, is located 50 km from the munici-
pality of Montes Claros - Minas Gerais state, Brazil, under
the
coordinates -16.416168° latitude and -44.003954° longitude
(Figure 1). According to Köppen and Geiger
classification,
the region climate is Aw, tropical with a dry
season. The mean
annual temperature is 22.7°C, mean
Cad. Ciênc. Agrá., v. 12, p. 01–10, https://doi.org/10.35699/2447-6218.2020.20601
3
Technical feasibility of forest management: a case study in a cerrado
sensu stricto
Legal Reserve in northern Minas Gerais, Brazil
annual precipitation of 1,029 mm and an altitude of 906 m
(Alvares et al., 2013).
Figure 1 –
Study area located in the Camelas community Legal Reserve in Montes Claros city, Minas Gerais state, Brazil.
In order of achieve previous information from the
area, the forest inventory was carried out from systematic
samplings of 10 plots of 10 x 100 m (1000 m²), totaling
one
hectare sampled (Moro and Martins, 2011). All trees
with
diameter at 0.30 meters above ground (DAG) grea- ter than 5
cm were measured. In addition, tree heights were measured
with telescopic measuring stick and the botanical material
were collected to later identification
through specialists,
specific literature (Silva-Júnior, 2012) and virtual herbaria
(Flora do Brasil, 2019; JBRJ, 2019). Hence, it was considered
the APG IV classification system
(2016). All measured trees were labeled with metal tags
describing the plant and plot number.
Afterwards, it was calculated the wood volume,
Shannon and Weaver diversity index (H’), Pielou equa-
bility (J) (Magurran, 2011) and phytosociological para-
meters (species richness, absolute and relative density,
relative frequency, relative dominance and importance value
index) (Mueller-Dombois and Ellenberg, 1974).
The following equation (Eq. 1), proposed by
Rezende et al. (2006), was used to estimate the wood
volume to the Legal Reserve.
V= 0.000109 * DAG² + 0.000451 *DAG² * H
R2 = 98.02% ; Syx = 25% (Eq. 1)
Where: DAS: Diameter at 0.30 meters above ground (cm); H: Tree height (m); V: Volume (m3); R2; Coefficient of determination; Syx: Residual standard
error.
In order to assess the diameter heterogeneity, the
trees were distributed in twelve diametric classes,
considering an amplitude of 3 cm (Scolforo and Thiersch,
2004). Then, the De Liocourt quotient (q) (De Liocourt,
1898) was calculated using the ratio between the number
of
individuals in successive classes after determining the
frequency (Hess et al., 2014).
To assess the diametric distribution pattern of trees
per hectare (Yj) by diameter class (Xi), it was fitted
the models
of Meyer, Mervart and Weibull (Scolforo, 1998)
(Table 1). The
use of probability density function, like the models fitted to
this study, allows to achieve infor- mation that may lead to
the planning of vegetation yield as well as to simulate
thinning procedures and ensure
the sustainable forest
management. Thus, the chi-square
Cad. Ciênc. Agrá., v. 12, p. 01–10, https://doi.org/10.35699/2447-6218.2020.20601
4
Campos, P. N. S. et al.
test, with a significance level of 95%, was applied to the
frequencies found searching to analyze the adjusted
models adherence by exponential distribution (Souza and
Soares, 2013).
Table 1 – Diametric distribution models used to estimate the expected frequency in the Legal Reserve area in Montes Claros
city, Minas Gerais state, Brazil.
Model
Equation
Meyer’s exponential
Mervart’s potential
Weibull with two parameters
Nj = β0 .ϵj
ϵβ
1Dj
Nj = β0 Dj β1.ϵj
F (Dj) = 1- exp
– (Dj/b)^y
Where: Nj is the number of trees per hectare in the j-th diameter class at 0.30 meters above ground (DAG); β0, β1, y: parameters to be estimated; F (Dj) is the
accumulated probability up to the j-th DAG class; ϵ: error for the j-th DAG class.
Lastly, regarding the individuals heights stratifi-
cation, they were split into nine classes with an amplitude of
one standard deviation (sd) (Souza and Soares, 2013).
as well as medicinal properties (Araújo et al., 2012; Flora
do
Brasil, 2019; Mota et al., 2014). The second species with
great importance value index, C. brasiliense, has great
relevance for the Cerrado due to its economic and cultural
value. Nevertheless, this species is protected by Law, being
its suppression allowed only in specific cases such as social
interest, urban area and anthropized ru- ral area until July
22, 2008 (Afonso et al., 2015; Minas Gerais, 2012).
Results and discussion
Considering the forest inventory procedure, it was
measured a total of 512 individuals, distributed in 34
species and 13 families. The population mean DAG was
equal to 7.87 cm and the maximum equal to 40.67 cm. In
addition, the mean height of the individuals was
3.5 m and the maximum height was 12.0 m. The total
absolute density was 512 trees.ha-1 and the basal area of
3.72 m2.ha-1, values lower than those found in other studies
of cerrado sensu stricto.
Species that have a relative density (RD) less than
or equal to 1% are considered rare (Almeida et al., 1993;
Pereira-Silva et al., 2004). We found in the area 20 species
with RD less than 1%, not being able to be management
(Minas Gerais, 2013; Reis et al., 2013). The Shannon
diversity index (H’) was 2.61 nats.ind-¹ and the Pielou
equability index (J) was 0.74. Also, the studied area showed
a species diversity minor than in other studies in the same
vegetation type, thus allowing to infer that the legal reserve
may have been explored by the surrounding community
(Silva Neto et al., 2016; Costa et al., 2010).
The horizontal structure to our study presents an
unusual pattern to the vegetation type, when compared
to
other studies, in which it is expected to find a balanced
diametric structure (Costa et al., 2010; Giácomo et al.,
2013). This result may be linked with possible anthropic
interventions such as agricultural and cattle raising ac-
tivities in which justifies the low intensity of individuals
(Paula et al., 2007).
Regarding the diametric distribution, the area
presented 80.47% of the individuals concentrated at the
first
class, in which the central value is 6.5 cm in diameter
(Figure
2). As for the De Liocourt quotient, it showed a non-
constant value between classes (9.16; 3.75; 1.71;
1.17; 0.86; 0.88; 1.14; 2.33; 0.00; 0.00; 0.67), resulting
an average value of 1.97.
As regard to the floristic aspects, the Combreta-
ceae family presented the highest number of individuals
(153), due to successive occurrence of the Terminalia
fagifolia Mart. species. However, the Fabaceae family was
the
one that had the largest number of species (14). The five
species with highest importance value index (IVI) in
decreasing order were Terminalia fagifolia Mart.; Caryocar
brasiliense Cambess.; Vatairea macrocarpa (Benth.) Ducke;
Qualea multiflora Mart. and Hymenaea stigonocarpa Mart.
ex
Hayne (Table 2).
The diametric distribution presented the J - in-
verse pattern, which is expected for heterogeneous forests
in
Brazil (Silva Neto et al., 2016). However, a minimal
number of trees was observed in the largest DAG classes,
besides to their absence in the 33.5 cm class of central
value. Similar results were found by Oliveira et al. (2015)
whom analyzed the cerrado sensu stricto vegetation in
western Bahia. The authors found a concentration of
96.33% of individuals in the first three diametric classes.
Considering the same vegetation in an area located in Sete
Lagoas - MG, 68% of the sampled individuals were
distributed in the first class (Pereira et al., 2013).
High density of T. fagifolia was detected in the
area, which may be associated with the morphology of its
fruit characterized as winged, allowing anemochory
dispersion, as well as by its irregular spatial distribution
(Ribeiro et al., 2018; Soares Neto et al., 2014). This species
is
commonly found in the Cerrado, with its occurrence in the
Brazil southeast region being only in Minas Gerais
state. The
T. fagifolia is a relevant species due its intrinsic
characteristics
such as high wood density and durability,
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5
Technical feasibility of forest management: a case study in a cerrado
sensu stricto
Legal Reserve in northern Minas Gerais, Brazil
Table 2 – Species phytosociology in the cerrado sensu stricto area located in the municipality of Montes Claros - Minas Gerais,
Brazil, in decreasing order of IVI.
Species
N
RD
RF
RDo
IVI
Terminalia fagifolia Mart. et Zucc
Vatairea macrocarpa (Benth.) Ducke
Qualea multiflora Mart.
Caryocar brasiliense Cambess.
Eriotheca pubescens (Mart. & Zucc.) Schott & Endl.
Aspidosperma macrocarpon Mart.
Aspidosperma subincanum Mart.
Dalbergia miscolobium Benth.
Hymenaea stigonocarpa Mart.ex Hayne
Bowdichia virgilioides Kunth
Qualea grandiflora Mart.
Eugenia dysenterica DC.
Indeterminate
Vochysia thyrsoidea Pohl.
Machaerium opacum Vogel
Machaerium acutifolium Vogel
Pouteria ramiflora (Mart.) Radlk.
Enterolobium gummiferum (Mart). J.F. Macbr.
Dimophandra mollis Benth.
Hancornia speciosa Gomes
Plathymenia reticulata Benth.
Stryphnodendron adstringens (Mart.) Corville
Copaifera langsdorffii Desf.
Aspidosperma tomentosum Mart.
Anonna emarginata (Schltdl.) H. Rainer.
Miconia ferruginata DC.
Strychnos pseudoquina A. St.-Hil.
Couepia grandiflora (Mart. & Zucc.) Benth
Schefflera macrocarpa (Cham. & Schltdl.) Frodin
Himatanthus obovatus (Müll. Arg.) Woodson
Handroanthus ochraceus (Cham.) Mattos Salvertia
convallariaeodora A.St.-Hil.
Machaerium vilosumm Vogel.
Chamaecrista sp. H.S. Irwin & Barneby
153
52
50
45
33
20
19
19
18
17
13
6
6
6
5
5
5
5
4
4
4
3
3
2
2
2
2
2
2
1
1
1
1
1
29.88
10.16
9.77
8.79
6.45
3.91
3.71
3.71
3.52
3.32
2.54
1.17
1.17
1.17
0.98
0.98
0.98
0.98
0.78
0.78
0.78
0.59
0.59
0.39
0.39
0.39
0.39
0.39
0.39
0.20
0.20
0.20
0.20
0.20
7.35
5.88
5.88
7.35
5.88
4.41
5.88
5.15
5.15
4.41
3.68
3.68
2.21
1.47
2.94
2.94
2.21
2.21
1.47
2.21
2.21
1.47
1.47
1.47
1.47
1.47
1.47
1.47
1.47
0.74
0.74
0.74
0.74
0.74
42.55
4.20
4.80
23.25
3.25
1.76
2.15
1.32
3.63
1.34
0.91
0.45
0.56
0.83
0.61
0.41
0.39
0.34
3.43
0.52
0.28
0.27
0.18
0.53
0.32
0.19
0.18
0.17
0.15
0.74
0.09
0.08
0.06
0.06
79.79
20.24
20.45
39.39
15.58
10.08
11.74
10.18
12.30
9.07
7.13
5.29
3.94
3.47
4.53
4.33
3.57
3.53
5.68
3.50
3.27
2.33
2.23
2.40
2.18
2.05
2.04
2.03
2.01
1.67
1.02
1.01
0.99
0.99
Where: N= number of individuals; RD = relative density (%); RDo = relative dominance (%); RF = relative frequency (%); IVI = importance value index
(%).
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Campos, P. N. S. et al.
Figure 2 – Diameter classes (cm) of individuals sampled in the cerrado sensu stricto Legal Reserve area located in Montes
Claros, Minas Gerais state, Brazil.
Where: N= number of individuals.
The community absence of balance is reflected in
the mean value of the De Liocourt quotient (Alves Júnior et
al., 2010; Hess et al., 2014). Thus, the values discrepancy
can mean the presence of a high mortality rate and low
recruitment between classes, especially regarding the lack of
individuals in the largest diametric classes (Cunha and Silva
Júnior, 2012). It is expected an imbalance between the
diameter classes to native forests, with a high concentration
of individuals in the lower classes (Calixto Júnior et al.,
2011; Silva Neto et al., 2016). However, areas with a
higher degree of conservation tend to be in close proximity
to balanced distribution. Instead, the study region is
characterized
by not favorable edaphoclimatic conditions, and
this fact may be not allowing a greater increment in the area,
thus justifying the presence of a greater number of individuals
in the first classes and resulting in a low volumetric yield
(Ávila et al., 2014; Lima et al., 2013).
According to the diametric distribution models
fitted using the observed frequency (OF) within each class,
it is observed that the Meyer model presented the
lowest
frequencies in relation to the frequencies observed in the study,
since all results were statistically significant,
presenting p-
values <0.05. Thus, the model does not describe the tree
community behavior, as it presents a discrepancy regarding
the observed frequency, which re-
sults in an unfeasible forest
management implementation.
Moreover, none of the models
represents correctly the
vegetal formation behavior, and
therefore did not present an efficient precision in adjusting
distributions (Table 3).
This result may be associated with
the heterogeneity of diameters present in the sample (Barros
et al., 1979) (Figure 3).
Table 3 – Chi-square test for the diametric distribution models used in the study in the cerrado sensu stricto Legal Reserve
area located in Montes Claros, Minas Gerais state, Brazil.
² test
Model
Meyer
Mervart
Weibull
2,190.12*
554.36*
37.64*
Where: * significant Chi-square (²) test for = 0.05.
Concerning to the height stratification, it is possi-
ble
to observe that 80.86% of the trees are concentrated in the
first and second classes. Thus, the stratification of height
allowed to predict about the height dominance in lowest
classes and this result is not an expected distribu- tion pattern
for cerrado sensu stricto, since it is usual to find a normal
distribution (Pereira et al., 2013) (Figure 4).
area, it was 2,189.6765 m³. Nevertheless, the estimated wood
volume includes individuals of the species Caryo- car
brasiliense Cambess and Ipê Amarelo of the genus
Handroanthus, which are protected by Law and their
suppression is not allowed (Minas Gerais, 2012). It also
includes species whose occurrence in the studied area is
considered rare.
Based on the results, Cerrado management legis-
lation of the state of Minas Gerais state and aiming to meet the
wood demand to the community in the generation of
The estimated wood volume per hectare was
79.9152 m³ and considering the total Legal Reserve
Cad. Ciênc. Agrá., v. 12, p. 01–10, https://doi.org/10.35699/2447-6218.2020.20601
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Technical feasibility of forest management: a case study in a cerrado
sensu stricto
Legal Reserve in northern Minas Gerais, Brazil
energy, it can be inferred that initially there is a need to
implement conservation and restoration measures for the
Legal Reserve area, since this possibly suffered
pressures
imposed by the surrounding community. Thus,
the implementation of sustainable management aiming at the
wood extraction to energy supply energy in the
process of
manufacturing “rapadura”, becomes unfeasible.
Figure 3 – Observed frequency according to the adjustment of the diametric distribution models for the cerrado sensu stricto
Legal Reserve located in Montes Claros city, Minas Gerais state, Brazil.
Where: OF is the observed frequency.
Figure 4 – Height classes (m) of individuals sampled in the cerrado sensu stricto Legal Reserve area located in Montes Claros
city, Minas Gerais state, Brazil.
Where: N= number of individuals.
Considering the current volumetric stock
(2,189.6765 m³) and a 10-year cycle for wood harvesting (as
established by law), there is a gross supply of 18.2473 m³.
month
-
¹ of firewood. According to the Cerrado mana-
gement
legislation, it is prohibits the clearcuting of the
rare species as well as seed-bearing trees because they must
be protected so the environmental sustainability of forest
management, since the Cerrado requires a longer time for its
recovery (Líbano and Felfili, 2006; Rezende et al., 2005).
Thus, when considering that in this gross
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8
Campos, P. N. S. et al.
monthly volumetric stock, there are species that are not
allowed to be cutting according to the law, it appears that
this
volumetric stock is not enough to sustainably meet the
demand (10.67 m3.month-1 of firewood) informed by the
rural community.
ecological processes, generating an imbalance in the
vegetation.
Acknowledgments
The authors express the gratitude to the Institute
of
Agrarian Sciences, Federal University of Minas Gerais
(UFMG) and the Federal University of Lavras (UFLA) for the
support and infrastructure to develop of the study.
Conclusion
The implementation of a forest management to the
Legal Reserve area is not viable, as it does not pre- sent
sustainability for the objective. Among the species
identified, approximately 59% are considered as rare
species, which do not allow to proceed a clearcut of them.
In
addition, the basal area indicates a low degree of site
occupation and a structure unable to provide the necessary
wood
turnover. The selective cutting would interfere in the
community’s resilience, affecting its dynamics and
Funding
This study was supported in part by the Coorde-
nação de Aperfeiçoamento de Pessoal de Nível Superior
- Brasil (CAPES) - Finance Code 001. Also, we thank to
the
Pró-Reitoria de Extensão from the University of Minas
Gerais.
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