**2. Material and methods**

Biological diversity or biodiversity are expressions that refer to the variety of life on the planet, or to the property of living systems to be distinct. It includes plants, animals, microorganisms,

The diversity is regarded as an indication of the ecosystem well-being. It indicates directly the protection of certain place, the higher the value, the larger the biodiversity of the ecosystem

Because it is an extremely complex structure, there is a problem to evaluate biodiversity, so we need to find simplified variables for its determination [4]. Some of them—as the composition, type of regeneration, introduced species, the presence of dead trees and the landscape have been defined according to the 4th Ministerial Conference on the protection of forests, in Vienna, 2002. Especially biodiversity is important, since it represents the state of conservation of ecosystems, including forests, where it can help evaluate the sustainability of the resources

Biological diversity is a central theme of ecological theory and has been the subject of many discussions. Currently, researchers have developed a large number of parameters for the measurement of biodiversity as an indicator of the state of ecological systems, with practical applicability for purposes of conservation, management, and environmental monitoring [5]. Biodiversity can be expressed in four levels: diversity of genes, species, and ecosystems settlement. It can be appreciated by the number (wealth) of different biological categories and relative abundance (evenness) of these categories; and also for variability in local level (alpha diversity), the complementarity between biological habitats (beta diversity) and variability between landscapes (gamma diversity) [6]. It includes, therefore, all the living or biological

Any environmental protection strategy must ensure the maintenance of biodiversity. All the living beings that inhabit a country constitute an irreplaceable heritage, because each species, as well as each population, has in its genetic composition information from millions of years of evolutionary adaptations. However, in order to exercise management plans and protection of nature reserves, trusted tools able to measure its variation in space and time are required. Assessing the biodiversity of an ecosystem by its forestry component assumes that the arboreal component is what sustains a forest ecosystem [7]. Already the quantification of diversity through natural regeneration allows a complete characterization of the forest as an ecosystem, and not only by its arboreal component. This approximate evaluation of possible interventions made in settlements, as well as the intensity and provides a rough overview of the volume of the existing biomass in the forest, whose presence can be very relevant with regard to

Considering the importance of the subject, the objective of this work is to evaluate the arboreal component and natural regeneration biodiversity in an Atlantic Rainy Forest area in Southern Brazil, through different diversity indices in order to find the variables that better represent

ecosystems, and ecological processes in a functional unit [2].

resources, genetic resources, and their components.

the current status of diversity in study environment.

fire prevention, energy potential, and characterization of biodiversity.

in question [3].

46 Selected Studies in Biodiversity

are managed [1].

#### **2.1. Characterization of the study area**

This study was conducted on National Forest (FLONA) of São Francisco de Paula, administered by the Chico Mendes Institute for Biodiversity Conservation (ICMBio), constituting a conservation unit of sustainable use. The aim of this type of conservation unit (UC) is to make nature conservation with the sustainable multiple uses of its natural resources and stimulate scientific research, with emphasis on methods for sustainable forest management [8].

The FLONA is located in the northeast of the State of Rio Grande do Sul, in southern Brazil, in the city of San Francisco de Paula. It has a total area of 1606.69 ha, which 9019 ha are occupied by native forests (Mixed Rainy Forest and Dense Rainy Forest), over 600 ha by planted forests (*Pinus* spp., *Araucaria angustifolia*, and *Eucalyptus* spp.) and the rest by other areas such as fields, lakes, infrastructure among others.

The region is one of the wetter of the State, with more than 2000 mm rainfall per year and with annual average temperature of approximately 14.5°C. According to the Köppen's climate classification, the climate is classified as "Cfb" mesothermic medium [9]. The average relative humidity is 83.9%. Summer is characterized by mild temperatures and winter by constant and intense cold, where the average temperature is close to 0°C. Frosts are common in the cooler half and may snow in winters.

The types of soil found in the FLONA are Cambisols, Chernozems, and Newsoils [10]. Geomorphology is marked by a strongly wavy relief in the northern part, with an altitude of 930 m and rugged in the South, forming canyons with more than 100 m in depth [11] (**Figure 1**).

The predominant forest vegetation belongs to the Mixed Rainy Forest. In addition to *Araucaria angustifolia* (Bertol.) Kuntze, which prints a physiognomic character in this vegetation, it is common to find other tree species such as *Sebastiania commersoniana* (Baill.) L. b. SM. & Downs, *Cedrela fissilis* Vell., *Podocarpus lambertii* Klotzsch ex Endl., among others. It has the peculiarity to be a transition zone between the Mixed Rainy Forest and Dense Rainy Forest, with endemic species as *Oreopanax fulvum* Marchal, typical of the Atlantic forest [12]. The author even describes the endemism does not get more accentuated because there is a physical barrier to the species by the existence of the Canyons.

#### **2.2. Sampling**

The work was performed in six permanent plots of 100 × 100 m (10,000 m<sup>2</sup> ), which were divided into 10 tracks of 10 × 100 m (1000 m2 ) and these subdivided into 10 subunits of 10 × 10 m (100 m2 ). Within each plot, 30 subunits were drawn, being three subunits by track from 10 total tracks in each unit of 100 × 100 m, where vegetation surveys and environmental parameters were made. The distribution of selected subplots in each parcel can be observed in **Figure 2**.

**2.3. Data collection**

**2.4. Biodiversity indices**

*2.4.1. Alpha diversity*

ral regeneration and for the arboreal component.

Species richness Margalef index *<sup>R</sup>*<sup>1</sup> <sup>=</sup> \_\_\_\_

Dominance Simpson index *D* = ∑*p*

Information Shannon index *<sup>H</sup>*′ <sup>=</sup> <sup>−</sup>∑*<sup>i</sup>*=1

Equity Pielou index *<sup>J</sup>*′ <sup>=</sup> *<sup>H</sup>*′ \_\_\_\_

Similarity Jaccard index *I*

**Table 1.** Alpha and Beta diversity indices used in the work evaluation.

index; *pi* = proportion of species in a Community (*pi* = *ni*

*c* = number of species present in both places (*A* and *B*).

specie = 1/*D*; *E* = Hill index. *Ij* = Jaccard index; *I*

All individuals over 1.30 m and with a circumference at breast height (CBH) from 3 cm, minimum, and up to the limit of 29.9 cm are considered as natural regeneration. As an arboreal component, we considered all individuals with CBH greater than or equal to 30 cm. Individuals sampled were numbered and identified botanically, collecting botanical material, in case of doubt, registering the number of plants and the common names. The identification in level of family, genus, and species, was carried out consulting the Herbarium of the Department of Forest Sciences at de Santa Maria Federal University, according to the APG II system [13].

Methods for Biodiversity Assessment: Case Study in an Area of Atlantic Forest in Southern Brazil

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49

Biodiversity indices (**Table 1**) that provided the evaluation for this work were presented by [14, 15]. These were calculated for each sampling unit leased in the study area, both for natu-

The majority of the proposed methods to quantify the biodiversity of species refer to the diversity within communities, namely as alpha diversity. Within this, there are methods based

Menhinick index *<sup>R</sup>*<sup>2</sup> <sup>=</sup> \_\_*<sup>S</sup>*

MacIntosh index *<sup>D</sup>* <sup>=</sup> \_\_\_\_ *<sup>n</sup>* <sup>−</sup> *<sup>U</sup>*

Alatalo index *<sup>F</sup>* <sup>=</sup> \_\_\_\_\_

Hill index *<sup>E</sup>*´ <sup>=</sup> \_\_\_

*R*<sup>1</sup> = Margalef index; *R*<sup>2</sup> = Menhinick index; *S* = total number of species; *n* = total number of individuals; *D* = Simpson

*J* = Pielou index; *H*′max = ln(*S*) = Alatalo index; *N* = number of abundant species = eH′; *N*2 = number of very abundant

of species present on the site *B*; *a* = number of species unique to the site *A*; *b* = number of species unique to the site *B*; and

Sorensen index *<sup>I</sup>*

(*S* − 1) ln*n*

> *i* 2

*n* − √ \_\_ *n*

*H*max ′

*N*2 − 1*N*1 − 1

> *N*2 *N*1

*<sup>j</sup>* <sup>=</sup> \_\_\_\_\_ *<sup>c</sup>*

*<sup>s</sup>* <sup>=</sup> \_\_\_2*<sup>c</sup>*

*<sup>a</sup>* <sup>+</sup> *<sup>b</sup>* <sup>+</sup> *<sup>c</sup>* <sup>=</sup> \_\_\_\_\_\_ *<sup>c</sup> A* + *B* − *c*

*<sup>a</sup>* <sup>+</sup> *<sup>b</sup>* <sup>=</sup> \_\_\_\_\_\_ <sup>2</sup>*<sup>c</sup> A* + *B* − *c*

*<sup>s</sup>* = Sorensen index; *A* = number of species present on the site *A*; *B* = number

/*n*); *d* = MacIntosh index (*i* = 1, 2, 3, …, *S*); *H*′ = Shannon index;

*s* (*p i* )(ln*p i* )

√ \_\_ *n*

**Figure 1.** View from the FLONA of São Francisco de Paula, Rio Grande do Sul, Brazil.

**Figure 2.** Scheme of subplots in each sampling unit used in this study in southern Brazil.

#### **2.3. Data collection**

All individuals over 1.30 m and with a circumference at breast height (CBH) from 3 cm, minimum, and up to the limit of 29.9 cm are considered as natural regeneration. As an arboreal component, we considered all individuals with CBH greater than or equal to 30 cm. Individuals sampled were numbered and identified botanically, collecting botanical material, in case of doubt, registering the number of plants and the common names. The identification in level of family, genus, and species, was carried out consulting the Herbarium of the Department of Forest Sciences at de Santa Maria Federal University, according to the APG II system [13].

#### **2.4. Biodiversity indices**

Biodiversity indices (**Table 1**) that provided the evaluation for this work were presented by [14, 15]. These were calculated for each sampling unit leased in the study area, both for natural regeneration and for the arboreal component.

#### *2.4.1. Alpha diversity*

The majority of the proposed methods to quantify the biodiversity of species refer to the diversity within communities, namely as alpha diversity. Within this, there are methods based


*R*<sup>1</sup> = Margalef index; *R*<sup>2</sup> = Menhinick index; *S* = total number of species; *n* = total number of individuals; *D* = Simpson index; *pi* = proportion of species in a Community (*pi* = *ni* /*n*); *d* = MacIntosh index (*i* = 1, 2, 3, …, *S*); *H*′ = Shannon index; *J* = Pielou index; *H*′max = ln(*S*) = Alatalo index; *N* = number of abundant species = eH′; *N*2 = number of very abundant specie = 1/*D*; *E* = Hill index. *Ij* = Jaccard index; *I <sup>s</sup>* = Sorensen index; *A* = number of species present on the site *A*; *B* = number of species present on the site *B*; *a* = number of species unique to the site *A*; *b* = number of species unique to the site *B*; and *c* = number of species present in both places (*A* and *B*).

**Table 1.** Alpha and Beta diversity indices used in the work evaluation.

**Figure 2.** Scheme of subplots in each sampling unit used in this study in southern Brazil.

**Figure 1.** View from the FLONA of São Francisco de Paula, Rio Grande do Sul, Brazil.

48 Selected Studies in Biodiversity

on quantification of the number of species (species richness) and those based on community structure, in the other hands, in proportion of the value of importance of each species. These can still be based on the information, on dominance or equity of the Community [15].

used within the category equity, and measures the proportion of diversity observed with respect to the maximum expected diversity. The value of this index varies from 0 to 1, and

Methods for Biodiversity Assessment: Case Study in an Area of Atlantic Forest in Southern Brazil

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51

The index of Hill is less used for vegetation, with greater use in wildlife studies. This index refers to the distribution of the abundance of the species, or the manner in which the abundance is distributed between the species in a community. When all species in a sample are also abundant, the equity index must take the maximum value, and decreases, tending to zero, as the relative abundances of species diverge from its equality. It has as parameters Simpson and Shannon indices. The Hill index can cause some misunderstandings in some particular cases: reaches high value when equity is high or when a species dominate the community [15].

Alatalo index is known as Hill modified index. This index will approaching zero as the smaller gender equality in the composition of species in different plots [16]. This index is not recommended because, when used in comparisons, tends to overvalue the equity, having a

Beta diversity or among habitats represents the degree of change of species, as well as biotic change through environmental gradients [6]. It is based in proportions or differences, that can be quantified based on indices or similarity coefficients of dissimilarity or distance between the plots, from quantitative or qualitative data, as well as by beta diversity indices themselves. The easiest system to measure beta diversity between pairs of localities is through the use of similarity coefficients [5]. The most used is the Jaccard and Sorensen indices (**Table 1**). These indices are designed to be equal to 1 if there are complete similarity cases (when the two species are identical) and equal to zero if the plots are dissimilar and have no species in common. One of the great advantages on these measures is your simplicity. However, this can also be a disadvantage, since the coefficients do not consider the abundance of species. All species have

The diversity indices calculated at work (**Table 2**) included the contents of Margalef and Menhinick (species richness); Simpson and MacIntosh (dominance); Shannon (information);

The value found by index of Margalef (3.81) featuring low diversity when compared to other regeneration areas. In a study of similarity in floristic composition between an area of natural regeneration of Mixed Rainy Forest and natural regeneration in an adult Brazilian pine plantation, in Irati, Paraná [21], the authors found a value of 10.68 floristic diversity in Margalef index for the Mixed Rainy Forest, denoting high floristic diversity. The low diversity in the present study may be explained by the fact that the index does not consider the size of the

when it reaches the value 1, it means that all species are equally abundant [15, 16].

non-linear relationship with this [15].

**3. Results and discussion**

**3.1. Natural regeneration**

an equal weight in the equation, whether abundant or rare [5].

Pielou, Alatalo and Hill (equity) and Jaccard and Sorensen (similarity).

sampled area, which in this case is less than the commonly found in the works.

*2.4.2. Beta diversity*

#### *2.4.1.1. Species richness*

The measures of species richness provide an understandable and instantaneous expression of diversity [5]. Within the species richness indices, we can cite the Margalef and Menhinick indices (**Table 1**). These indices do a relationship between the number of species and the number of individuals, and the larger the area of the sampling unit. The greater the number of species entered, the greater the value of the index [5, 15, 16]. One of the great advantages of Margalef and Menhinick index is its ease calculation, being used successfully in several scientific papers [5].

#### *2.4.1.2. Information*

The most commonly indices used are those based on information theory. These indices are based on the logic that the diversity, or information, in a natural system, can be measured in a similar way to information contained in a code or message [5]. Shannon and Wiener obtained the function known as Shannon-Wiener index (**Table 1**). In many works, researches wrongly named it as "Shannon-Weaver" [17, 18]. This index considers that individuals are sampled at random from a population "indefinitely large" [5, 16, 19].

The Shannon index assumes zero value when there is only one species and the logarithm of the number of species, when the same number of individuals represents all species [5]. Shannon values generally vary between 1.3 and 3.5, and may exceed 4.0, and reach around 4.5 in tropical forest environments [20]. The authors even claim that this index assigns greater value to rare species and is one of the best indices to be used in comparisons, if there is no objective in separating abundance to rarity.

#### *2.4.1.3. Dominance*

The indexes based on dominance are inverse parameters to the concepts of uniformity or equity of the community. These indices take into account the representativeness of the species with the highest value of importance, without evaluating the contribution of other species [15]. Among these, we can cite the Simpson and MacIntosh indices (**Table 1**). The Simpson index shows the probability that two individuals taken at random from a given community are of different species. This index is heavily influenced by the most abundant species of sampling unit while it is least sensitive to species richness [5, 16]. The Simpson index varies from 0 to 1, and the closer to 1 the more dominance. On the other hand, the MacIntosh will introduce greater dominance when their values are closer to 0. The index of MacIntosh is not a dominance index; however, it can be calculated as a measure of diversity or dominance, which is independent of the total number of individuals [5].

#### *2.4.1.4. Equity or uniformity*

The equity or uniformity indices show how the number of individuals are distributed among the species, denoting less or greater uniformity in the composition of the parcels. Among these, we can cite the Pielou, Hill, and Alatalo (**Table 1**). Pielou index is the most commonly used within the category equity, and measures the proportion of diversity observed with respect to the maximum expected diversity. The value of this index varies from 0 to 1, and when it reaches the value 1, it means that all species are equally abundant [15, 16].

The index of Hill is less used for vegetation, with greater use in wildlife studies. This index refers to the distribution of the abundance of the species, or the manner in which the abundance is distributed between the species in a community. When all species in a sample are also abundant, the equity index must take the maximum value, and decreases, tending to zero, as the relative abundances of species diverge from its equality. It has as parameters Simpson and Shannon indices. The Hill index can cause some misunderstandings in some particular cases: reaches high value when equity is high or when a species dominate the community [15].

Alatalo index is known as Hill modified index. This index will approaching zero as the smaller gender equality in the composition of species in different plots [16]. This index is not recommended because, when used in comparisons, tends to overvalue the equity, having a non-linear relationship with this [15].

#### *2.4.2. Beta diversity*

on quantification of the number of species (species richness) and those based on community structure, in the other hands, in proportion of the value of importance of each species. These

The measures of species richness provide an understandable and instantaneous expression of diversity [5]. Within the species richness indices, we can cite the Margalef and Menhinick indices (**Table 1**). These indices do a relationship between the number of species and the number of individuals, and the larger the area of the sampling unit. The greater the number of species entered, the greater the value of the index [5, 15, 16]. One of the great advantages of Margalef and Menhinick index is its ease calculation, being used successfully in several scientific papers [5].

The most commonly indices used are those based on information theory. These indices are based on the logic that the diversity, or information, in a natural system, can be measured in a similar way to information contained in a code or message [5]. Shannon and Wiener obtained the function known as Shannon-Wiener index (**Table 1**). In many works, researches wrongly named it as "Shannon-Weaver" [17, 18]. This index considers that individuals are sampled at

The Shannon index assumes zero value when there is only one species and the logarithm of the number of species, when the same number of individuals represents all species [5]. Shannon values generally vary between 1.3 and 3.5, and may exceed 4.0, and reach around 4.5 in tropical forest environments [20]. The authors even claim that this index assigns greater value to rare species and is one of the best indices to be used in comparisons, if there is no

The indexes based on dominance are inverse parameters to the concepts of uniformity or equity of the community. These indices take into account the representativeness of the species with the highest value of importance, without evaluating the contribution of other species [15]. Among these, we can cite the Simpson and MacIntosh indices (**Table 1**). The Simpson index shows the probability that two individuals taken at random from a given community are of different species. This index is heavily influenced by the most abundant species of sampling unit while it is least sensitive to species richness [5, 16]. The Simpson index varies from 0 to 1, and the closer to 1 the more dominance. On the other hand, the MacIntosh will introduce greater dominance when their values are closer to 0. The index of MacIntosh is not a dominance index; however, it can be calculated as a measure of diversity or dominance,

The equity or uniformity indices show how the number of individuals are distributed among the species, denoting less or greater uniformity in the composition of the parcels. Among these, we can cite the Pielou, Hill, and Alatalo (**Table 1**). Pielou index is the most commonly

random from a population "indefinitely large" [5, 16, 19].

which is independent of the total number of individuals [5].

objective in separating abundance to rarity.

can still be based on the information, on dominance or equity of the Community [15].

*2.4.1.1. Species richness*

50 Selected Studies in Biodiversity

*2.4.1.2. Information*

*2.4.1.3. Dominance*

*2.4.1.4. Equity or uniformity*

Beta diversity or among habitats represents the degree of change of species, as well as biotic change through environmental gradients [6]. It is based in proportions or differences, that can be quantified based on indices or similarity coefficients of dissimilarity or distance between the plots, from quantitative or qualitative data, as well as by beta diversity indices themselves.

The easiest system to measure beta diversity between pairs of localities is through the use of similarity coefficients [5]. The most used is the Jaccard and Sorensen indices (**Table 1**). These indices are designed to be equal to 1 if there are complete similarity cases (when the two species are identical) and equal to zero if the plots are dissimilar and have no species in common. One of the great advantages on these measures is your simplicity. However, this can also be a disadvantage, since the coefficients do not consider the abundance of species. All species have an equal weight in the equation, whether abundant or rare [5].
