Spatial characterization of species Copaifera langsdorffii and Xylopia brasiliensis located in an urban forest fragment of the Atlantic Forest domain

Caracterização espacial das espécies Copaifera langsdorffii e Xylopia brasiliensis localizadas em um fragmento de floresta urbana do domínio Mata Atlântica

ABSTRACT:

It is estimated that the Atlantic Rain Forest currently occupies about 12% of its original area, predominantly composed of fragments resulting from high deforestation rates. Fragmentation alters the natural habitat of trees, potentially impacting the level of competition among native species in the biome. Understanding current tree relationships is essential for assessing the impacts of fragmentation on forest dynamics. Thus, this study analyzed the spatial distribution of the two most populous native tree species (C. langsdorffii and X. brasiliensis) in a Montane Semideciduous Forest fragment within the Atlantic Rain Forest biome, located in the city of Lavras, MG, Brazil. The spatial characterization of the species was conducted through first- and second-order analysis using marked and unmarked inhomogeneous point process methods. The results indicated that, individually, the species exhibit a non-homogeneous distribution and tend to occur in an aggregated manner within the forest fragment. Furthermore, the data suggested the absence of interaction between the species, indicating no significant competition for resource availability. These findings also highlighted the importance of using methods that consider inhomogeneous processes in the analysis of spatial dependence among native tree species.

Key words:
forest ecology; tropical forests; spatial configuration; Kernel estimator; nonhomogeneous J- and L- functions; Monte Carlo method

RESUMO:

Estima-se que a Mata Atlântica ocupe atualmente cerca de 12% de sua área original, composta majoritariamente por fragmentos resultantes das altas taxas de desmatamento. A fragmentação altera o habitat natural das árvores, podendo impactar o nível de competição entre espécies nativas do bioma. A compreensão das relações arbóreas atuais é essencial para avaliar os impactos da fragmentação na dinâmica florestal. Assim, o objetivo deste estudo foi de analisar a distribuição espacial das duas espécies arbóreas nativas (C. langsdorffii e X. brasiliensis) mais populosas do fragmento de floresta semidecídua Montana no bioma Mata Atlântica localizado na cidade de Lavras, MG, Brasil. A caracterização espacial das espécies foi feita através da análise de primeira e segunda ordem por meio dos métodos de processos pontuais não homogêneos marcados e não marcados. Os resultados indicaram que, individualmente, as espécies apresentam uma distribuição não homogênea e tendem a ocorrer de forma agregada no fragmento florestal. Além disso, os dados sugerem a ausência de interação entre as espécies, indicando que não há competição significativa pela disponibilidade de recursos. Esses resultados mostraram ainda a importância da utilização de métodos que considerem processos não homogêneos na análise da dependência espacial entre árvores de espécies nativas.

Palavras-chave:
ecologia florestal; florestas tropicais; configuração espacial; estimador Kernel; funções J e L não homogêneas; método de Monte Carlo.

INTRODUCTION

Brazilian forest cover has been significantly reduced over the past centuries due to historical, social, and economic factors (BARBOSA & MANSANO, 2018). The Atlantic Forest is recognized as one of the 25 biodiversity hotspots, with a high rate of endemic species, and is the most affected ecosystem by deforestation in Brazil (BARBOSA & MANSANO, 2018; MARQUES & GRELLE, 2021; VANCINE, 2024). It is estimated that currently, only about 12% of the biome remains preserved in the country, predominantly composed of fragments smaller than 50 hectares (SOS MATA ATLÂNTICA, 2016).

The fragmentation of native vegetation forests causes significant transformations in habitat and the spatial configuration of species, directly impacting the morphological, physiological, and ecological processes of plants (OLIVEIRA, 2020). These processes influence essential aspects such as growth, performance, reproduction, mortality, immigration, and emigration of species. Among the most severe and often irreversible damages caused by fragmentation are changes in the microclimate, the availability and quality of resources, biodiversity loss, and species extinction (SLATTERY & FENNER, 2021; WIEGAND et al., 2007). Because of these transformations in ecosystem dynamics, there is a shift in competition levels among species, both intra- and interspecific, which can substantially alter the structure and functioning of the fragmented forest (D’ARROCHELLA, 2020; FERNANDES, 2024; THOMAZINI & THOMAZINI, 2000).

Competition results from the biological interaction between two or more species with similar characteristics or niches. In the arboreal synusia, it plays a crucial role in forest organization, ensuring the optimal utilization of available resources. However, fragmentation and anthropogenic actions can lead to the extinction of native species and the emergence of invasive plants, altering the structure of the forest community (CASTRO & GARCIA, 1996; OLIVEIRA, 2020; ORELLANA & VANCLAY, 2018). In this context, discussions and analyses of interactions among native tree species are essential not only for understanding forest dynamics but also for aiding in the creation of management plans aiming environmental recovery and conservation (VANCINE, 2024; RODER, 2023; ZAÚ, 1998). The Fabaceae, Myrtaceae, Annonaceae, and Lauraceae families are the most representative in the Atlantic Forest, playing a crucial ecological role in the composition and dynamics of forest ecosystems. These families have a high abundance of species and contribute significantly to the structure and functioning of the forest (VANCINE, 2024). In the studied forest fragment, the predominant species are Copaifera langsdorffii (Fabaceae family) and Xylopia brasiliensis (Annonaceae family) (CARVALHO, 2014).

Studying these species is fundamental to understanding how they persist in the habitat and interact with each other, especially regarding intra- and interspecific competition for resources (LIU, 2024). Interaction patterns among native species are commonly observed and can manifest in aggregated or segregated forms. These patterns generally result from the spatial distribution of plants in sub-regions that offer more favorable soil and microclimate conditions (SLATTERY & FENNER, 2021). However, understanding these patterns requires appropriate statistical approaches.

Several studies in the literature have investigated intra- and interspecific interactions among native vegetation species. Scientists such as BATISTA et al. (2019), DUARTE et al. (2019), POTTKER et al. (2016), and SOUZA et al. (2020a) recommend the use of statistical methods based on the theory of spatial point processes, as these methods allow for the investigation and characterization of species distribution and interaction patterns at different distance scales. However, many studies assume that the spatial point process is homogeneous, which is not always the case. Methods addressing the inhomogeneity of the spatial point pattern are still underutilized in forest studies but are essential for understanding the complexities of interactions in fragmented ecosystems.

This study applied various spatial point process methods to characterize the spatial distribution and interaction between C. langsdorffii and X. brasiliensis in a Montane Semideciduous Forest fragment within the Atlantic Forest domain. We highlighted the use of descriptors (L and J functions) from BADDELEY et al. (2015), CRONIE & LIESHOUT (2016), DIGGLE (2013), and LIESHOUT (2010), considering the inhomogeneity of the spatial distributions of both species.

MATERIALS AND METHODS

Description of the data

The data used in this study were collected in the forestry inventory conducted in 2017. The forest fragment is classified as Seasonal Semideciduous Montana, Atlantic Forest domain and is located on the campus of the Universidade Federal de Lavras (UFLA). The forest remnant, known as Matinha, covers an area of approximately 6.48 hectares and is located at coordinates 21°13’43.4” S and 44°58’16.1” W, with an average altitude of 950 meters (Figure 1). According to the Köppen-Geiger climate classification, the climate identified in the study region is characterized as subtropical with dry winters and rainy summers (DANTAS, 2007). The soil is classified as a typical Dystroferric Red Latosol (Oxsol), well drained and with a clayey texture (NUNES, 2003).

Figure 1
Location of the study forest fragment, Lavras-MG, Brazil.

The data consisted of locations in UTM (Universal Transversal Mercator) coordinates of 1147 native trees of the two most representative species of the forest fragment under study. To obtain the coordinates, the region was divided into plots whose vertices had a known UTM coordinate. From these coordinates, the Cartesian coordinates (x, y) of each tree located within the plot were obtained. Subsequently, these Cartesian coordinates were transformed into UTM coordinates, obtaining the locations of 505 individuals of the species C. langsdorffii and 642 individuals of the species X. brasiliensis.

Xylopia brasiliensis

X. brasiliensis is popularly known in Brazil by the names pidaíba, pindaíba-boca-seca, pindaibinha, among others. The taxonomy of the species is hierarchical according to the division Magnoliophyta (Angiospermae), class Magnoliopsida (Dicotyledonae), order Magnoliale, family Annonaceae and genus Xylopia. This species occured naturally in coastal plains, Atlantic Rain Forest, fast-draining soils with high chemical fertility and sandy soils. Its wood has grayish-white heartwood, with an average density of 0.70 g/cm³, and is widely used in the construction of boxes, clogs, rafters, beams, among others. Predatory exploitation and fragmentation of its habitat can lead to the extinction of the species (CARVALHO, 2014).

Copaifera langsdorffii

C. langsdorffii or copaíba (or oleo-capaíba), as it is popularly known in Brazil, belongs to the family Fabaceae in the order Fabales of the class Dicotyledonae and division Angiospermae. It is a tree that reaches up to 15 m in height and can be found mainly in the Atlantic Forest domain (FREITAS & OLIVEIRA, 2002). It presents a high compatibility with edaphic conditions, appearing both in drained soils and, in general, grows best in soils of riparian and semideciduous forests (CARVALHO, 2014). The species has a rough, dark trunk with petiolate and penulate leaves. The flowers are small, apetaled, hermaphrodite and arranged in axillary panicles. The fruits contain an ovoid seed surrounded by an abundant and colorful aril. The seed dispersal of the species usually occurs by birds or other animals that consume its fruits (VEIGA JUNIOR & PINTO, 2002). The species is exploited for its oil, which is appreciated for its benefits to human health, in addition to being highly valued in medicines and other products. The species may be threatened due to unsustainable exploitation practices.

Point process

The arrangement of data into points corresponding to the random location of each native tree in the studied region defines a point process. Thus, the statistical analyses applied in this study are based on spatial point process methods. Through these methods, it is possible to efficiently describe spatial distribution and interaction patterns, considering data inhomogeneity, which contributes to a more precise understanding of the underlying ecological processes, thereby enabling the achievement of the proposed objectives in this study (BADDELEY et al., 2015; ILLIAN, 2008). Mathematically, a spatial point process is obtained through a collection of random variables defined by

$X=\{X\left(\mathit{s}\right),\mathit{s}\in S\}$(1)

where $S\subset {\mathbb{R}}^d,d=2,\mathit{}\mathit{s}=(x_i,y_i)$and X(s ) is a stochastic probabilistic mechanism that governs the distributions of events in space, receiving 1 with the occurrence of the event in s and 0 otherwise. The interest of the point process analysis is to analyze the intensity of event occurrence (points or locations) and determine the pattern of spatial distribution of points in the study area (SCALON, 2024).

The exploratory analysis of spatial point patterns begins with the characterization of the point process that generated the events, i.e., by analyzing the first- and second-order properties (CRESSIE, 1993; SCALON, 2024).

The analysis of first-order effects makes it possible to determine the intensity at each location and thus characterize trends in the point pattern. For this, parametric or nonparametric methods can be used (SCALON, 2024). In this study, the nonparametric method based on kernel smoothing was used.

Kernel smoothing

Let s ₁,…,s _n locations of n events of a region A. The kernel estimator proposes that the intensity estimate for a pointx of A is given by

${\widehat{\lambda }}_{\tau }\left(\mathit{x}\right)=\frac{1}{{\tau }^2}\sum _{i=1}^{n}k\left(\frac{d({\mathit{s}}_i,\mathit{x})}{\tau }\right),d\left({\mathit{s}}_i,\mathit{x}\right)\le 0$(2)

where d(s _j,x ) is the Euclidian distance between a generic point (not an event) x and the s _i event, τ is known as the bandwidth that determines the amount of smoothing (τ ≥ 0) and k(.) is a suitably chosen bivariate probability density function, symmetric about the origin, known as the kernel (TERRELL & SCOTT, 1992).

There are several possibilities for the function k(.), such as uniform, quartic, triangular, Epanechnikov, and Gaussian. Any of these functions lead to the same level of smoothing (DIGGLE, 1985). We used the Gaussian function in this study.

Unlike the choice of k(.), the smoothing parameter is a crucial element for the kernel estimator. Different choices of the bandwidth radius can lead to different degrees of smoothing (SCALON, 2024). The main proposals that exist to obtain τ are: the relationship between the number of points and spatial dimensions (TERRELL & SCOTT, 1992), Campbell’s formula (CRONIE & LIESHOUT, 2018), minimization of the root mean square error (DIGGLE, 1985) and, maximization of the point process likelihood cross-validation criterion (LOADER, 2006). In this paper, we used τ obtained from the Campbell´s formula which relates the distribution of a point pattern with the intensity of occurrence in other locations, providing reliable estimates for the intensity of a point process. In addition, this measure produced intensity estimates that are reliable for the correction of spatial heterogeneity. (CRONIE & LIESHOUT, 2018).

Second-order (or local) analysis was used to characterize the spatial dependence of the phenomenon. Several descriptor functions have been proposed for this purpose (e.g., F, G, K, J and L). For these functions, it is assumed that the spatial process is homogeneous (SCALON, 2024). If there are indications of heterogeneity, nonhomogeneous versions of these functions can be used. RESEARCHERS CRESSIE (1993), BADDELEY (2000) and DIGGLE et al. (2003) advocate the use of inhomogeneous descriptors, such as the J _inhom (t)- and L _inhom (t)-functions which consider the spatial heterogeneity present in the study area. It is well known that descriptors that do not account for the variation in intensity may detect interaction in patterns with no interaction at all (SOUSA & SCALON, 2018).

J_inhom (t)-function

The J _inhom (t)-function is obtained from the ratio between the G _inhom (t)- and F _inhom (t)-functions. Its estimator is given by

${\widehat{J}}_{inhom}\left(t\right)=\frac{1-{\widehat{\mathrm{F}}}_{inhom}\left(t\right)}{1-{\widehat{G}}_{inhom}\left(t\right)\mathrm{}}$(3)

Where ${\widehat{G}}_{inhom}\left(t\right)=\frac{{\sum }_{i=1}^n{I}_t(t_i,r_i)}{{\sum }_{i=1}^n{I}_t\left(r_i\right)\widehat{\lambda }\left(t_i\right)}\mathrm{}$ corresponds to the estimator of the inhomogeneous distance function from an event to the nearest event where n is the number of events, I _t (t _i ,r _i ) is an indicator function that assumes 1 when t _i ≤ t e r _i > t simultaneously and, 0 otherwise. I _t (r _i ) is an indicator function that assumes 1 when r _i > t and, 0 otherwise and, $\widehat{\lambda }\left(t_i\right)$is the weight of the intensity estimates of the inhomogeneous process. The ${\widehat{F}}_{inhom}\left(t\right)=\frac{{\sum }_{i=1}^m{I}_t(t_i,r_i)}{{\sum }_{i=1}^m{I}_t\left(r_i\right)\widehat{\lambda }\left(t_i\right)}\mathrm{}$ is the estimator of the inhomogeneous function of the distance from an arbitrary point to the nearest event where m is the number of random points x _i ,i = 1,…, m, I _t (t _i ,r _i ), is an indicator function that assumes 1 when t _i < t and r _i > t simultaneously and 0 otherwise. I _t (r _i ) is an indicator function that assumes 1 when r _i > t and 0 otherwise and is $\widehat{\lambda }\left(t_i\right)$ equivalent to weighting intensity of the inhomogeneous process (LIESHOUT, 2010).

L_inhom (t) -function

The L _inhom (t)-function is a transformation of the K _inhom (t)-function which, in addition to facilitating the interpretation of spatial dependence, also reduces the variance for large values of t (ILLIAN, 2008). This function considers the average number of events found within the distance t of the reference event with resizing by the product of the first-order intensities at the two corresponding locations (DIGGLE, 2013). The estimator of the L _inhom (t)-function corrected for the edge effect is obtained by

${\widehat{L}}_{inhom}\left(t\right)=\sqrt{\frac{{\widehat{K}}_{inhom}\left(t\right)}{\pi }}-t,$(4),

where ${\widehat{K}}_{inhom}\left(t\right)=\frac{1}{\left|A\right|}\sum _{i=1}^n\sum _{\left(j\ne i\right)=1}^n\frac{I_t\left(t_{ij}\right)}{{\omega }_{ij}\widehat{\lambda }\left(u_i\right)\widehat{\lambda }\left(u_j\right)}$

is the estimator of the nonhomogeneous K(t)-function being │A│ the area of region A , n is the number of observed occurrences, w _ij corresponds to the factor of correction for edge effects that is equivalent to the proportion of the circumference of the circle centered on the event u _i containing u _j that is within the study region, I _t (t _ij ) is an indicator function which assumes 1 when t _ij ≤ t and $\widehat{\lambda }\left(u_i\right)$ and $\widehat{\lambda }\left(u_j\right)$correspond to the estimated intensity values (BADDELEY et al., 2015).

The Monte Carlo method was used to test the null hypothesis of complete spatial randomness (CSR). Distances between 0 and 12 meters were considered for the J _inhom (t)-function and 0 to 70 meters for the L _inhom (t)-function. We performed 999 Monte Carlo simulations under the CSR hypothesis for the construction of the 0.998 confidence envelopes. The analysis was performed for each species under study.

Spatial marked point process

A spatial marked point process is defined by adding information (or attributes) to the event locations, and is defined by

$X_M=\{\left(\mathit{s},m_{\mathit{s}}\right),\mathit{}\left(\mathit{s},m_{\mathit{s}}\right)\in X\times M\}$

where s ∈ X corresponds to the locations of the events and m _s = m(s ) to the marks. Marks can be quantitative or qualitative. In this paper, only bivariate qualitative marks (two species) were considered.

In the analysis of bivariate marked point processes, the interest is not only in the spatial distribution of events but also in verifying the interaction or dependence between the two sub processes defined by the marks (DIGGLE, 2013). The first- and second-order effects can be analyzed as in the unmarked case, and the intensity function is estimated for each sub process separately. Bivariate inhomogeneous $J_{12}^{inhom}\left(t\right)$- and $L_{12}^{inhom}\left(t\right)$-functions were used for second-order analysis.

$J_{12}^{inhom}\left(t\right)$ -function

The bivariate $J_{12}^{inhom}\left(t\right)$ -function is obtained from the ratio between $G_{12}^{inhom}\left(t\right)$ - and $F_2^{inhom}\left(t\right)$ - functions and can be estimated by

$J_{12}^{inhom}\left(t\right)=\frac{G_{12}^{inhom}\left(t\right)}{F_2^{inhom}\left(t\right)\mathrm{}}$(5)

Where $G_{12}^{inhom}\left(t\right)=\frac{{\sum }_{i=1}^n{I}_t(s_{1i},s_2)}{{\sum }_{i=1}^n{I}_t\left(s_{1i}\right){\widehat{\lambda }}_1\left(t_i\right)}$ is the intensity-weighted cumulative distribution function of the distance from an event of type 1 to the nearest event of type 2, where n is the number of events of phenomenon 1, s ₂ corresponds to the set of events of phenomenon 2, s _1i represents the i _th event of type 1. I _t (s _1i , s ₂) is an indicator function that receives 1 when the distance between events s _1i and s ₂ is less than t and 0 otherwise. I _t (s _1i ) is an indicator function that receives 1 when s _1i is at a distance equal to or greater than t from the edge from study area A and 0 otherwise. ${\widehat{\lambda }}_1\left(t_i\right)$is the intensity weighting of process 1. The function $F_2^{inhom}\left(t\right)=\frac{{\sum }_{i=1}^m{I}_t(z_i,s_2)}{{\sum }_{i=1}^m{I}_t\left(z_i\right){\widehat{\lambda }}_2\left(t_i\right)}$is the cumulative distribution function of the distance from a randomly generated point to the nearest event of type 2 events weighted by the relative intensity of the same phenomenon, where m is the number of points Z _i ,i = 1,…, m generated from a random process and s ₂ is the set of points of type 2. I _t (z _i ,s ₂) corresponds to an indicator function that assumes 1 when the distance between z _i and s ₂ is less than t and assumes 0 otherwise. I _t (z _i ) corresponds to an indicator function that assumes 1 when z _i is at a distance greater than t from the edge of the study area and ${\widehat{\lambda }}_2\left(t_i\right)$ is the intensity weighting of process 2 (CRONIE & LIESHOUT, 2016).

$L_{12}^{inhom}\left(t\right)$-function

The estimator of the nonhomogeneous bivariate $L_{12}^{inhom}\left(t\right)$-funcion is given by

${\widehat{L}}_{12}^{inhom}\left(t\right)=\sqrt{\frac{{\widehat{K}}_{12}^{inhom}\left(t\right)}{\pi }}-t,$(6),

where ${\widehat{K}}_{12}^{inhom}\left(t\right)=\frac{1}{\left|A\right|}\sum _{i=1}^{n_i}\sum _{j=1}^{n_2}\frac{I_t\left(t_{ij}\le t\right)}{{\omega }_{ij}\widehat{\lambda }\left(u_{1i}\right)\widehat{\lambda }\left(u_{2j}\right)}$

is the estimator of the nonhomogeneous bivariate ${\widehat{K}}_{12}^{inhom}\left(t\right)$- function, where t _ij = │u _1i - u _2j │corresponds to the distance between the i _th event of type 1 and the j _th event of type 2. W _ij corresponds to the edge correction, n ₁ and n ₂ correspond to the number of events of type 1 and 2, respectively, and $\widehat{\lambda }\left(u_{1i}\right)$and $\widehat{\lambda }\left(u_{2j}\right)$correspond to the intensity values estimated for the two processes (BADDELEY et al., 2015; CRESSIE, 1993).

To analyze the spatial pattern of interaction between species, maximum distance of 12 meters was defined for the function $J_{12}^{inhom}\left(t\right)$ and 70 meters for the $L_{12}^{inhom}\left(t\right)$, with confidence envelopes constructed through 999 Monte Carlo simulations under the assumption of independence between the two species. All analyses were performed using functions provided in the spatstat library (BADDELEY & TURNER, 2005) and/or developed in R (R CORE TEAM, 2023).

RESULTS AND DISCUSSION

First-order analysis for each species

First-order analysis is the first step in the analysis of a spatial point pattern (SCALON, 2024). We carried out a kernel density (intensity) estimation using an isotropic Gaussian kernel and bandwidth radii (Campbell´s formula) of 25.63 meters for C. langsdorffii and 30.83 meters for X. brasiliensis. The results are presented in figure 2.

Figure 2
Spatial distribution of intensity estimates by kernel smoothing for C. langsdorffii (A) and X. brasiliensis (B).

Visual inspection of the intensity maps presented in figure 2 indicates that both tree species were distributed non-homogeneously throughout the study region. The heterogeneity could be observed by the differences in intensities in different regions of the study area for both species. In the spatial distribution of C. langsdorffii, a variation in local intensity was identified from 20 to 120 trees/ha, while for the species X. brasiliensis, the intensity variation was more expressive (from 50 to 250 trees/ha).

Although, this study did not directly investigate the abiotic factors present in the region, such as soil properties, it is possible that these factors influence the heterogeneity of the spatial configuration of species in the fragment (SOUZA et al., 2020b). The analysis of such variables could enrich the understanding of the ecological processes involved (HIGUCHI, 2010). In addition, other factors that could influence this heterogeneous configuration are the presence of rivers or lakes, variations in altitude or relief, among others. However, these factors can be ruled out because our study area is small.

Nevertheless, these results are important to conduct the analysis of second-order effects; that is, these results indicated the need to consider the heterogeneity in the second-order analysis.

Univariate second-order analysis for both species

Descriptor functions of the second-order properties of homogeneous point configurations have been used extensively to detect patterns of native species in several studies (BATISTA et al., 2009; BADDELEY et al., 2015; DIGGLE, 2013; LIESHOUT, 2010; POTTKER et al., 2016; SOUSA & SCALON, 2018; MØLLER & WAAGEPETERSEN, 2017). Unfortunately, descriptor functions that consider the inhomogeneity of the spatial point pattern are still little used. The results of the spatial dependency analysis for the species C. langsdorffii, using the inhomogeneous J _inhom(t)- and L _inhom(t)-functions are presented in figure 3.

Figure 3
Envelopes of Monte Carlo simulations of inhomogeneous univariate L _inhom (t) (A) and J _inhom (t) (B) functions for C. langsdorffii. The gray areas indicate lower and upper limits under the CSR hypothesis, the solid black line indicates the estimated function and the dashed red line indicates the theoretical function.

Analyzing the graphs in figure 3, for the species C. langsdorffii, the null hypothesis of complete spatial randomness was rejected in the direction of a pattern that exhibits clusters. The behavior of the L _inhom (t)-function (Figure 3A) indicates that the null hypothesis is rejected for distances between approximately 10 and 20 meters. By J _inhom (t)- function (Figure 3B), it is observed that the rejection of the null hypothesis occurs for distances above 10 meters.

Some studies with the species C. langsdorfii corroborate the results obtained in this study, that is, indicate that individuals of this species tend to form clusters in several regions, such as Chapada do Araripe (VIEIRA, 2021), the remnant of Seasonal Semideciduous Forest (ARRUDA & DANIEL, 2007) and in a fragment of the cerrado biome (SOUZA et al., 2020a). The results for the species X. brasiliensis are shown in the graphs in figure 4.

Figure 4
Envelopes of Monte Carlo simulations of inhomogeneous univariate functions L _inhom (t) (A) and J _inhom (t) (B) to X. brasiliensis. The gray areas indicate lower and upper limits under the CSR hypothesis, the solid black line indicates the estimated function and the dashed red line indicates the theoretical function.

Analyzing the behavior of the L _inhom (t)-function (Figure 4A), it can be observed that the aggregate pattern is also identified for the species X. brasiliensis for approximate distances between 5 and 55 meters. For the other analyzed distances, randomness was identified. By using the J _inhom (t)-function (Figure 4B), the clusters occur for distances above 4 meters.

The results obtained in this study corroborated the findings of a similar study that detected an aggregate pattern in the study of the spatial distribution of a population of X. brasiliensis in an experimental area of Montana Seasonal Semideciduous Forest (HIGUCHI, 2010).

Based on the results obtained in both analyses for spatial characterization, the aggregate pattern seems to be a characteristic of both species under study. These considerations corroborate the statement that the aggregate pattern is one of the most recurrent in the spatial distribution of native plant species (LEGENDRE & FORTIN, 1989).

It is important to highlight that authors cited before did not used non-homogeneous functions and; therefore, the clusters detected by them may be the result of first-order effects and not due to the spatial dependence of the trees of this species.

There are several causes that can lead to this type of spatial pattern. There may be relationships with the size, availability of resources, environmental conditions and location of the forest fragment under study (SCALON et al., 2012). Thus, small and isolated areas can become vulnerable to illegal exploitation, causing large deforestation in certain areas, leaving others intact, and giving rise to clusters.

Although, the degree of heterogeneity of the environment in the availability of resources can influence species distribution in cluster formations, it cannot yet be ruled out that the aggregate pattern refers to the persistence of the microenvironmental heterogeneity of available resources (VIEIRA et al., 2021; SOUZA et al., 2020a; POTTKER et al., 2016).

Bivariate second-order analysis of the species

The results of the spatial interaction analysis between the species C. langsdorffii and X. brasiliensis, conducted using the inhomogeneous bivariate descriptor $J_{12}^{inhom}\left(t\right)$ - and $L_{12}^{inhom}\left(t\right)$-functions are presented in figure 5.

Figure 5
Envelopes of Monte Carlo simulations of the $J_{12}^{inhom}\left(t\right)$ -function (A) and $L_{12}^{inhom}\left(t\right)$-function (B) for the interaction of C. langsdorffii and X. brasiliensis. The gray areas indicate lower and upper limits under the null hypothesis of independence, the solid black line indicates the estimated function and the dashed red line indicates the theoretical function.

The results indicated that the null hypothesis of independence between the two species should not be rejected for all tested scales. In this case, it is observed that the species are independently distributed, meaning that both species coexist without affecting each other’s presence (ORELLANA & VANCLAY, 2018). This suggests that there is no direct competition between them for resources, indicating that C. langsdorffii and X. brasiliensis occupy different ecological niches within the forest fragment (KLIPEL, 2022; UMARANI, 2024). This result must be evaluated carefully because in the Atlantic Rain Forest fragment under study there are several species that were not considered in the analysis and that could, eventually, interfere in the spatial interaction between species C. langsdorffii and X. brasiliensis. It is well known that homogeneous (SCALON, 2024) and inhomogeneous (BADDELEY et al., 2015) bivariate descriptors and other methods for analyzing bivariate point processes should only be applied when there are only two point processes (two species) in the study region.

Due to the small size of the fragment and the fact that these are the two most populous species, the observed pattern becomes particularly interesting. This is because competition between them could significantly affect the ecosystem dynamics and the preservation of the forest area (SLATTERY & FENNER, 2021). Although we did not find studies in the literature that specifically analyzed the spatial interaction between C. langsdorffii and X. brasiliensis, there are studies that have analyzed and detected spatial interaction among native tree species (ALMEIDA, 2018; MACHADO et al., 2012).

A study conducted by MACHADO et al. (2012) at the Jardim Botânico, Curitiba, Brazil, detected spatial dependence relationship between the native species Araucaria angustifolia, Casearia sylvestris and Cedrela Fissilis. The authors argued that the positive spatial dependence among these species may be due to factors such as the availability of sunlight and soil nutrients that may affect the spatial interaction between these species that have similar ecological characteristics.

The hypothesis of spatial independence among the native species Dipteryx odorata, Apuleia leiocarpa and Ceiba samauma was also rejected in a research by ALMEIDA (2018), indicating a tendency of repulsion between the native species. The author adds that such results may be associated with competition for resources below and above the ground but emphasizes that one should not rely only on such analysis to draw conclusions.

OLIVEIRA (2020) performed pairwise spatial point pattern analysis for native tree species (C. langsdorffi, Vochysia tucanorum, Xylopia aromatica and Ocotea corymbosa) located in a Conservation Unit of the State of São Paulo, Brazil, and showed that these three species are spatially dependent and tend to attract each other.

It is worth to point out that, unlike the statistical methods used in the present paper, studies found in the literature, including those described above, use methods that consider spatial point patterns as homogeneous. However, this is a debatable fact, once it is expected that tropical forests would present heterogeneous structures due to soil conditions, climate, relief, altitude, etc. as we can see in CONDIT et al. (2002), RODRIGUES (2018) and, WIEGAND et al. (2007) to name but a few. Thus, when the assumption of homogeneity is used during the spatial point pattern analysis of native species of trees, and when this assumption is false, the analysis detects patterns of spatial interaction between species that are, in fact, the result of the different species intensities in the study region.

CONCLUSION

Through the analysis of the kernel maps, it was possible to identify that the two species analyzed have a nonhomogeneous distribution in the study region, which is an important fact for conducting second-order analyses.

The nonhomogeneous second-order univariate analyses showed that both species have trees that exhibit some spatial dependence (aggregation) in the forest fragment. Two things may be occurring: The availability of some species-specific resource or adaptations to climate change.

The nonhomogeneous bivariate analysis revealed that there was no evidence to reject the null hypothesis of independence between the two species, indicating that there is no competition or attraction between these two species. This may suggest that the availability of resources in the forest fragment (such as nutrients in the soil) is sufficient to maintain both species and would not affect their spatial patterns.

The results obtained in this study showed that spatial point process methods applied to the analysis of first- and nonhomogeneous second-order effects, coupled with Monte Carlo methods enable a detailed spatial characterization of the species C. langsdorffii and X. brasiliensis trees in the Atlantic Rain Forest fragment

ACKNOWLEDGMENTS

This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), Brazil - Finance Code 001. The authors also acknowledge the financial support provided by the Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG), the only research funding agency of the state of Minas Gerais, under Agreement nº 5.02/2022. Additionally, the authors acknowledge the availability of the CAPES Journal Portal, which provides access to scientific literature.

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• CR-2024-0132.R1

• DECLARATION OF CONFLICT OF INTEREST
  The authors declare no conflict of interest. The founding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results.

• DECLARATION OF USE OF ARTIFICIAL INTELLIGENCE
  Artificial intelligence tools were used only for language refinement of the manuscript. All AI-assisted corrections were carefully reviewed by the authors to ensure that the scientific content was not altered.
• DATA AVAILABILITY STATEMENT
  Not applicable.

Edited by

• ASSOCIATE EDITOR:
  Alessandro Dal’Col Lúcio (0000-0003-0761-4200)

• SCIENTIFIC EDITOR:
  Frederico Costa Beber Vieira (0000-0001-5565-7593)

Data availability

Not applicable.

Publication Dates

• Publication in this collection
  17 Nov 2025
• Date of issue
  2026

History

• Received
  11 Mar 2024
• Accepted
  12 May 2025
• Reviewed
  01 Oct 2025