INTRODUCTION

The structure of less affected natural stands by activities humans can represent the optimal distribution of plant species in a particular habitat (Zhang et al., 2014). The stand structure is an irreplaceable component in maintaining the functions of the forest ecosystem (Zhang et al., 2021); it can reflect the competitiveness, spatial distribution pattern, diversity of species, and the development trend of the forest in the future (Xue et al., 2021). Therefore, studying stand structure helps reveal structural factors influencing changes in forest productivity and discover the unlying processes that maintain and promote species coexistence in plant communities (Xin et al., 2020), providing a theoretical basis for practical production following near-natural management (Zhang et al., 2021).

Since the early 1990s, biodiversity conservation has become a global responsibility of the global (Bai et al., 2020). Forest stands are assessed as an important part of forest biodiversity, and their structure has a significant influence on the diversity of animals, plants, insects, and microorganisms in the soil (Franzreb, 1978; Zheng et al., 2007). The stand’s structure can describe the forest’s characteristics; the information it provides is the key to the most scientific and rational management of the forest (Wu et al., 2021). Based on the characteristics and location of the forest tree individuals, the stand structure is divided into spatial and non-spatial structures (Quy et al., 2022a). Studying the spatial structure and non-spatial structure of the stand has radical differences. The non-spatial structure of the stand is essentially the traditional forest study; it reflects the basic characteristics of the stand, such as species composition, diameter structure, height structure, and the density of the stand (Quy et al., 2021b).

Meanwhile, the spatial structure of the stand refers a lot to the spatial distribution and interaction of tree species (Tao et al., 2020); it can describe the spatial attributes of individuals and reflect the ecological relationships of species, such as spatial associations between individuals in a population, population-environment interactions, and processes that control the coexistence of species (Liu et al., 2014). The spatial structure of the stand is the decisive factor determining the nutritional space competitive advantage of forest trees, directly affecting the growth and development of individuals in the plant community (Zhao et al., 2010). On the other hand, the spatial structure of the stand is also the easiest adjustment structural element in the forest management process (Quy et al., 2021b). Hence, studying the spatial structural characteristics of the stand has always been of particular interest to those doing scientific research and forestry managers.

Silviculturists have carried out a lot of research on forest structure in the last 50 years; some authors have proposed parameters to quantify the spatial structural characteristics of the stand (Zhang et al., 2018). However, when applied, these parameters have certain limitations, such as consuming a lot of time and human resources in the surveying and collecting data process (Quy et al., 2021a). Stemming from the requirements of scientific research and production practice, Hui et al. (1999) proposed four forest spatial structure indices based on the relationship of neighboring trees to analyze and evaluate precisely the stand spatial structure. Four forest spatial structure indices of these authors can reflect four respects, including the spatial distribution pattern of forest trees (Uniform angle index—W), the difference in diameter or height between the target tree and its neighbors (Dominance index—U), the mixing degree of species (Species mingling index—M), and the degree of canopy competition or density of the forest tree in the stand (Crowding index—C). Many forest studies have used four forest spatial structure indices of M–U–W–C in China and worldwide. These four indices are evaluated as one 4‑indices combination that cannot be separated in quantitative studies on the spatial stand structure (Zhang et al., 2018).

The evergreen broadleaved forest is one of the main vegetation types in Vietnam; its plant resources are wealthy and diverse (Thin, 2014; Quy et al., 2022b). This forest type plays a vital role in Vietnam’s environmental protection and economic and social development (Trung, 1978). The evergreen broadleaved forest is distributed in many North to South Vietnam provinces, such as Cao Bang, Thanh Hoa, Ha Tinh, Dong Nai, Kien Giang, Lam Dong, etc. (Lan et al., 2006). Since 1975, many researchers have carried out studies on the structure of the evergreen broadleaved forest in South Vietnam (Quy et al., 2022b); most of these authors focus on the non-spatial structural characteristics of the stand. In recent years, the study of forest spatial structure has attracted the attention of several Vietnamese scientists. However, these studies often used the univariate distribution of spatial structure indices, even though many studies only used three among four spatial structure indices to describe the spatial structure of the forest quantitatively (Hai et al., 2018a; Viet et al., 2020; Quy et al., 2021a, 2021b); this may be because some software is often used to analyze the forest spatial structure (Crancod, Winkelmass) stopped updating the version and adding new spatial structure indices. Using the univariate distribution of the forest spatial structure indices or the lack of any one of four indices would be inadequate to reflect the spatial structure of the inherently complex stand comprehensively (Zhang et al., 2018).

The tree species composition of tropical forest communities is very diverse, but most species have low density (Dien and Hai, 2016; Quy et al., 2022b). The dominant tree species are usually the highest density species in the stand; they are vital and significantly influence the forest plant community stability (Quy et al., 2021a). In addition, dominant species can decide the morphology, structure of the stand, and environmental characteristics in the plant community (Wen et al., 2017). To simplify the spatial stand structure adjustment during the management process, researchers often focus on quantitatively describing the spatial structure of the dominant tree species in the stand (You et al., 2015). The spatial structure of dominant species reflects their spatial distribution and the diversity of their neighboring species (Wei et al., 2019). For this reason, the spatial structure of the dominant species can also fully reflect the characteristics of the stand (Liu et al., 2022). On the other hand, studying the spatial structure of dominant species, especially their spatial models, helps to capture the ecological characteristics and interactions of species (Wei et al., 2021); this information helps select tree species and planting hole spacing when planting new forests in areas where forests have been destroyed.

The biological characteristics of plant species cannot explain the diversity of species in rainforests; tropical flora results from long-term interactions between individuals and the environment (Liu et al., 2022). The maintenance of plant species diversity depends mainly on forest structure, population dynamics, and species interactions in plant communities (Hu et al., 2019). Although studying the spatial structure of species based on their relationship with neighboring species can reflect interspecific interactions, it mainly works well at the community level (Quy et al., 2022c). This method can only provide forest trees’ overall spatial distribution pattern that cannot show interspecific interactions at various scales. Meanwhile, spatial statistical functions and the model of individual species-area relationships (ISAR) can overcome the above shortcoming (Ma et al., 2014); however, these two methods also have weak points, they can work well at the population level but cannot reflect the forest spatial structure according to the vertical plane (Quy et al., 2022c). A simultaneous combination of three methods, based on the relationship of neighbor trees, spatial statistical functions, and ISAR models in the same study, is a unique idea for studying the spatial structure of the species-rich natural forests in Vietnam.

In this study, we aim to analyze the spatial structure characteristics, ecological relationships of dominant species, and their influence on the diversity of neighborhood species in the stand. Besides, the spatial structure characteristics of the stand where dominant species appeared are also described quantitatively. To understand the spatial structure unit of dominant species, we used the bivariate distribution of spatial structure indices by combining pair indices such as species mingling index (M)—height dominance index (U), uniform angle index (W)—crowding index (C). The spatial structure of the stand was also described by the bivariate distribution of the spatial structure indices; in addition, it is also represented by the quadrivariate distribution when combining these four indices simultaneously (M, U, W, and C). To clarify the ecological relationship of dominant species, we used the bivariate pair correlation function to analyze the interaction of species pairs (positive or negative interactions) at various scales. In addition, we used the ISAR model to measure interactions between dominant species and their neighbors. Four research questions will be addressed: (1) Is there a difference in the spatial structure of dominant species and the stand where they are distributed? (2) What are the spatial association patterns of the dominant species in the stand? (3) What is the effect of dominant species on the diversity of their neighbors?

MATERIALS AND METHODS

Study Area

This study was conducted in the evergreen broadleaved forest of Dong Nai Cultural Nature Reserve, Dong Nai Province, South Vietnam. This nature reserve has geographical coordinates from 11°05′10′′–11°22′31′′ N, 106°54′19′′–107°09′03′′ E (Fig. 1). The total natural area of the Dong Nai Cultural Nature Reserve is 100 572 ha (forest and forestry land area is 68 052 ha, 32 520 ha of wetlands area). The study area has a subtropical monsoon climate, less affected by natural disasters, fertile soil (mostly soils with thick organic layers), and two contrasting seasons (dry and rainy). The topography of the study area is relatively flat, the average altitude is 105 m above sea level, and the slope is 5°–20° (Vietnam Administration of Forestry, 2021).

Fig. 1.
figure 1

The research area map. Map of Vietnam (left) and study area (right).

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The study plot is located at coordinates 13°33′17.62′′ N and 107°43′25.19′′ E. The plant community of the study area has some dominant species belonging to the families Dipterocarpaceae, Myrtaceae, Ebenaceae, and Sapindaceae (Tuan, 2017).

Our study was carried out from October 2021 to March 2022 with six field surveys.

Data Collection

A 4 ha—study plot (200 m × 200 m) was established in the evergreen broadleaved forest type in the Dong Nai Cultural Nature Reserve. We used the grid method to divide the study plot into 200 subplots of 200 m2 (20 m × 20 m) to facilitate the survey and avoid omitting survey trees. All woody trees of the study plot with dbh ≥ 2.5 cm were identified as species names and fully mapped. We used a tree caliper and Blume-Leiss meter to measure trees’ dbh and overall height.

All investigated trees in the study plot were divided into one of three life stages, namely juvenile trees (dbh < 5 cm), premature trees (5 cm ≤ dbh < 10 cm), and mature trees (dbh ≥ 10 cm) (Quy et al., 2021c).

Data Analysis

In this study, the nearest neighbor trees statistical technique was used to determine the spatial structural units of dominant species and the stand. We used four spatial structure indices proposed by Hui et al. (1999), including species mingling index, height dominance index, uniform angle index, and crowding index in spatial structure analysis with Eqs. (2)–(5).

In addition, we used the bivariate pair correlation function and the species-area relationship (ISAR) model to analyze the spatial associations of dominant species and their interactions with neighboring species.

Identify dominant species. The dominance of a species is the expression of its spatial control in the stand (You et al., 2015). The dominant species are determined based on the importance value index of each species. The formula for calculating the importance value index is as follows:

$${\text{IVI}}\% = \frac{{{\text{N}\% } + {\text{BA}\% }}}{2},$$
(1)

where, IVI% is the important value index of the species, N% is the percentage of tree individuals of species compared to the total number of tree individuals in the study plot, BA% is the percentage of the total basal area of the species compared to the total basal area of all species. In the stand, only species with IVI% >5% must be genuinely ecologically significant (Marmillod, 1982).

Forest spatial structure indices. Species mingling (M): reflects the analogy in species composition between the target tree and its nearest neighbors. Species mingling is defined as the proportion of the four nearest neighbor species to the target tree. The calculation formula of species mingling is as follows:

$${{M}_{i}} = ~\frac{1}{4}\sum\limits_{j = 1}^4 {{{{v}}_{{ij}}}} ,$$
(2)

where, j is the nearest neighbor of the target tree i; vij = 1 if the nearest neighbors and the target tree are not of the same species; vice versa, vij = 0. The Mi value ranges from 0 to 1. The higher the Mi value, the more diverse the neighboring species composition of the target tree. The specific values of Mi and its biological significance are shown in Fig. 2.

Fig. 2.
figure 2

Nominal value scales for forest spatial structure indices.

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Crowding (C): reflects the canopy competition between the target tree and its four nearest neighbors. The calculation formula is as follows:

$${{C}_{i}} = \frac{1}{4}\sum\limits_{j = 1}^4 {{{y}_{{ij}}}} ,$$
(3)

where, yij = 1 if the canopy of the target tree and four neighbor trees intersect; vice versa, yij = 0. Crowding reflects the level of competition for nutrient space between the target tree and its neighbors and can also indicate the canopy cover and density of the stand. The Ci value ranges from 0 to 1. The higher the Ci value means, the denser the density of forest trees in the stand (Fig. 2).

Height dominance (U): reflects the relationship between the height of the target tree and the four nearest neighbors. Calculation formula of height dominance:

$${{U}_{i}} = \frac{1}{4}\sum\limits_{j = 1}^4 {{{k}_{{ij}}}} ,$$
(4)

where, kij = 1 if the height of neighboring trees is lower than the target tree; vice versa, kij = 0. The Ui value ranges from 0 to 1. The higher the Ui value indicates that the height of the target tree is superior compared to its neighbors (Fig. 2).

Uniform angle index (W): reflects the spatial distribution pattern of the target trees on the forest ground. It is the proportion of trees with angle α < αo (72°) in the four reference neighbors of the target tree. The calculation formula of the uniform angle index is as follows:

$${{W}_{i}} = \frac{1}{4}\sum\limits_{j = 1}^4 {{{z}_{{ij}}}} ,$$
(5)

where, zij = 1 if angle α < αo; vice versa, zij = 0. The uniform angle index represents the dispersion of the four nearest neighbors relative to the target tree. The Wi value ranges from 0 to 1. The Wi value increases when the forest tree changes from regularity distributed to randomly distributed and then to clustered distribution (Fig. 2).

Three indices are species mingling (M), crowding (C), and uniform angle index (W), which describe the spatial structure of the stand according to the horizontal plane. In contrast, the height dominance (U) reflects the vertical spatial structure of the stand. Spatial structure indices were calculated using R software version 4.1.3 with Package “forestSAS” (https://rdrr.io/ cran/forestSAS/). The distribution map of forest tree species was created with the “spatstat” (https://cran.r-project.org/web/packages/spatstat/) and “ggplot2” packages (https://cran.r-project.org/web/packages/ggplot2/) in R 4.1.3 software (R Development Core Team, 2021).

Pair correlation function. Ripley’s K function is a spatially important statistical function, the cumulative distribution function of points in a range of distances r (Wiegand and Moloney, 2004). This study used the bivariate pair correlation function to analyze species pairs’ ecological relationships (spatial association). The pair correlation function g(r) is the derivative of Ripley’s K function with g(r) = K'(r)/(2πr), which gives the expected density of points at a distance r from any point (Ripley, 1976).

For the same type of points (one species or one group of tree species), we have a univariate pair correlation function g11(r). In contrast, there will be a bivariate pair correlation function g12(r) with two different species.

For the function g11(r), if g11(r) = 1, the points are completely randomly distributed; g11(r) > 1, cluster distribution points; g11(r) < 1, the points are regularity distributed.

Similar to the univariate version, for the function g12(r), if g12(r) = 1, the two species are independent in space; if g12(r) > 1, then they are spatially positively correlated (attraction); and vice versa, if g12(r) < 1, then they are spatially negatively correlated (repulsion).

The null model used to analyze the spatial association of dominant species is an independent model. In this null model, species 1 will be fixed unchanged, and the position of species 2 will be moved randomly around species 1 to estimate simulation values (Wiegand et al., 2007a).

The model of individual species-area relationship. The individual species-area relationship (ISAR) model was used to estimate the number of species occurring in a circle of radius r with an individual of the dominant species as the circle’s center. This model can quantify the structure of neighbor species diversity around the dominant species. The ISAR model operates based on species interactions at different scales. The value of the ISAR function is calculated according to the following formula (Wiegand et al., 2007b):

$${\text{ISAR}}\left( r \right) = \sum\limits_{j = 1}^N {[1 - ~{{P}_{{ij}}}(0,~r)]\,\,(i \ne j)} ,$$
(6)

where i is the dominant species, j is the neighbors of the dominant species i, N is the total number of species in the study plot, and Pij(0, r) is the probability that species j does not appear in the circle with a radius r and center of a circle is an individual of species i. If α = πr2, the function ISAR(α) is the traditional species-area relationship (SAR) function (Wiegand et al., 2007b).

The null model was selected to test the difference between the observed ISAR model and the simulated model based on analyzing the homogeneity of environmental conditions in the study plot. If the habitat of the study plot is homogeneous, the null model is the complete spatial randomness model. In contrast, the null model will be the inhomogeneous Poisson process (IPP) model if the habitat of the study plot is heterogeneous. If the calculated value of ISAR is greater than the simulated value, the neighboring species of the dominant species with high diversity and the dominant species is called diversity accumulator. If the calculated value of ISAR is smaller than the simulated value, the neighboring species of the dominant species with low diversity and the dominant species is called diversity repeller. Conversely, suppose the calculated value of ISAR does not differ from the simulated value. In that case, the dominant species is said to be neutral (no neighbors diversity promoting or inhibiting effect).

Analysis of the spatial association patterns and the ISAR models of dominant species were performed using Programita November 2018 (http://programita.org). We used 199 Monte Carlo simulations; the fifth lowest and highest values of simulations were used to create an approximate 95% confidence interval.

RESULTS

Spatial Structure of Dominant Species and Forest Stand

A total of 4583 tree individuals belonging to 101 species of 59 plant families were identified in the study plot (Table A1, Supplementary Information). Among 101 species recorded, only five species were Shorea guiso (Blanco) Blume (family Dipterocarpaceae), Vatica odorata (Griff.) Symington (family Dipterocarpaceae), Diospyros venosa Wall. ex A.DC. (family Ebenaceae), Croton delpyi Gagnep. (family Euphorbiaceae), and Syzygium zeylanicum (L.) DC. (family Myrtaceae), they are ecologically dominant species (IVI ≥ 5%), and they contribute up to 54.41% of the total number of trees in the study plot. In the group of five dominant species, S. guiso and V. odorata are the two species with a higher number of individuals and IVI% than the other three dominant species (D. venosa, C. delpyi, and S. zeylanicum) and 96 others in the stand. This result proved that S. guiso and V. odorata could occupy the living space much better than others that grow with them.

M–U bivariate distribution. The M–U bivariate distribution of five dominant species and the forest stand has the common characteristic that most of the frequency values are concentrated at M = 0.75 and M = 1. On the other hand, the mean value of the species mingling index (M) for five dominant species and the forest stand ranged from 0.74 to 0.92 (Table A1). These two results showed that the neighbor species composition of five dominant species has a high diversity. The frequency values of the height dominance index (U) for the five dominant species are the same as the forest stand, and they do not have too much difference (Fig. 3). The frequency values of the height dominance index (U) were a relatively uniform distributed at the levels U = 0 to U = 1; this result indicated that the number of trees in the forest canopy layers was not a big difference; in other words, the species are relatively uniformly distributed in the forest canopy layers.

Fig. 3.
figure 3

M–U bivariate distribution of dominant species and forest stand (M—Species mingling index, U—Height dominance index, N—number of tree individuals).

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W–C bivariate distribution. The analysis results of the W–C bivariate distribution showed that the spatial distribution patterns of five dominant species and the stand tended to shift from clustered to random distribution with frequency values concentrated mainly at W = 0.5. The random distribution of five dominant species and the stand was also reflected in their mean value of the uniform angle index, ranging from 0.45 to 0.54 (Table A1). The crowding index (C) of five dominant species and the stand shown in Fig. 4 differed significantly. Among five dominant species, S. guiso and V. odorata are two species with the frequency values of the crowding index distributed mainly at two levels, C = 0.75 (dense density) and C = 1 (very dense density). In comparison, three other dominant species (D. venosa, C. delpyi, and S. zeylanicum) and the forest stand have the frequency values of crowding index mainly distributed at C = 0 to 0.5 (density from very sparse to medium). The analysis results of the crowding index for five dominant species and the stand according to W–C bivariate distribution are utterly similar to the individual density of dominant species in the stand; this shows that two species, S. guiso and V. odorata, compete fiercely with their neighbors.

Fig. 4.
figure 4

W–C bivariate distribution of dominant species and forest stand (W—Uniform angle index, C—Crowding index, N—number of tree individuals).

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M–U–W–C quadrivariate distribution. The analysis results of the M–U–W–C quadrivariate distribution showed that the forest trees in the stand are mainly concentrated at M = 1, W = 0.5, C = 0.5, and U = 0–1 (Fig. 5). At the same time, this result also indicated no difference in the spatial structure of the stand when it is represented by two distribution types (bivariate and quadrivariate distributions) of spatial structure indices.

Fig. 5.
figure 5

M–U–W–C quadrivariate distribution of forest stand (M—Species mingling index, U—Height dominance index, W—Uniform angle index, C—Crowding index).

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Spatial Associations of Dominant Species

We used the bivariate pair correlation function to analyze 20 spatial association patterns of five dominant species in the stand. The results revealed that independence accounted for a higher proportion than attraction and repulsion at spatial scales r of 0–50 m (Fig. 6). The results also indicated that interactions between dominant species were two-way interactions (Fig. A1, Supplementary Information). Except for two species pairs S. guiso and C. delpyi (0–3 m), S. guiso and S. zeylanicum (2–7 m), they were repulsed each other; the spatial associations between D. venosa and C. delpyi as an attraction (0.5–2 and 30–40 m); while spatial associations of other species pairs are independent at all spatial scales r of 0–50 m (Fig. A1, Supplementary Information).

Fig. 6.
figure 6

Analysis results of spatial associations of five dominant species.

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ISAR Model of Dominant Species

Testing the homogeneity of habitat in the study plot was performed based on the spatial distribution pattern of mature trees (Fig. A2, Supplementary Information). The results showed that the mature trees were inhomogeneously distributed, which proves that the habitat of the study plot was not heterogeneous. Therefore, the selected null model was the model of IPP when analyzing the ISAR model of dominant species.

The analysis results of the ISAR model for five dominant species showed that the number of neighbor species of dominant species ranges from 40 to 50 species at a scale above 40 m (Figs. 7f–7j). Testing the difference between the observed ISAR model and the null model of IPP indicated that two dominant species were diversity repellers (S. guiso and V. odorata), one dominant species was diversity accumulator (C. delpyi), and two dominant species were neutrals (D. venosa and S. zeylanicum) (Figs. 7k–7o).

Fig. 7.
figure 7

Analysis results of ISAR model for five dominant species. Distribution map of five dominant species (a–e). The number of neighbor species of dominant species at different scales (f–j); the red lines show the mean value of the ISAR function; the green and blue lines show the minimum and maximum values of the ISAR function. The ISAR models of five dominant species (k–o); the red lines show ISAR(r)–ISARexp(r), the observed ISAR function minus the expectation of the IPP null model; gray areas show the simulation envelopes minus the expectation of the null model.

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DISCUSSION

Spatial Structure of Dominant Species and Forest Stand

Plant populations are not only the association of individuals with communities but also the important components of the forest ecosystem (Wu et al., 2018). The spatial structure of forest trees is one of the critical characteristics of the population, helping to quantitatively describe the spatial structure of the population in the community (Zhang et al., 2018). Each plant population has its own specific morphological and ecological characteristics, and these characteristics are the basic structural units of the forest ecosystem (Zhang et al., 2014). In traditional forest management, sustainable logging is the primary goal (Nuske et al., 2009). Therefore, traditional forest research methods are often directly related to the stand volume, ignoring the forest tree species’ spatial characteristics—the stand’s most critical characteristic when studying its structure, dynamics, and stability (Hu et al., 2019). In modern forest management, the most effective measure that managers aim for is to control the density of forest stands reasonably (Liu et al., 2022). Through the control of forest stand density, it is possible to improve the living conditions of forest trees to increase the effectiveness of using the living space of species, and there are forest stands with higher productivity than before (Wei et al., 2021).

In this study, the analysis results of the spatial structure of dominant species and the stand showed that the stand has high species diversity. The forest trees tend to shift from clustered to random distribution. The number of trees in the forest canopy layers was relatively uniform, and the stand density was medium. Our study results have many similarities compared to previous studies on the spatial structure of evergreen broadleaved forests in Vietnam. Quy et al. (2022b) have shown that the evergreen broadleaved forest type in South Vietnam has a very high species diversity but a low density of each species; most forest trees have a random distribution. These authors found that juvenile trees often have cluster distribution in the early stages of their development due to the limited dispersal of the mother tree. However, as tree age increases, the nutrition of forest tree requirements will increase. High demand for nutrients from individuals living close to each other will lead to fierce competition, and weaker competitors will be eliminated and appear self-thinning of forest trees; for this reason, the distribution of forest trees often tends to switch from clustered to random or regular in their developmental stages. Viet et al. (2020) also considered that evergreen broadleaved species could have a cluster, random, or regular distribution, but random distribution is generally still predominant. Wan et al. (2019) also found that the species mingling index is positively correlated with the species diversity of the community. Many other studies also highlighted that using the species mingling index can accurately reflect species diversity in the plant community (You et al., 2015; Xu et al., 2018; Wen et al., 2022).

Some previous studies have suggested that adjusting the spatial structure of evergreen broadleaved forests should only focus on adjusting the forest’s spatial structure according to the horizontal plane (Cao et al., 2020; Quy et al., 2021b). Our analysis results showed that the species were distributed in relatively equal numbers in the forest canopy layers. Therefore, our study supports the view that adjusting the structure of the broadleaved evergreen forest stand according to the vertical plane is unnecessary. Furthermore, adjusting the structure of the broadleaved evergreen forest stand according to the vertical plane is also more challenging than adjusting the stand structure according to the horizontal plane. The analysis results of the species mingling index in our study also provide vital information to evaluate the species diversity between the stands and forest types in future studies, serving the purpose of biodiversity conservation and proposing forest management measures at Dong Nai Cultural Nature Reserve. In addition, the intense competition of two dominant species (S. guiso and V. odorata) are reflected by their crowding index. This result will be beneficial in selecting tree species belonging to the dominant species group (five species) for planting a mixed forest in areas with similar topography, soil, and climatic conditions compared to the study area.

With the analysis results of this study’s bivariate and quadrivariate distributions, we agree with some previous studies that these two frequency distributions are not fundamentally different (Zhang et al., 2019; Quy et al., 2021b). However, using the M–U–C–W quadrivariate distribution enriches the methods of describing the spatial structure of the forest but also reflects more intuitively than using the bivariate distribution. Zhang et al. (2019) indicated that the U–C–W quadrivariate distribution could accurately describe the spatial structure of the stand in the most comprehensive way; this frequency distribution type has very great significance in proposing the adjusting measures for the spatial structure of the stand. In forest management, using the M–U–C–W quadrivariate distribution can simplify the spatial structure description of the stand and accelerate the transformation of the spatial structure of the forest from the real to the ideal spatial structure (Xu et al., 2018; Quy et al., 2021b).

Spatial Associations of Dominant Species

The spatial association of forest trees refers to positive interactions (attraction) or negative interactions (repulsion) (Quy et al., 2022c). Positive interactions between species indicate that species are interdependent or have similar responses to their surroundings (Long et al., 2015). In contrast, negative interactions suggest that species compete with each other or that their reactions to the environment are different (Ma et al., 2014). In addition, the spatial association between species can also be non-interactive (independence), meaning that their interactions are not apparent to be positive or negative (Long et al., 2015).

The analysis results of spatial associations of dominant species in our study indicated that the spatial distribution of forest trees is closely related to the spatial scale. Many previous studies have demonstrated that one species can have positive interactions with another at a small scale but has negative interactions or independence at a large scale (Ma et al., 2014; Long et al., 2015). For example, among the five dominant species of this study, S. guiso and C. delpyi have positive interactions at the small scale of r < 10 m, but there are independent relationships at the large scale of r > 10 m. Because of the dependence on a spatial scale, traditional spatial analysis methods such as subplot-based or occurrence frequency of species pairs cannot reflect the ecological relationships of tree species at different spatial scales (Bai et al., 2020). The spatial point pattern analysis method can perform spatial analysis at any scale (Hu et al., 2019); it takes the spatial coordinates of the forest trees as fundamental data, considers each tree as a point in the two-dimensional space plane, and performs spatial analysis based on a point distribution map (Quy et al., 2021c). The spatial point pattern analysis method has broken the limitations of the analysis scale. It uses the information of the forest trees (spatial and non-spatial attributes) so that the analysis results will be realistic and more reliable (Long et al., 2015). On the other hand, in reforestation or afforestation, determining the appropriate spacing of the planting hole is very important (Quy et al., 2022b). Our study’s spatial association analysis for the five dominant species is a valuable reference for species selection and planting hole spacing in practical forestry production in Vietnam.

ISAR Model of Dominant Species

All species interact directly or indirectly with other species; thus, species interactions are considered at the core of ecological and evolutionary processes (Burslem et al., 2005). In ecological research, some researchers have proposed the research idea of plant root length to discover the coexistence mechanism of species (Liu et al., 2014). These authors suggest that combining species with different root lengths can help them achieve the best use of resources (Burslem et al., 2005). Theoretically, this research direction is significant, but it is challenging to implement because tropical forest trees have tens of thousands of species. Studies on the spatial patterns of forest trees have shown that the spatial distribution of species and plant-plant interactions are closely related to each species’ biological and ecological characteristics (Quy et al., 2022b). Therefore, studying the coexistence of species can be done by studying their spatial patterns and interactions (Quy et al., 2022c).

The ISAR model is a development of the SAR (species-area relationship) method combined with Ripley’s K statistical function (Hai et al., 2018b). It estimates the number of neighbor species of a local species based on their interactions (Yang et al., 2013). In the ecological relationship of tree species, the target species significantly affects the spatial distribution, growth, and development of neighbors (Ma et al., 2014). According to the law of species interactions, if the interaction of a species with neighbors is positive, then there will be more living species around it and vice versa (Quy et al., 2022c).

Based on the analysis results of the ISAR model for dominant species, our study showed that among five analyzed dominant species, two species were diversity repellers (S. guiso and V. odorata), two species were neutrals (D. venosa and S. zeylanicum), and only one species was diversity accumulator (C. delpyi). The analysis results of the ISAR model, spatial structure, and ecological relationships of the five dominant species in this study were not inconsistent. The results indicated that S. guiso and V. odorata were two tree species with intense competition with their neighbors. C. delpyi was a diversity accumulator species because its size was smaller than neighboring species (Table A1, Supplementary Information); this result is consistent with the asymmetric competition principle. This principle holds that larger trees exploit disproportionately greater resources when competing with smaller trees (Weiner, 1990). In addition, C. delpyi is also shade-tolerant species (Ho, 1999), so its light competition is less likely with neighboring trees. Jia et al. (2016) also suggested that competition for light rather than soil nutrients underlies the coexistence of tropical forest tree species. Our findings are a basis for adjusting the density of dominant species within the stands where silvicultural measures can be implemented in Dong Nai Cultural Nature Reserve.

CONCLUSIONS

This study provides essential scientific information for the management and functional improvement of evergreen broadleaved forests in Vietnam. A 4-ha study plot of the evergreen broadleaved forest has been established to collect data in Dong Nai Cultural Nature Reserve, Dong Nai Province, South Vietnam.

A total of 4583 individuals belonging to 101 species of 59 plant families were recorded in the study plot. Among the 101 identified species, five species (S. guiso, V. odorata, D. venosa, C. delpyi, and S. zeylanicum) are ecologically significant. Five dominant species and the forest stand have a high degree of mixed species, and their density was medium. The tree species of the stand were uniformly distributed in the forest canopy layers. Five dominant species tend to be randomly distributed on the forest ground.

In the five dominant tree species group, S. guiso and V. odorata competed fiercely with other species and were diversity repellers. C. delpyi was a diversity accumulator, while the other two dominant species (D. venosa and S. zeylanicum) were neutrals. Dominant species interactions were two-way interactions, and their spatial associations were independent primarily at spatial scales r of 0–50 m. Attraction and repulsion patterns of dominant species accounted for a low proportion. Attraction patterns appeared for the species pair D. venosa and C. delpyi at scales r of 0.5–2 and 30–40 m. The spatial associations between S. guiso and C. delpyi (0–3 m), S. guiso and S. zeylanicum (2–7 m) were repulsions.

Our findings suggest that adjusting the stand structure of the evergreen broadleaved forest should only focus on the stand structure in the horizontal plane. In describing the spatial structure of the stand, the bivariate and quadrivariate distributions have no difference. Still, the quadrivariate distribution can reflect the spatial structure of the forest in detail and more visually. Limited dispersal and natural self-thinning can be processes that adjust the spatial associations and distribution patterns of dominant species in the stand.

Appropriate human intervention can accelerate succession processes of forests, stabilize forest stand structures and provide better ecological functions. However, the study plot is located within a strictly protected zone in Dong Nai Cultural Nature Reserve, so all measures affecting the stands need to comply with current legal provisions on special-use forest management in Vietnam.

The spatial association analysis result of five dominant species in this study is a reference in choosing species and appropriate planting hole spacing when forest restoring or planting new forests in areas similar to the study area of climatic and soil conditions.