Intraspecific competition between trees is a key interaction in shaping forest stands and makes analyzing the underlying ecological processes possible. This interaction may affect growth and spatial distribution of trees and result in a specific horizontal and vertical stand structure. For this reason, competition is known as one of the primary processes that influence population size, community structure and its diversity. In order to understand competitive interactions of trees in forests, several methods have been developed to assess spatial scale of competition among individual trees and show the effect of competition their biometric characteristics. Therefore, this study was aimed to investigate the effect of intraspecific competition between Persian oak coppice trees on their biometric attributes in Zagros arid and semi-arid forests using spatial analysis.
A 300 m × 300 m plot purely cover with Persian oaks was selected close to Yasuj city, Kohgiluye - BoyerAhmad province. The point map of all 1113 coppice trees was obtained by azimuth and distance technique. Kolmogorov-Smirnov test was primarily applied to investigate the difference between the distribution of coppice trees and homogeneous Poisson process. Spatial analysis of Persian oak coppice trees was then performed using pair correlation function g(r), O-ring function O(r), and mark correlation function kmm(r). In mark correlation function, biometric characteristics of total height, crown height, diameter at root collar, crown mean diameter and area were implemented as marks. Moreover, Monte Carlo test was used to test the significance of the results.
Comparison with homogeneous Poisson process showed that the observed pattern of Persian oaks was significantly homogeneous (α=0.05). The results of pair correlation function g(r), and O-ring function revealed that there was intraspecific competition between Persian oak coppice trees that was significant up to spatial scale of 5 m (α=0.05).In addition, the results of mark correlation function demonstrated that total height, crown height, and diameter at root collar were very sensitive to intraspecific competition, while crown attributes (i.e. mean diameter and area) showed less sensitivity to competition.
In general, it was concluded that there were competitive interactions between Persian oaks in the studied pure stand that negatively affected their biometric characteristics. Competition between coppice trees negatively influenced their growth, although this negative interaction had less effect on crown attributes as the distance between coppice trees because of their low density (123.7 coppice trees ha-1) reduced the crown competition.

Non-native plant species have been introduced to provide various goods and services. Some species have not shown negative effects on the ecosystem, while others cause habitat disturbances. Considering this issue, it is necessary to know these species' positive and negative effects. Paulownia is an exotic industrial tree species, and there are debates on the positive and negative effects of its plantation in forests and non-forest areas among experts and scientists. There are few studies on paulownia invasion behaviour based on the literature review in Iran. This study tries to investigate the competitive behaviour of Paulownia using scientific methods in reforested mixed stands in the educational and research forest of Shast-Kalate. Data were collected in the educational and research forest of Dr. BahramNia (Shast Kalateh) in the two areas. An area of 2.5 hectares of native species mixed with non-native species of Paulownia and another area of 2.5 hectares that only had native species (control). All trees in the study area were recorded. The measured variables for each tree include tree species, diameter at the breast height (DBH), tree height, and crown diameter. All trees with a diameter at the breast height above 5 cm are included in the surveying. The spatial coordinates of all trees were also recorded. The trees included the non-native species of Paulownia fortunei, and the native trees included Acer velutinum bioss, Acer cappadocicum Gled, and Carpinus betulus L. In order to investigate the interaction between species, bivariate O-Ring statistics and bivariate mark correlation functions were used based on distance. The independent T-statistic was used to compare the biometric variables of native species. The graphs obtained from the O-Ring statistic between Paulownia species and native species indicate that the relationships are generally of the attraction or independent type. Also, the mark correlation function results indicate negative and independent interactions based on the DBH and crown diameter and negative for tree height between Paulownia and Acer cappadocicum. Interactions between Paulownia species and Carpinus betulus in all distances were independent based on DBH and negative and independent regarding crown diameter and tree height. Also, positive, negative and independent interactions were seen regarding tree height and crown diameter between Paulownia species and Acer velutinum and attraction and independent interactions were seen in terms of DBH. The independent t-statistics indicate that the average DBH and crown diameter of the Acer cappadocicum Gled in Paulownia mixed plantation is more than the control area, there is no significant difference in tree height. The average DBH and crown diameter of Acer velutinum bioss were higher, and tree height was less in Paulownia mixed plantation compared to the control area. The tree height of the Carpinus betulus L. was higher, and the crown diameter was less in the control than the Paulownia mixed plantation. No significant differences were seen in DBH between the two study areas. Considering Paulownia's growth nature, a higher tree height, DBH, and crown diameter can be expected, and the results confirmed this. In contrast, this growth rate does not exist in native species. On the other hand, the marks used in the mark correlation function include the variables of tree height, DBH and crown diameter, so the negative marked correlation function results can be attributed to this property. In order to introduce a species as invasive, comprehensive research is needed for its effects on the regeneration of native species, composition of vegetation, and soil properties.

One of the most prominent issues indicating the future quality and quantity of natural forest ecosystems is spatial pattern and distribution of disturbances consequences manifested as canopy gaps (CGs). The main purpose of this study was to illustrate the CGs distribution pattern in one of the Hyrcanian mixed-beech (Fagus orientalis Lipsky) forests, so-called preserved Glandroud forests. All CGs areas were measured based on full callipering on the basis of the radius method, and the coordinate of each CG was recorded in the forest. The univariate Ripley’s L-function, mark correlation function (MCF), and density function (DC) in turns were used for analyzing the spatial patterns, size correlation, and frequency of the CGs distribution at the observation scale. Furthermore, the statistical significance of all ordination analyses was tested by the Monte Carlo permutation method. The results showed that the frequency of small gaps (0-2 R), medium gaps (2-5 R), and in turns were almost 32%, 49% in the study forest. Only the small CGs distribution was clustered at a specified distance of 14–20 meters, though the other CGs size classes were completely randomly distributed in the forest. Integrating whole CGs size classes on the basis of Ripley’s L-function showed that the CGs spatial pattern in the studied forest was clustered at a distance of 40 m. According to the mark correlation function (MCF) and density correlation (DC) analyses, there in turns were found that the location and number of size classes in each aggregation were totally significantly independent and random based on the specific distance in the forest. Pertaining to these results, it is possible to introduce mosaics consisting of forest stands which may include specified tree stands with various tree species composition, different developmental stages, and structures in the forest. Therefore, each mosaic can be a base area for monitoring disturbances consequences and implementing optimum managements.

Point pattern analysis based on the spatial distribution of a mark, e.g., diameter; could be implemented using Mark Correlation Function (MCF). The purpose of this study was to quantify the spatial interaction and competition in the intact beech stands of Hycanian forests of Iran using MCF. To this end, nine 1-ha sample plots were established at three developmental stages of initial, optimal and decay in three intact natural, unmanaged and uneven-aged beech (Fagus orientalis Lipsky) stands in the north of Iran. Diameter at breast height (DBH) of all trees greater than 7.5 cm along with their coordinates were recorded and fully mapped in the plots. Analysis of intra-specific competition of beech trees using MCF showed that DBH in the initial stage had a negative correlation indicating high spatial competition at all distances, while it was independent or positive in optimal and decay stages, except at distances up to 12 meter. Consequently, there was no intra-specific competition in each of these two stages. The results demonstrates the utility of second – order analysis of marked point processes for characterizing the competition in the beech stands and planning silvicultural interventions, e.g., thinning, based on the competition intensity of trees.

Recently, forest decline has outburst in Zagros forests region in the west of Iran, especially in Ilam province. In this research, we selected an 83 ha infected forest area in Zarab, Ilam and the dried trees were fully investigated for variables including dbh, height, drought intensity, crown cover, origin and Cartesian coordinates. Their spatial structure, spatial patterns and spatial correlation were analyzed using variogram analysis, O-ring statistic and Mark correlation function (MCF), respectively. Results showed that the density of dried trees was 27 N/ha which is more comprised of coppice trees in small and medium diameter classes. A cluster spatial pattern of dried trees was determined up to 35 m and after that it was uniform, implying dried trees created patches with 3850 m2 surface area. Variogram analysis showed that only dbh and drought intensity of dried trees had strong spatial structure which was mapped using Kriging interpolation method of Geostatistics. Mark correlation function graph showed that adjacent dried trees were similar according to drought intensity while were not similar based on their dbh. In general, the results illustrated that all of the trees in the studied area were infected by drought with different biometric characteristics as well as at different geographical aspects. These results can be used as an instruction for sustainable management of the stands based on their spatial characteristics.

Forest reserves are a shrinking pattern of biosphere reserves in which unique and rare or endangered species grow naturally. Juniper genus is one of the few indigenous conifers of Iran with habitats in large areas of the country. However, nowadays, despite its importance, there is a declining trend that is particularly critical in areas without control and management. The purpose of the study was to investigate and quantify the inter-specific competition of juniper trees (Juniperus excelsa) with the main associated species, namely pistachio (Pistacia atlantica) and maple (Acer monspessulanum), in Kandirigh forest reserve in Ardabil Province of north-west of Iran. For this purpose, full census inventory was taken in a protected area of 13.2 hectares, and variables of DBH, total height and crown diameter and spatial coordinates of all tree species were recorded. Then, the bivariate O-ring statistic and mark correlation function (MCF) were used to evaluate the competition between the junipers with pistachio and maple. Bivariate O-ring statistic showed that most of the interactions of these three species are independent or, ultimately, at small scales are attractions. Univariate and bivariate mark correlations function also showed that the interested variables of DBH, total height and crown diameter were spatially independent. All of this is due to the lack of significant competition between juniper trees and the associated species in this forest reserve. Thus, pistachio and maple can be introduced as associated species for the reforestation and enrichment of the other juniper habitats with similar conditions.

Quantifying spatial structure is one of the most important components, describing natural ecosystems and their biodiversity. In this study, a set of indices and functions related to spatial structure using 102 established plots with an area of 1000 m2 were presented. To achieve spatial structure of Carpinus-Fagus type, a set of indices (Clark & Evans, uniform angle, Shannon-Wiener, mingling and DBH/Height dimension) and functions (pair correlation and mark correlation) were applied. The indices and functions demonstrated the diversity of tree positioning, species, and tree dimension. The mean values of Clark & Evans and uniform angle indices were 0.86 and 0.53, respectively, indicating a distribution between random and cluster patterns. Also, pair correlation function indicated trees with inter-tree distance smaller than 5.5 m were more than the same forest with a random distribution. The mean values of Shannon-Wiener and mingling indices were computed 1.17 and 0.36, respectively. Mingling index properly showed a low mixture of beech and hornbeam and a high mixture of other species. Furthermore, the mean values of both DBH/Height dominance indices were 0.51, which indicated that some species such as linden and alder were dominance and species including elm and persimmon were conquered. Mark correlation function showed that trees with inter-tree distance less than 7.5 m had a smaller DBH rather than the average of forest. The utilized indices and functions in this study had a high ability in describing of available species structure in Carpinus-Fagus forest type, so the result could be applied in sustainable forest management.

Understanding of distribution of plants and analyzing their spatial pattern reveal the interactions of plants and environment. Nebka as an indicator phenomenon of plant-sediment interaction, plays an important role in protecting of vegetation and sand stabilization. The aim of the present study was to evaluate the interaction of Nebka and plant based on a field study, measuring the morphometric parameters, and precise point positioning. Therefore, 322 Nebkas and 119 plants were determined in the northern region of Aq-Qala, Golestan province. In order to investigate and determine the spatial pattern and interactions of Nebkas and plants, and impact of soil parameters on their distribution pattern, univariate and bivariate functions including g and mark correlation functions were used. The pair correlation function showed that spatial pattern of plant at distance of less than 23 m was irregular. This means there is no competition between plants at distance of less than 23 m. Furthermore spatial pattern of Nebka was irregular at distance of less than 23 m. Bivariate g function at distances less than 50 m indicated positive correlation between plant and Nebka. Therefore, all plants and Nebkas have a positive impact on formation and distribution of each other. Results of the MCF function with 95% probability showed that soil properties such as EC, pH, OM, SAR, and skewness of Nebka sediments influence the Nebka’s pattern in the study area.

Climate change and global warming, primarily driven by increased fossil fuel consumption, necessitate a reduction in greenhouse gas emissions. Carbon sequestration in plant biomass and soil offers a straightforward solution for lowering atmospheric carbon dioxide levels, thereby improving air quality and enhancing soil productivity. The present study was conducted in the year 2021 in the Chaparquimeh region of Golestan Province, aimed to assess carbon sequestration levels in both soil and Atriplex vegetation, considering human-made disturbances such as road. To accomplish, soil and vegetation samples were collected from locations featuring Atriplex plant species. The measured carbon sequestration levels were utilized to create a carbon sequestration map using by the InVEST software package. moreover, by extracting the coordinates of the plants in the region, spatial analysis of the sequestered carbon was conducted using spatial functions in the R software environment and Programita (including Ripley's k functions, g functions and marked correlation function (MCF)). Spatial analysis of the Atriplex species revealed a scattered distribution pattern, with the highest carbon sequestration occurring near the road (Gonbad-Inche Borun), reaching 828.85 kg/m2, and decreasing with distance 258.13 kg/m2. The overall average carbon sequestration in the study area was 489.3 kg/m2. The spatial pattern of Atriplex, according to the results of the g(r) function, is uniform and scattered at distances greater than 5 meters and is acceptable at a 5% significance level. The MCF function indicated that the spatial distribution pattern of Atriplex has no significant impact on the amount of carbon sequestration in the area. Understanding native species compatible with carbon storage capabilities can underscore the importance of developing and preserving natural ecosystem services. This knowledge can contribute to land management practices and the restoration of degraded lands, ultimately improving carbon sequestration efforts.

Intraspecific interaction is important because it occurs between the same species individuals that have similar ecological nests. The objective of this study was to evaluate intera-specific interaction of poplar trees (Populus euhratira Olivier.) using mark correlation functions.

The position of all trees with DBH>2.5 cm were recorded in two pure and mixed stands in Behbahan Chaharasyab area with area of 4.5 and 9.1 ha, respectively. Tree height (H), diameter at breast height (DBH), crown diameter (CD) and light crown length (LCL) were measured as mark variables. Point spatial pattern analysis was used to study the spatial pattern and intraspecific interaction. Marked correlation (MCF) function was used to reveal the spatial relationships between the poplar individuals trees in terms of various characteristics such as total tree height, diameter at breast height, crown diameter and light crown length.

The results showed that in pure stand, a significant negative correlation was observed between the DBH of trees at a distance of less than 5 and more than 20 m. Between distances of 5 to 20 m, an independent state was observed between the individuals. There was a positive and negative correlation between the crown diameter of poplar trees from a distance of 5 to 40 m and more than 45 m, respectively. There was a significant positive correlation between the total height and the light crown length of the trees from a distance of 5 to 30 m. At a distance of more than 30 m, the independence was seen between the individuals. In mixed stand, the independence status was observed between DBH of trees up to a distance of 40 meters. A positive correlation was observed at distances greater than 40 m. There was a negative correlation between trees CD at all distances. The independence was seen between H and LCL of trees at most distances.

In pure stand, depending on different distances and marks, various states of interaction including negative, positive and independence were seen between the tree individuals. While in mixed stand, except for the state of negative interaction that was seen in relation to the crown diameter, in other cases, the condition of independence between different individuals was observed in terms of the studied marks. DBH showed similar conditions in both pure and mixed stands. CD showed positive and negative correlations between individuals in pure and mixed stands, respectively. There was a positive correlation between H and LCL of individuals in pure stand while independence was observed in mixed stand. Overall, it is useful to study the interaction between poplar trees to understand the dynamics, growth process and mechanisms that endanger this valuable species.