Chinese Stellaria (Stellera chamaejasme L.) is a indicator plant of degraded grasslands. With its robust vitality, once it emerges in grassland ecosystems, it undergoes extensive growth and rapid expansion, leading to grassland degradation as an inevitable consequence. The establishment and invasion of S. chamaejasme disrupts the ecological balance of grasslands in Qilian Mountains. This study was conducted in a grassland on the eastern slope of the Qilian Mountains, employing point pattern analysis to investigate the spatial distribution patterns of S. chamaejasme and the relationships among different age classes. The population was categorized into three growth stages: young, sub-adult, and mature plants. The results revealed that the spatial distribution of this population is primarily dominated by subadult plants, accounting for up to 75.48% of the total, with an overall transition trend from aggregated to random distribution. No significant spatial correlations were observed among different age groups (young, subadult plants, and mature plants), indicating that mature plants do not exert significant inhibitory effects on the growth of young individuals. In high-density areas, the population exhibited a radiating distribution outward from mature plants as the center, with high-density cores predominantly concentrated within 0-5 m. Significant density variations were observed between regions, with the highest total density estimated at approximately 9.57 plants/m2 and the lowest at 2.68 plants/m². The invasion mechanism of S. chamaejasme is closely associated with the spatial independence of its age groups and a distribution pattern dominated by subadult plants. During the initial invasion phase, S. chamaejasme spreads predominantly around mature plants. After securing sufficient growing space (0–1 m), it further competes for territory through shifts in distribution patterns—transitioning from aggregated to random distribution. Additionally, significant differences in distribution density and expansion patterns across regions provide critical theoretical foundations for targeted ecological management strategies.

Aggregation patterns are often visually detected in sets of location data. These clustersmay be the result of interesting dynamics or the effect of pure randomness. We build anasymptotically Gaussian test for the hypothesis of randomness corresponding to ahomogeneous Poisson point process. We first compute the exact first and second moment ofthe Ripley K-statistic under the homogeneous Poisson point process model.Then we prove the asymptotic normality of a vector of such statistics for different scalesand compute its covariance matrix. From these results, we derive a test statistic that ischi-square distributed. By a Monte-Carlo study, we check that the test is numericallytractable even for large data sets and also correct when only a hundred of points areobserved.

Spatial analysis can be used to relate the patterns of tree species to their regeneration syndromes – pioneer to late-successional – and is a first step in refining hypotheses about the species traits and biotic and abiotic factors that give rise to forest community dynamics. This study examines the spatial pattern of the most abundant trees in three 0.45-ha plots in species-poor lowland rain forests on oceanic islands in Tonga, Western Polynesia, that experience frequent natural disturbance and have a 3000-y history of shifting cultivation. We contrast secondary vs. remnant late-successional forest, with particular attention paid to the spatial dispersion and clustering of tree species, and the presence of spatial dependence in the density of seedlings and saplings. Shade-tolerant species were not strongly clustered at any scale. They did not appear to be dispersal limited, in late successional forest, and only some showed patterns consistent with density-dependent mortality (more clumped when small). Shade-tolerant species were more clumped in secondary forest, and may be dispersal-limited there because vertebrate dispersers prefer primary forest. Shade-intolerant species were clumped in gaps in late-successional forest, but some were also clumped in secondary forest, indicating that they too may be dispersal limited during secondary succession. We also compared the species composition of seedlings and saplings in the centre of plots with trees in the surrounding area and inferred that active dispersal (by vertebrate frugivores) contributed as much as 50% to site species richness.