The patterns and scales of tree distribution influence forest structure and dynamics through complex interactions involving crown architecture differences between species (Haq et al., 2023), soil properties (Waheed et al., 2022), water availability constraints on tree height (Klein et al., 2015), disturbance effects (Zhang et al., 2022), and the integration of dynamics across various spatial scales within forest ecosystems (Mitchell et al., 2023). Changing spatial patterns can strengthen or weaken interactions within and among tree populations, and between them and their environment (Kuehne et al., 2018). Several empirical studies have found that spatial patterns significantly influence forest recruitment rates (Yang et al., 2008; Hai et al., 2014; Rendenieks et al., 2022). In a forest, the spatial arrangement of different-sized stems within tree populations can influence competition for resources, which, in turn, affects tree growth and mortality rates (Beyns et al., 2021). In particular, stem aggregation or dispersion could explain the certain spatial processes observed (e.g., density dependence, thinning, and predation) in a forest through spatial point pattern analysis (Nguyen et al., 2022; Salas-Eljatib et al., 2022; Muñoz-Gallego et al., 2023).

The spatial point pattern analysis is a fundamental tool for exploring the spatial processes and patterns of an ecosystem (Illian et al., 2008). In a spatial point pattern analysis, every single tree can be considered a point (Ripley, 1976), which allows the estimate of the spatial distribution of individual trees mapped in a given area (Diggle, 2003; Wiegand and Moloney, 2004; Illian et al., 2008; Law et al., 2009; Wiegand and Moloney, 2014). Therefore, by analyzing spatial point patterns, we may infer certain properties or behaviors of related or underlying spatial processes involved (Baddeley et al., 2015; Xin et al., 2022). However, different ecological mechanisms and processes such as competition and disturbance may result in the same spatial patterns (Detto and Muller-Landau, 2013). Exploring the underlying ecological dynamics that drive these spatial patterns remains a significant challenge in ecology.

In forest stands, density dependence is an important mechanism that could change the spatial distribution of trees (Piao et al., 2013; Kuang et al., 2017; Miao et al., 2018; Ma et al., 2024). As the density of recruits increases beyond the maximum threshold that the environment can support, resource competition occurs. Thereafter, negative density dependence leads to a lower probability of survival close to parent trees. For instance, in pure Norway spruce forests in Switzerland, the small dead trees tend to gather close to large trees, and this aggregation effect decreases as the distance increases (Bianchi et al., 2021). A study of Japanese larch forests revealed that density dependence did not play a role, and the further away seedlings were from the seed tree, the greater their survival rates (Im et al., 2023). However, in tropical mountain rainforests, the densities of saplings and small and medium trees increased and then decreased with the distance from old-growth trees, which exhibited a consistent pattern of density dependence (Miao et al., 2018). In Barro Colorado Island forests, the research found a high probability of recruitment in the vicinity of adult trees of other species (Condit et al., 1992). Consequently, further research is needed to investigate whether density dependence is consistent across different forest stands and under various environmental conditions.

Arid mountain forests harbor a significant proportion of global biodiversity, acting as reservoirs for diverse species and providing essential ecosystem services such as soil protection and habitat creation (Zhang et al., 2023). In this study, we aimed to examine the arid mountain forest ecosystem of the Luoshan Mountains in Ningxia, northwest China, situated in the transitional zone between grassland and desert. The forest stands in this area are dominated by Qinghai spruce (Picea crassifolia), Chinese pine (Pinus tabulaeformis), and Aspen (Populus davidiana) (Liang, 2018). P. davidiana, a common pioneer species that emerges in the aftermath of human disturbances, is known to function as effective sites for seedling recruitment (Bouchard et al., 2018). Unlike P. crassifolia and P. tabulaeformis (seedlings from seed germination), P. davidiana reproduces asexually through root sprouting, and this method can result in more dense individual trees around adult trees. We aimed to investigate how the spatial correlation of different sizes distributes in P. davidiana stands in this arid mountain forest. We also sought to determine whether there is density dependence between recruits and adult trees, and if the death of seedlings is random or density-dependent? Therefore, we aimed to answer these questions from five perspectives.

1 We use the univariate O-ring statistic O₁₁(r) under the heterogeneous Poisson null model to analyze whether the spatial distributions of various P. davidiana size classes transition from an aggregated pattern to a uniform or random pattern. As tree sizes increase, stems should exhibit more regular spatial patterns at small scales, due to self-thinning resulting from competition (Salas-Eljatib et al., 2022).

2 Then, by using the bivariate O-ring statistic O₁₂(r) under an antecedent condition null model (Wiegand and Moloney, 2004), we could analyze the spatial associations among different size classes. The antecedent condition null model conveys the relationships between living adult trees and saplings or seedlings (Wiegand et al., 1999), enabling us to examine the influence of adult trees upon seedlings and saplings across a range of spatial scales.

3 The mark-correlation functions could quantify the similarity or dissimilarity between neighboring trees in terms of their attributes (such as size, height, and biomass). Researchers can identify patterns of positive or negative associations among tree attributes at different spatial scales. Positive correlations indicate that similar tree attributes tend to cluster together, while negative correlations suggest a tendency for dissimilar attributes to be spatially segregated. By using mark-correlation functions k_m1m1(r) under the independent marking null model, we could test the similarity of two neighboring trees separated by distance (Illian et al., 2008; Wiegand and Moloney, 2014).

4 The trivariate random labeling null model enables the study of how an extra (previous) pattern affects the processes associated with a distinctly identified pattern (Holík et al., 2021). Within this method, pairs of points are chosen based on a set distance r, with the initial point originating from the primary pattern (adult tree) and the subsequent point from another clearly defined pattern (whether the seedlings and saplings are dead or alive). The cumulative non-normalized r-mark correlation function C^cum_.,m2 based on a trivariate random labeling null model was applied to examine the impact of living adult trees on seedling mortality (Wiegand, 2014).

5 We aimed to test the random mortality hypothesis, which posits that individual mortality events occur randomly in space (Wang et al., 2019). According to this hypothesis, spatial correlations between individual mortality events should not be observed, and the mortality of adjacent individual trees should not increase in response to neighborhood density. In contrast, we propose that the spatial positioning of individual trees may have an impact on the mortality of its neighboring trees. To test this alternative hypothesis, we employed the g12, g22-g11, and g2, 1 + 2-g1, 1 + 2 functions under the random labeling null model (Stoyan and Stoyan, 1994; Raventós et al., 2010; Wiegand and Moloney, 2014).

For Analysis1, our comparison of the spatial distributions O₁₁(r) of different-sized Populus davidiana trees is consistent with earlier findings of Miao et al. (2009) and lends further support to the hypothesis that tree population’s spatial distribution transitions from aggregated to random through ontogeny in most temperate forests.

Based on the spatial association results of O₁₂(r), we found a high positive correlation between conspecific adult trees and seedlings (Analysis 2). This is easily explained because P. davidiana seedlings originate from root sprouts of reproductive individual trees and are therefore expected to exhibit strong positive spatial correlations with these adult trees (Qin and Shangguan, 2006). However, for Analysis 3, as the seedlings grow and recruit into saplings, the stem density-related limitations and greater competition for the resource (i.e., light, water, and nutrient) strongly influenced the distance and size of individual trees, especially asymmetrically vis-à-vis taller neighboring trees (Figure 4A). Therefore, at a spatial position away from adult trees (1-14 m in our result, Figure 3B), seedlings tend to have a better potential to reach the sapling stage (Shao et al., 2011; Gao et al., 2014), which, in turn, enhances their prospects for adult recruitment into the canopy.

To explore the possible reasons for seedling mortality of P. davidiana, we hypothesized that it was the outcome of an excessively high local density, leading to intense intraspecific competition and self-thinning effects (Analysis 4 and Analysis 5). Although g₂₁ did not detect a significant negative spatial correlation between dead and live seedlings, the function g_2,1 + 2-g_1,1 + 2 > 0 indicated that the mortality of seedlings was density-dependent (Figure 5D). As a result of high-density seedlings from root sprouting, P. davidiana adult trees showed a positive association with seedlings (Figure 3A). Therefore, the seedling mortality is density dependent due to the presence of adult trees. The results from C^cum_.,m2 evidenced that adult trees contribute to a higher risk of seedling mortality that nonetheless declines with distance (Figure 4B). As seedlings were negatively correlated with saplings at both medium and small spatial scales, the initially high density of seedlings may have led to higher post-dispersal mortality risks faced by P. davidiana at the stage when its individual trees are most vulnerable. Thus, the closer the seedlings are to an adult tree, the stronger the negative conspecific impact in the form of higher mortality (Liang et al., 2016).

The g₂₁-g₂₂ and g₂₂-g₁₁ functions together discover the dead seedlings that emerged more cluster around dead ones and depart with live seedlings (Figures 5B,C). For P. davidiana, its dead seedlings display higher aggregation than the surviving seedlings, which rejected the random mortality hypothesis. However, we did not investigate why having an excessive density of seedlings makes them prone to die off in a clustered spatial pattern. Additionally, we did not know the maximum density limit that causes mortality at the seedling. Seedling mortality is a result of a complex causes. At different scales, different dominant causes lead to their death. For instance, forest research on negative density-dependent dynamics in trees has confirmed that local high densities of the progeny of the same species could lead to disproportionately high levels of seedling mortality caused by soil pathogens (Janzen-Connell hypothesis) (Liu et al., 2007). Such a negative density-dependent feedback driven by the soil microbial community is actually common and ecologically important in many temperate tree species (Packer and Clay, 2000; Liang et al., 2016; Jevon et al., 2020). Moreover, Yamazaki et al. (2009) found that vertebrate herbivores (mainly rodents) were the major cause of mortality for large-seeded tree species, whereas the disease was most important for small-seeded species. Therefore, further investigation is needed on where and how the density impacts seedling mortality in arid mountain forests.

The spatial patterns of trees in an arid region, such as the Luoshan Mountains in China, are influenced by plant competition. To gain insights into the stand dynamics and guide regeneration strategies, we investigated the spatial distribution of individual trees at different growth stages (sizes) in P. davidiana forest in the Luoshan Mountains.

Spatial point pattern analysis confirmed that the spatial distribution of individual trees shifted from an aggregated distribution to random distribution as seedlings grew and developed into adult trees. Additionally, we found that more seedlings emerged around adult trees while high seedlings’ mortality happened in clusters. Further research is arguably needed to elucidate the causes of P. davidiana mortality, and the close relationship between its adult trees, seedling density, and seedling mortality was prominent in this arid mountain forest.

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

JuY: Conceptualization, Funding acquisition, Project administration, Software, Writing – original draft, Writing – review & editing. JiY: Funding acquisition, Resources, Writing – review & editing. GW: Investigation, Methodology, Visualization, Writing – review & editing. XL: Conceptualization, Project administration, Resources, Writing – review & editing.