The Chinese Loess Plateau (CLP) is naturally vulnerable to soil erosion, with approximately 72.3% of the total 650× 10³ km² land being subjected to severe soil erosion (Peng, 2013; Kang et al., 2014). The soil erosion on the CLP had been greatly exacerbated before the late-20^th century by massive human activities such as land reclamation, deforestation and overgrazing (Zhao, 1991). The direct adverse consequences of soil erosion, naturally occurred or/and human induced, are intensive declines in land productivity and extensive reductions in vegetation coverage (Li et al., 2005; Qin et al., 2006; Shao et al., 2008; Wang et al., 2009; Guo and Wang, 2012; Peng, 2013). Among the human activities that had exacerbated the soil erosion on the CLP, deforestation, as well as the associated removal of non-forest vegetation was the most notorious (Zhao, 1991). It means that reforestation or natural forest regeneration can be an effective measure in controlling the soil erosion and thus in ameliorating the ecological environment on the CLP.

During reforestation or natural forest regeneration, internal competition among plants for limited resources has been proven to be the driving factor for the success of a forest succession (Tilman, 1994; Pillay and Ward, 2012; Fraver et al., 2014). For example, Zhang et al. (2015) found that the internal competition of a community drived the forest dynamics in western Canada while the external factors played a minor role. A number of models were proposed to elucidate the mechanisms of the internal competition. Followings are our brief critiques on some of those models. Grid-based models explained the interspecies competition but ignored the heterogeneity of resources (Goldberg and Barton, 1992). Tessellation models considered the forest as a homogenous unit but ignored the possible influcence of the neighboring plant species (Berger et al., 2008). Distance-size models or Hegyi’ s models (Hegyi, 1974; Weiner, 1990) took account of the size and height of plant species (Sandoval and Cancino, 2008; Linkevič ius et al., 2014; Saha et al., 2014), and these models did appreciate the complexity of the competiting processes at different spatial scales (Houston et al., 1988; Berger et al., 2008).

Most published studies focused on the community composition and the soil factors in understanding reforestation processes, whereas research on the spatial patterns of tree competition at various development stages is still lacking (An et al., 2007; Li et al., 2008; Liang et al., 2010). This study took advantages of two large patches of Quercus wutaishanica (oak) forest (secondary forest) in Ziwuling Mountains on the CLP to investigate the spatial patterns of tree competition at various development stages using Hegyi’ s models (Kang et al., 2014; Sun et al., 2015).

Figure 2 shows that P. tabulaeformis (PT) and Q. wutaishanica (QW) had higher CI values than B. platyphylla (BP) and P. Davidiana (PD), suggesting an intensive competition between these two species (PT and QW) in the early development stages of oak forests. However, the fact that the CI values of nearly 70% the studied Q. wutaishanica trees were lower than the average CI value suggested that the CI-indicated intensive competition was probably skewed by a limited number of individuals of its population. Moreover, B. platyphylla also displayed a similar competition pattern with Q. wutaishanica, although B. platyphylla tree was a mild competitor. In the mixed forest, P. davidiana had the smallest number of trees and also the lowest CI value.

Fig. 2

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Fig. 2 Competition index (CI) of each tree species in the early (a) and late (b) development stages. QW, Quercus wutaishanica; BP, Betula platyphylla; PT, Pinus tabulaeformis; PD, Populus davidiana(Notes: Short lines above and below the boxes are the maximal values and minimal values; small white squares are the means; boxes are numerical ranges of CI between 25% and 75%; horizontal lines in the box are medians.)

A significant negative correlation between DBH (diameter at breast height) and CI (competition index) of each tree species in the early development stage of oak forests was found for all studied tree species (Figs. 3a-d) and the strongest negative correlation was shown in the species P. tabulaeformi (R²=0.43; Fig. 3c). The overall relationship between DBH and CI for all of the four studied species was also negative (R²=0.21; Fig. 3e), suggesting that the larger the trees, the less competitive they were, and that thus implying that the older the trees, the less competitive they were.

Figure 4 shows the spatially-distributed (i.e., Kriging-interpolated) CI values or the spatial distribution of CI values on the 50 m× 50 m plots. A positive relationship between CI and tree density was found in both of the plots (Figs. 4a and b), implying that the forest with higher density was more competitive. Patches of high CI value were found in all development stages. The patches with high CI showed a wider range in the early development stage than in the late developmental stage, indicating that the competition intensity declined with forest development in the study area. However, the fact that the patches with high CI did not disappear in the late development stage indicated that long-term asymmetric competitions occurred in the oak forest during the succession process.

Interspecies and interspecies relationships among tree species in the early development stage were analyzed using univariate and bivariate O-ring statistics. Points higher than the confidence interval indicated clumped distributions or positive correlations; points lower than theconfidence interval indicated segregated or overdispersed distributions or a negative correlation; points within the confidence interval suggested random distributions or no significant correlations (Kang et al., 2014). Figure 5 shows that Q. wutaishanica and P. tabulaeformis had significant self-correlation at small spatial scales, whereas no significant correlation was observed at large spatial scales. The spatial patterns of oak forests are associated with the biological characteristics of species. For instance, the heavy seeds of Q. wutaishanica were clustered at small-scales within the vicinity of the mother trees, and thus resulted in a clumped population. By contrast, B.

Fig. 3

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	Fig. 3 Relationship between diameter at breast height (DBH) and CI (competition index) in the early (a, Quercus wutaishanica; b, Betula platyphylla; c, Pinus tabulaeformis; d, Populus davidiana) and late (e, Quercus wutaishanica) development stages of oak forests on the Chinese Loess Plateau (CLP)

Fig. 4

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	Fig. 4 Kriging interpolation analysis of individual CI (competition index) (a, Plot 1; b, Plot 2)

platyphylla and P. davidiana could produce a large number of winged seeds, which exhibited strong dispersion ability. Thus, they had no significant self-correlations at all spatial scales. Interspecies correlation analysis (Fig. 6) revealed that Q. wutaishanica was negatively correlated with B. platyphylla and P. tabulaeformis at small spatial scales, whereas no significant correlations were observed at large spatial scales and among other studied species. The result suggested that clumped Q. wutaishanica limited the recruitment of B. platyphylla and P. tabulaeformis at small-scales. We divided the trees into three classes based on the sizes (i.e., DHB), i.e., small trees (S, DBH< 15 cm), middle trees (M, 15 cm≤ DBH˂ 25 cm) and adult (large) trees (A, DBH≥ 25 cm). The spatial relationships of intraspecies competition based on different sizes of oak trees were then analyzed using univariate and bivariate O-ring statistics for the two development stages.

In the early development stage, clumped distribution of small and middle trees was found (Figs. 7 a-c). However, due to the lack of adult (large) and middle oak trees, self-correlation of adult trees and the spatial relationships of intraspecies competition were meaningless (Figs. 7d-f).

Fig. 5

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	Fig. 5 Spatial relationships in intraspecies competition by univariate O-ring statistics (O(r)) of main tree species in the early development stage (a, Quercus wutaishanica; b, Betula platyphylla; c, Pinus tabulaeformis; d, Populus davidiana)

Fig. 6

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	Fig. 6 Spatial relationships in interspecies competition by bivariate O-ring statistics (O12(r)) in the early development stage (a, Quercus wutaishanica-Betula platyphylla; b, Quercus wutaishanica-Pinus tabulaeformis; c, Quercus wutaishanica-Populus davidiana; d, Betula platyphylla-Pinus tabulaeformis; e, Betula platyphylla-Populus davidiana; f, Pinus tabulaeformis-Populus davidiana)

However, in the late development stage, small oak trees showed positive spatial self-correlations at scales of 2-5 m (Fig. 8a). No obvious self-correlations were found between middle trees and adult (large) trees (Figs. 8b and c). Negative correlation was found between adult (large) and middle trees and also between adult (large) and small trees (Figs. 8d and e), and a weak positive correlation was found between middle and small trees at small spatial scales (Fig. 8f). It implied that smaller trees were impeded by the surrounding larger trees. Correspondingly, interspecies competitions were replaced by intraspecific competition from different sizes in late development stage.

Fig. 7

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	Fig. 7 Intraspecies spatial relationships between different sizes of oak trees in the early development stage based on univariate (O(r)) and bivariate (O12(r)) O-ring statistics (a, adult trees; b, middle trees; c, small trees; d, adult-middle trees; e, adult-small trees; f, middle-small trees)

Fig. 8

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	Fig. 8 Intraspecies spatial relationships between different sizes of oak trees in late development stage based on univariate (O(r)) and bivariate (O12(r)) O-ring statistics (a, adult trees; b, middle trees; c, small trees; d, adult-middle trees; e, adult-small trees; f, middle-small trees)

We found a positive self-correlation and high intensity of competition in Q. wutaishanica and P. tabulaeformis. These findings can be attributed to the biological characteristics of these tree species. That is, the heavy seeds of Q. wutaishanica and P. tabulaeformis clumped at small spatial scales, and the clumped seeds resulted in an intensive competition. By contrast, white birch (Betula platyphylla) produces a large number of winged seeds that can be dispersed readily by airflow. In addition, birch seeds tend to sprout in areas where competition is weak (Zhang et al., 2010; Gao et al., 2011). Our results further confirmed the early findings that birch trees were not strong competitors in oak forests.

Our study showed that the competition index (CI) expressing the competition intensity was negatively correlated with the sizes (DBH) of all tree species and the dependency of the competition intensity on the size (DBH) became weaker at the late development stage (see Fig. 3). This finding is consistent with those by Tilman (1994) and Pedersen et al. (2012) who found that the competition intensity generally decreased with the growth of trees. At the early development stage of oak forests, oak and pine trees had high competition intensities (see Fig. 4a), suggesting that interspecies competition may have played an important role in the spatial distribution of tree species. Oak has a relatively high tolerance towards droughts and shades, promoting its dispersal in less habitable areas and thus becoming pioneer species on the CLP. In comparison, birch and aspen trees have narrow crowns and high intraspecies competition due to their clumped seedlings at small-scales. This finding is in agreement with that by Petritan et al. (2014) who found the same patterns in an old growth stage of Quercus petraea-Fagus sylvatica forest in western Romania. Again, the interspecies competition decreased at the late development stages primarily due to failures of those weak competitors (see Fig. 4b). Our finding that a forest tended to be homogenized in the late succession stage in terms of its species composition is quite similar with those reported by others (e.g., Barot et al., 1999; Getzin et al., 2006).

It should be mentioned that light was reported to have played an important role in interspecies competition. For example, Rees and Bergelson (1997) and del Rí o et al. (2014) suggested that asymmetric light competition might have resulted in different outcomes of interspecies competition. It means that the canopies of taller tree species may overshadow those of shorter tree species, thus resulting in stronger competitions of taller oak and pine trees and weaker competitions of shorter white birch and aspen trees (Qin et al., 2006; Su et al., 2009; Shao et al., 2012). It is our regret that we were not able to examine the relationship between light and interspecies competition simply due to our failure in finding a feasible method to accurately measure the crown width.

The spatial patterns and interspecies relationships of dominant species in mixed forests determine the community dynamics. This research found that intensive interspecies competition drove the diffusion of successor species (such as the oak trees on the CLP) and the successful diffusion was partially resulted from the failure of pioneer species in the interspecies competition during the early stages. After the invasive species replaced the pioneer species in some areas, interspecies competition drove the decreasing of the replaced population. In short, competition led to a reshaping of population structure, and even drove further changes of spatial patterns.