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Stratification is an important phenomenon in natural forests. The mixed pine-oak forests along the Nanpan River in southwest China was clearly formed by two layers in the vertical direction. These forests developed in an area where the virgin forests suffered clear-cutting. After excluding habitat heterogeneity, we divided two plots into upper and lower layers according to the tree height, and then analyzed the spatial pattern, species distribution, and size differentiation using the pair correlation function _{mm} (

A forest is a three-dimensional ecosystem, and its structure can vary in both the vertical and horizontal directions. The horizontal distribution pattern of trees has always been a research hotspot. It is believed to be directly related to ecological processes within the forest community (

Vertical stratification of trees is an important phenomenon in natural forests (

The understory may also affect regeneration, seedling growth, and forest dynamics by changing the soil seed bank, invading and occupying forest gaps, which will eventually have an impact on the upstory structure and species composition (

The species composition of forests in temperate regions is relatively simple and, due to the particular renewal and growth characteristics of some species (

The purpose of this study was: (1) to identify the distribution pattern and spatial correlation of trees in the early stages of a secondary forest; and (2) to determine the spatial distribution of tree species and tree size in the vertical layers of the forest.

The study site was located in Yachang Township, Leye County, Baise City, Guangxi Zhuang Autonomous Region (Fig. S1 in Supplementary material). The Nanpan River, which originates in Yunnan Province, separates Guangxi and Guizhou provinces as it passes through this region. The southern part of Guangxi Zhuang Autonomous Region has a typical karst landform, with limestone as the main rock type, but there are also some large mountains comprised of weathered rock. Historically, the majority of the township was part of the state-owned Yachang Forest Farm, which was later renamed the Guangxi Yaychang National Orchid Reserve due to the depletion of forest resources, together with the existence of a large number of wild orchid communities and the natural landscape of the “Tiankeng Group”. Temperature, soil types, and rainfall in the region vary dramatically with elevation and geomorphology (

The sample site was located on a mud hill, 20 km from the administrative center of Yachang township. The elevation was about 760 m a.s.l. and the study site was about 250 m from the river. The forest stand was divided into two vertical layers. The upper layer mainly contained

We established two rectangular standard plots (plot 4: 100 m × 60 m, up-slope, 106° 19’ 20" N, 24° 51’ 15.95" E; plot 5: 80 m × 70 m, mid-slope, 106° 14’ 9.5" N, 24° 27’ 28.9" E) in 2016-2018. The two sample sites were approximately 120 m apart, and had similar vegetation components. First, we divided each area into several subplots (20 × 20 m each) and determined the location of each living tree, standing dead trees, and fallen dead wood using a total station instrument (Southern Mapping Company, Johannesburg, South Africa - precision is 2mm + 2ppm). We measured all stems with at least 1 cm DBH. Then, we measured the tree height, DBH, and crown width of all standing trees. We also recorded species name and marked each living individual with a unique reference number. For fallen trees, the grade of decay (i-v), length of branches, and size of both ends were measured and recorded (

Tree height is a particularly important index of vertical structure and can be used to describe the stand (

A pair correction function (PCF), g(_{11}(_{12}(_{11}(_{11}(_{11}(_{11}(_{11}(_{12}(

where _{ij }is the edge-correction weighting, and

Tree species and size differentiation are also closely related to scale (_{f }(_{f} (^{th} and^{th} neighbors at a distance _{f} (_{1} and _{2}), which are the corresponding possible marks. When the mark is DBH, _{1}, _{2}) = _{1 }× _{2}, and when tree species are the mark, _{1}, _{2}) = 1(_{1 }_{2}). In _{ij} is the conditional expected value of the ^{th} and ^{th} trees at distance r in the point process ^{th} and ^{th} trees. In the denominator, _{f} (

In the above analysis, the Monte Carlo (MC) method was used to randomly simulate the observation values of all observation scales 199 times, and the five maximum and five minimum values were obtained as the upper and lower 95% confidence intervals, enabling the significance of the deviation of the observed value from the theoretical value to be determined. For the spatial pattern, the g_{11}(_{12}(_{2}. An observed value outside the upper confidence limit indicated an aggregated distribution or positive association. An observed value falling outside the lower confidence limit indicated a regular distribution or negative association. An observed value within the envelope between the confidence intervals indicated a random distribution and random association (_{mm}(_{mm}(_{mm}(_{mm}(_{mm}(_{mm}(

In plot 4, the clumped pattern of all populations extended for 14 m and then became a random distribution at larger scales (

The populations of the main species of the upper layer of the two stands were mostly randomly correlated, and there were no positive correlations. The upper layer of plot 4 was all randomly correlated (

In plot 4, both the community and upper layer are a conspecies aggregation up to 15 m, but the aggregation of the community was much higher than that of the upper layer. At larger scales (

In plot 4, small trees were aggregated together at small to medium scales (

An aggregated distribution of species is a common pattern in nature, especially in the early stages of succession (

The distribution pattern of the upper forest layer at each scale was significantly closer to a random distribution than that of the lower layer (

At all observation scales, the main populations in the understory in both forests were mostly randomly correlated,

Conspecies tend to aggregate in nature. This is generally considered to be the combined result of seed dispersion restrictions, habitat flittering, habitat heterogeneity and ecological preferences (

These effects may have existed simultaneously in the plots studied here, but the niche complementarity is more important. The uneven distribution pattern of the upper layer results in patchy light conditions in the forest, and light-dependent species become established in locations with less shade, forming an aggregated distribution (

Asymmetric competition results in size differentiation and death of adjacent trees. Therefore, tree size is often used to assess the intensity of competition between adjacent trees and to predict changes in the community distribution pattern (

There was almost no difference in the size differentiation of the upper layers at small observation scales between both plots (

The following abbreviations have been used throughout the manuscript:

MCF: mark correlation function

DBH: diameter at breast height

PCF: pair correction function

HP: habitat heterogeneity

CSR: complete spatial randomness

MC: Monte Carlo

This study was supported by the national natural science foundation of China (314 00542) and the Guangxi natural science foundation (2016GXNSFBA380233). Students from college of forestry, Guangxi University (Wenyan Tang, Xianyu Yao, Ting Pan, Jiafeng Long, Junmo Xu, Haihui Lu, Yao Li and Zhongfei Liu) participated in the wild investigation. We are very grateful for the comprehensive field service provided by the Guangxi Yachang national orchid natural reserve.

Distribution of trees species in the sampling plots (a: plot 4; b: plot 5). Rings and crosses represent the locations of understory and upstory plants, respectively.

Tree height distribution in the vertical layers of the forest in both plots (plot 4, a; plot 5, b). The boundary of the vertical layers was close to 6 m. The understory mainly consisted of shrubs and a few tree species, while the upstory was dominated by several tree species. In plot 4, the proportion of the number and population for understory and upstory were 55.58%:44.42% and 84.61%:15.39%, respectively, and they were 53.44%:46.56% and 89.47%:10.53% in plot 5.

A pair correction function (PCF) and Lest heterogeneity test based on the null model of complete spatial randomness (CSR), indicating no significant heterogeneity in either forest stand. The red dashed lines are theoretical values, and the grey lines denote the 95% confidence limits of a Monte Carlo (MC) simulation. The black solid lines represent observed values and

Spatial distribution and spatial correlation of the upstory and understory in both plots. The grey background in each figure denotes the 95% confidence limits of an MC simulation. The black solid line represents the observed value and the red dashed lines are theoretical values.

Statistical plots of the spatial correlation of the main tree species among the upstory and understory, and the relationship between the upstory and understory. After calculating the inter- and intra-specific spatial correlations in the different vertical layers by pairs, we considered the same type of spatial correlation (

Distribution pattern of species based on the null model of CSR. The grey background in each figure denotes the 95% confidence limits of a MC simulation. The black solid line represents the observed value and the red dashed lines are theoretical values.

Spatial pattern of tree sizes based on the null model of CSR. The grey background in each figure denotes the 95% confidence limits of a MC simulation. The black solid line represents the observed value and the red dashed lines are theoretical values.

Fig. S1 - The location of our study sites, Yachang Township, Leye County, Baise City, Guangxi Zhuang Autonomous Region.

Fig. S2 - The secondary pine-oak forests subjected to clear-cutting 57 years ago currently displays two layers: the understory species mainly consists of evergreen broad-leaved shrubs, while the upstory mainly contains several deciduous broad-leaved species and

Tab S1 - The parameters of main populations occurred in our sampled plots (the number of living trees ≥ 40) and their ecological characteristics.