Ethics statement

The Management Bureau of Xishuangbanna National Nature Reserve gave us the authority to conduct tree census works in the 20-ha plot. With the authority of the principal investigator of the Barro Colorado Island (BCI) plot, we downloaded topographic data, soil data and tree data for that plot from the website of the Center for Tropical Forest Science (http://www.ctfs.si.edu/).

Site description

Data from two seasonal tropical forests were used to investigate the mechanisms underlying the SARs and the g-functions. The first of these datasets was from the 20-ha forest dynamics plot in Bubeng village, Xishuangbanna National Nature Reserve, Southwest China (Data S1). This area is dominated by a typical monsoon climate which results in a typical dry season (November to April) and wet season (May to October). In 2007, we finished the first census of the Bubeng plot. We recorded 95,498 stems of which 468 species or morphospecies were identified, belonging to 213 genera and 70 families. The altitude of the Bubeng plot ranges from 709 to 869 m. Detailed descriptions of the climate, geology, and flora of the Bubeng plot can be found in Lan et al. [32] and Hu et al. [33]. The second dataset originated from the 50-ha forest dynamics plot on Barra Colorado Island (BCI), Panama. This plot is also located in an area with an alternation of wet and dry seasons. The plot supports lowland semideciduous moist forest with 301 species and 229,049 stems with DBH ≥1 cm. The topography of the BCI plot is flat with an altitudinal range of only 38 m. Detailed descriptions of the climate, geology, flora and fauna of the BCI plot can be found in Croat [34], Leigh et al. [35] and Gentry [36]. In keeping with the data from the Bubeng plot for which we used the first census data, we used the tree data from the first census of the BCI plot [37]. The tree census of both plots followed the agreed protocol for the global network of forest research plots overseen by the Center for Tropical Forest Science [38].

To quantify the effects of environmental variables on the SARs and g-functions, we used topographic and soil variables as environmental variables. Based on topographic survey data, mean elevation, convexity, aspect, and slope in each 20×20 m cell were calculated and used as topographic variables at both sites [21], [39], [40]. For the Bubeng plot, we sampled soils using a regular grid of points every 30 m, generating 252 nodes. Every second node was paired with an additional sample point at 2 m and 5 m, 2 m and 15 m or 5 m and 15 m along a random compass bearing away from its associated node. In total, 756 soil samples were taken. For each sample, 500 g of topsoil (0–10-cm depth) were collected. Nine soil attributes - available nitrogen, exchangeable potassium, extractable phosphorus, organic matter, soil pH, total potassium, total nitrogen, total phosphorus and soil bulk density - were analyzed as described by Liu et al. [41]. We used Kriging interpolation, to generate maps of the nine soil attributes using 20×20 m cells. To avoid over-fitting, we computed the principal components from the nine soil attributes and used the first three components as soil variables for the Bubeng plot. These condensed variables explained 83.5% of the total variance in the nine soil attributes. For the BCI plot, the Kriged estimates of Zn, Al, B, Ca, Fe, K, Cu, Mg, Mn, N, P, N (mineralisation) and pH values were calculated for 20×20 m cells. Again, we computed the first three principal components of the soil attributes, which explained 78.5% of the total variation, and used these to represent soil variables at the BCI plot.

Testing size-class effect on the SARs: size-class categorization

To model size-class effect on species’ distributions, we classified trees into different DBH size-classes as an effective option for handling the tree size issue. We modelled species’ distributions using 3 DBH size-classes:, viz.

The three DBH class categorization was partly to be consistent with the studies by Hu et al. [33], [42], making our results comparable and ensuring that enough individuals can be found in the large DBH class. For each of the 3 DBH classes, species with an abundance of at least 50 were included in the point process model. When input that did not incorporate size effects was required these three size-classes were simply combined and conventionally designated, together,as Class ‘0’.

Point process models

Following Shen et al. [21], we used the inhomogeneous Poisson process (to model environmental impacts), the homogeneous Thomas process (modelling dispersal) and the inhomogeneous Thomas process (modelling the joint-effects of environment and dispersal) to simulate tree species’ distributions. The simulations using the three point-process models were realized in the R statistical language (version 3.0.2) [43] using the R code of Shen et al. [21].

Inhomogeneous poisson process

Models incorporating the inhomogeneous Poisson process use quadrat-based environmental variables to determine the density of target tree species in the corresponding quadrats. This model, accordingly, is useful for simulating species/habitat associations and we have used this model to determine the contribution of niche differentiation to species assembly. It employs the following function:(1)where >0, is a vector of regression parameters, is a vector from the matrix of environmental variables - topographic and soil variables in this study.

Thomas process models

Both homogeneous and inhomogeneous Thomas processes are varieties of Cox processes that drive patterns of clumping [21]. They can be used, therefore, to simulate processes generating patterns of aggregation [28], [44]. We used these models to simulate how parent trees dispersed offspring around themselves. We used the homogeneous version to explain dispersal-only limitation and the inhomogenous version to simulate the joint-effect of dispersal and environment. These models simulate the contribution to species assembly of neutral process and the joint-effect of niche and neutral process, respectively [21]. The Thomas point process X was a superposition of ‘mother’ points c in a stationary Poisson point process of intensity , with associated ‘offspring’ clumps Xc viz.:(2)where >0, is a probability density function depending on a parameter δ >0 determining the spread of offspring points around c. represents the covariance between event density and environment at point s. When  = 1, the function represents an homogeneous Thomas process; when the value is greater than unity, then the function is an inhomogeneous Thomas process. A more detailed description of the algorithms, parameter estimation and R-code for these three models can be found in Shen et al. [21].

Simulating entire communities

To produce simulated communities incorporating the effects of size-classes, we firstly generated 100 simulated communities using a point process model for each of the three DBH classes: then by randomly superimposing the simulated assemblages of classes 1 to 3 together, 100 simulated communities with the size-class effect were created for each point process model. This does not model species interactions and intraspecific relationships among different size-classes. To represent simulated communities without the size-class effect, 100 simulated communities were generated directly using point process models of Class 0 (that is: with the three size-classes combined).

An SAR was constructed by generating an increasing series of 200 different sizes of randomly selected rectangular sampling cells from each specific simulated or real community [21]. The performance contrasts for these SARs between the point process models with and without the size-class effect were compared using an approximation of Akaike’s information criterion (AIC) [45]. As there were 100 simulated communities for each point process model, a Kruskal-Wallis rank sum test was used to identify the statistical difference between the AIC values of point process models with and without size-class effect. We also used AIC values to compare the performance of the three models. The AIC values of the three models can be approximated from the following formula [23], [45]:(3)where n is the number of sampled areas and equals 200, R is the sum of residual squares, and k is the number of parameters. The number of parameters of the inhomogeneous Poisson process, the homogeneous Thomas process and the inhomogeneous Thomas process are 2, 3 and 5, respectively [21]. As we had 100 simulated communities for each of the three point process models for each DBH class, we computed SAR AIC values for each simulated community. Again, we a Kruskal-Wallis rank sum test to compare the SAR AIC value differences between the point process models with and without the effect of size-class. We used pairwise Wilcoxon rank sum tests to assess the differences in SAR AIC values among the three point-process models for each DBH class.

Testing size-class effect on the g-function

To evaluate the effect of incorporating size-classes on the point patterns of species’ distributions, the pair correlation function (i.e., the g-function) was computed for all the simulated and real species’ distributions. The g-function may effectively identify the occurrence of point-point interactions at a certain scale and evaluate the degree of aggregation. The g-function statistic is defined as(4)where g(r) is the g-function, K(r) is Ripley’s K-function, and r is distance [46].

Specifically, we first computed the g-function value for each species of all the simulated and real communities at circumferences with a series of radii at 5, 10, 15, 20, 25, 30, 35, 40 and 45 m. To compare the degree of conspecific aggregation of the simulated distributions with and without the effect of size-class at the community level, we fitted them to the observed g-function using major axis regression [47]. Using this technique, if the fitted line is below the identity line (that is: where the fitted value is equal to the observed value of the g-function), then the point process model underestimates the degree of spatial aggregation: alternatively, the model overestimates the degree of spatial aggregation. By displaying the fitted lines of all the point process models against the identity line, we can identify the degree of deviation of the simulated patterns from the real data. In a manner similar to that used to calculate the SAR AIC values (see above), we computed the g-function AIC values to determine the performance of the three models. As before, we used Kruskal-Wallis rank sum tests to compare the differences in the AIC values of g(r) with and without size-class effects. We used pairwise Wilcoxon rank sum tests to evaluate differences in the AIC values of g(r) among the three point process models for each DBH class. The calculation of the g(r) and major axis regressions were also implemented in the R statistical language using the spastat [48] and lmodel2 [49] packages, respectively.

The SAR results

For the Bubeng plot, 158 tree species were used in the analyses designated as size-class 0. Out of these species, there were 148 species in size-class 1, 43 in class 2 and 52 in class 3. For the BCI plot, there were 169 tree species at class 0, 161 tree species at class 1, 83 tree species at class 2, and 77 tree species in class 3. Figure 1 shows the SAR patterns of the simulated communities produced using the three point-process models with and without an size-class effect for Class 0 of the Bubeng plot and the BCI plot. Using the inhomogeneous Poisson process, there was almost no shape difference in shape in the relative SAR patterns between the simulated communities with and without an size-class effect for both plots. For the inhomogeneous Thomas and the homogeneous Thomas processes, there were significant shape differences in the relative SAR patterns between the simulated communities with and without size-class effect across the two plots. The SAR AIC value distributions at class 0 and the Kruskal-Wallis rank sum test results on them verified the differences statistically (Fig. 2 and Table 1). The p-values of Table 1 suggest that the SAR AIC values are remarkably reduced when size-class effects are introduced into the homogeneous Thomas process for class 0 of the Bubeng plot and the BCI plot. However, the SAR AIC values were only similarly reduced by the size-class effect for the inhomogeneous Thomas process for class 0 for the BCI plot.

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Figure 1. The observed and predicted species–area curves for the three process models with and without the size-class effect for Class 0 (that is: size-classes 1, 2 and 3 combined) of the Bubeng plot and the BCI plot.

The bars represent 95% confidence intervals.

https://doi.org/10.1371/journal.pone.0108450.g001

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Figure 2. Boxplots of AIC value distributions of the SARs generated by the three process models with and without the size-class effect at Class 0 (that is: size-classes 1, 2 and 3 combined) forthe Bubeng plot and the BCI plot.

HT.l = the homogeneous Thomas process with size-class effect; HT.w = the homogeneous Thomas process without size-class effect; IP.l = the inhomogeneous Poisson process with size-class effect; IP.w = the inhomogeneous Poisson process without size-class effect; IT.l = the inhomogeneous Thomas process with size-class effect; and IT.w = the inhomogeneous Thomas process without size-class effect.

https://doi.org/10.1371/journal.pone.0108450.g002

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Table 1. The p-values from Kruskal-Wallis rank sum tests on SAR and g(r) AIC values across the point process models with and without size-class effect at DBH class 0 (that is: size-classes 1, 2 and 3 combined).

https://doi.org/10.1371/journal.pone.0108450.t001

The inhomogeneous Poisson process always overestimated the SAR patterns from class 0 to 3 for both plots (Figs. 1 and 3). Among the three point-process models, the inhomogeneous Thomas process always led to the most accurate SAR estimation from Class 0 to 3 (Figs. 1–4, Tables 2 and Table S1). As the DBH class increased, so the SAR AIC value differences between the homogeneous Thomas and the inhomogeneous Thomas processes were gradually reduced, again for both plots (Fig. 4 and Table 2). Because the inhomogeneous Thomas process modelled the joint-effects of environment and dispersal, the reason for this trend may be that dispersal is always more influential than environment.

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Figure 3. The observed and predicted species–area curves for the three process models for size-classes 1, 2 and 3 of the Bubeng plot and the BCI plot.

The bars represent 95% confidence intervals.

https://doi.org/10.1371/journal.pone.0108450.g003

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Figure 4. Boxplots of AIC value distributions of the SARs generated by the three process models for size-classes 1, 2 and 3 of the Bubeng plot and the BCI plot.

HT = the homogeneous Thomas process; IP = the inhomogeneous Poisson process; IT = the inhomogeneous Thomas process.

https://doi.org/10.1371/journal.pone.0108450.g004

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Table 2. The p-values of pairwise Wilcoxon rank sum tests on SAR and g(r) AIC values among the three point process models for the three DBH classes.

https://doi.org/10.1371/journal.pone.0108450.t002

The g(r) results

There was no significant difference in g(r) AIC values between the simulated species’ distributions with and without size-class effects for any of the three point-process models for Class 0 of the two plots (Fig. 5 and Table 1). In contrast to the SAR results, the g(r) AIC values of from the model based on the inhomogeneous Thomas process were always the highest of any of the three models evaluated and the difference is significant for Class 0 (Fig. 5 and Table S1). This was also true for Classes 1 to 3 (Fig. S2 and Table 2). The major axis regression results on degree of conspecific aggregation showed that the point-process models with size-class effects overestimated the degree of conspecific aggregation compared with those without the size-class effect (Fig. 6).

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Figure 5. Boxplots of g(r) AIC value distributions generated by the three processe models with and without the size-class effect at Class 0 (that is: size-classes 1, 2 and 3 combined) of the Bubeng plot and the BCI plot.

https://doi.org/10.1371/journal.pone.0108450.g005

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Figure 6. Comparison of observed g(r) of species at DBH Class 0 (that is: size-classes 1, 2 and 3 combined) with g(r) simulated by three point process models with and without size-class effect.

Abbreviations as for Figure 4.

https://doi.org/10.1371/journal.pone.0108450.g006

Of the three point-process models, the lines fitted using major axis regression from the inhomogeneous Poisson process were below the identity line for Classes 0 to 3 (Figs. 6 and S1). This suggests that the simulated patterns of species’ distributions using this model were always less clumped than the real species’ distributions. Conversely, the other two point-process models always overestimated the degree of conspecific aggregation across all size-classes (Figs. 6 and S1).

Performances of the models

The SAR and, especially, the g-function results (Figs. 2, 4, 5, S1 and S2), suggest that the model based on the homogeneous Thomas process performed well across all DBH classes for the two forests. Although the SAR AIC values using the homogeneous Thomas process were not the lowest of the three models, the differences in AIC values between the homogeneous Thomas and the inhomogeneous Thomas process gradually decrease (Figs. 3 & 4). On the other hand, the ecological factors inherent in the models based on inhomogeneous Thomas processes and the inhomogeneous Poisson process play important roles in determining spatial patterns at the community and species levels, respectively. In previous studies models based on the inhomogeneous Thomas process are close to the best performing of the three basic kinds of point process models that have investigated SARs and distance decay curves at the community level [20], [21], with L-function patterns at species level [25], with species abundance distributions, and with nearest-neighbor distance functions at both the species and community levels [23]. This is not the case, however, in our study.

Unlike other studies only that of Wang et al. [20], for the Changbaishan 25 ha plot in China, have found that the inhomogeneous Poisson process generated the best distance-decay curve for larger trees (DBH ≥10 cm). With respect to the g(r) results (Figs. 6 & S1), for instance, for the Bubeng plot, the point patterns of simulated distributions of Mezzettiopsis creaghii, Alchornea tiliifolia, Castanopsis echidnocarpa and Knema furfuracea produced by the inhomogeneous Thomas process are much more aggregated than their real distributions (Figs. S3–S6). In fact, of the three models, the inhomogeneous Poisson process can even produce the best g(r) patterns at the species level (Figs 5 & S2).

A comparison of the three point-process models within our study indicates that the summary characteristics used can strongly affect the study results and the conclusions. This is because critical characteristics of the complex patterns underlying species’ distributions may be emphasized differently by different summary characteristics [24]. Our conclusion, based on SARs and g(r) functions which detect spatial patterns at community and species levels, may be more robust than those based on summary characteristics that incorporate species’ distribution patterns at either, but not both, of community or species levels.

Contributions of the ecological processes

After synthesizing the results of the SARs and g(r), reflecting community and species levels patterns, respectively, we have demonstrated that dispersal largely controls species’ distributions within the two forests evaluated. Moreover, as it shown in Figures 3 & 4, the role of dispersal in driving species’ distributions increases with size-class increasing, whereas that of environment decreases. This pattern is consistent with a recent finding that the contributions of neutral processes to tree species survival shift with the change from juvenile to reproductive stages at the BCI plot [10]. At the Bubeng plot, it has once been verified, using regression and ordination methods on the tree lattice data, that dispersal is the dominant process in shaping species’ distributions [33], [42]. At the BCI plot, Levine and Murrell [50] have suggested that dispersal is important for species’ distributions at the species level. Our results demonstrate that dispersal is also crucial in determining species’ distributions at both community and species levels. Moreover, the finding that dispersal dominates the structuring of species’ distributions of trees from small to large size is consistent with the reports by Seidler and Plotkin [1] and Leithead et al. [51]. Specifically, Seidler and Plotkin [1] demonstrated that species’ distributions are related to dispersal mode from saplings to mature trees and Leithead et al. [51] showed that the dispersal process is important for species spatial patterns for the BCI plot. Our results also suggest that dispersal can be the principal process shaping community spatial pattern on plots with large elevation ranges (160 m for Bubeng). This is also true for the Gutian 24 ha plot which has an elevational range of 268.6 m [52]. In contrast, at the Sinharaja 25 ha plot with only a 151 m elevation range, Gunatilleke et al. [53] demostrate that environment dominantes species distributions. The contrasting results from these plots indicate that the contribution of environment to species distribution does not necessarily relate to elevation range. To sum up, dispersal is a dominant process in shaping species’ distributions in both forests.

Size-class effects

The effects of size-class serve as an essential supplementary mechanism for understanding the patterns of species area relationships. Our results show clearly that the incorporation of size-classes improves the accuracy of SAR estimation using models based on homogeneous Thomas processes for the two forests, and the accuracy of those using inhomogeneous Thomas process at the BCI plot (Fig. 2). As we have already indicated, dispersal is a dominant process determining species’ distributions; we hypothesize, therefore, that several crucial mass dispersal phases at different life stages that shape the real species’ distributions in the two forests may exist. For the BCI plot, the finding by Seidler and Plotkin [1] that tree distributions from saplings to adults are strongly related to dispersal provides direct evidence for this hypothesis. Previous studies also demonstrated that, at the Bubeng plot, the distributions of tree species are predominantly determined by neutral spatial processes across size-classes [42]. In summary, we suggest that the size-class effect is important for determining tree species’ distributions through influencing dispersal characteristics from juvenile to adult trees.

On the other hand, the concordant SAR patterns produced using the inhomogeneous Poisson process with and without size-class effects suggest that species’ habitat preferences at different DBH classes are almost uniform. This is consistent with the finding that most of the species tend to maintain their habitat preferences across different DBH size-classes in a 24-ha subtropical forest plot in China [6]. Why do the habitat preferences of species become homogenous across different size-classes? By studying habitat-driven assemblages of species in three size-classes from the BCI plot, Kanagaraj et al. [10] found that species’ habitat preferences become weaker as they age. Figures 3 and 4 further suggest that such habitat preferences are basically formed at an early stage of life. This is because SAR patterns of the inhomogenous and homogenous Thomas processes only differ greatly from each other at Class 1, and little for Classes 2 and 3. This is consistent with the predictions of the theory of regeneration niche differentiation which predicts that species’ habitat preferences most likely form at an early stage of life and this preference is maintained through later size stages [54]. What we have shown is consistent with the theory when a rigorous quantitative statistical analysis is applied.

The size-class effect might be affected by the location of the plot (i.e. via its environmental heterogeneity). As it shown in Figure 2, the influence of size-class shows, on the one hand, that the trend of impact on dispersal processes is the same but its influence on the joint process (environment+dispersal) exhibits differential impacts on the two plots. This suggests that the addition of environmental factors to the point process model may result in a different performance of the joint process. As the site location of interest is the major source of environmental variation, using more plots and conducting meta-analyses may shed light on to this issue.

The importance of the size-class effect on species’ distributions at the community level is significantly different from that at the species level, having a significant impact on the SAR patterns but not on the g(r) patterns in either of the two forests examined. A possible reason for this distinction is that SARs and g(r) functions reflect species’ distributions at different scales. SARs are related to the spherical contact distribution, which fundamentally describes the vacant area between clumps [28] and thus is less capable of reflecting the pattern at smaller species-level scales. On the contrary, the g(r) function describes the details of clumps of individual species and focuses on patterns at that scale [31]. It is most likely, therefore, that the effect of size-class principally influences species’ distributions at relatively large scales.