2.4 Data analysis
We compared the structural characteristics of the communities at the three sites on the basis of the size structure. According to our previous observations, the maximum DBH of woody plants in the studiedD. pectinatum communities is typically greater than 60 cm. Thus, we clustered the adult individuals into twelve size classes representing 5 cm intervals (i.e., 5 cm-10 cm, 10 cm-15 cm, 15 cm-20 cm, …, ≥60 cm). Based on previous experience, individuals with a DBH less than 4 cm were regarded as regenerating individuals (Gao et al. 2017). Due to the high mortality of seedlings in tropical forests, the number of seedlings we surveyed was limited, and thus we classified seedlings and saplings with a DBH of less than 5 cm and a height of less than 4 m as regenerating individuals.
The mortality rates were analyzed using the exponential function and power function model to fit the size structure of the adult individuals and the height structure of the regenerating individuals (Hett and Loucks 1976). Hett and Loucks assumed a constant probability of mortality over time if the height or DBH structure fit an exponential function and a decrease in mortality over time if a power function provided a better fit. Therefore, we classified the regenerating individuals into groups according to a height interval of 0.5 m (i.e., 0 m-0.5 m, 0.5 m-1 m, …, 3.5 m-4 m) and combined the size levels of the adults to simulate the mortality at the three sites with the following transformation models involving the exponential or power function. The analysis was performed in IBM SPSS Statistics 20.0 for Windows (SPSS Inc., Chicago, IL, USA).
Power function model
loge (y ) = loge(y0 ) + b x
Exponential function model
loge (y ) = loge(y0 ) + b loge (x )
where y represents the number of regenerating individuals or adult individuals in any height class x ,y0 represents the number of individuals in the minimum height class, and b represents the mortality rate (Hett and Loucks 1976).
Species density and richness were used to compare the changes in regeneration patterns across the three sites. These variables were calculated using the total number of regenerating individuals recorded in each plot. Density represents the total number of regenerating individuals in each species. Richness represents the total number of species.
To explore how the regeneration dynamics were related to environmental factors, we explicitly modeled regeneration dynamics using two linear mixed-effect models (LMMs), one modeling the species richness of regenerating individuals and one modeling their total density. In the first LMM, the dependent variable was defined as the species richness in each plot. To eliminate the impacts of sites and plots on the LMMs, we added sites and plots as random variables, and ten environmental factors (SOM, pH, TN, AP, AK, elevation, slope, aspect, slope position, canopy density and adult density) were included as fixed variables. The formula of the LMM was as follows:
Linear mixed-effect model
Yi = [α + Xiβ ]fixed part +[μs|p + μp ]random part
where Yi represents the species richness of thei th plot. In the fixed part, α and β refer to an intercept and a vector of coefficients of explanatory variables,x , respectively. In the random part, μsand μs|p represent the spatial autocorrelation at the plot and site scale, respectively (Heming et al. 2016).
With the second LMM, density was also analyzed based on the method used for the first LMM. In both LMMs, only environmental factors withP <0.05 were ultimately retained. The analysis was performed with the R package “lme4”.