2.3 Statistical analyses
The alpha diversity, beta diversity, dominance of plant functional types, and elevational range of each plant group, as well as the total number of plants, were calculated to examine the validity of the existing hypotheses. Alpha diversity was defined as the species richness of each plant group within a plot, and its correlation with the elevation was fitted by generalised linear models (GLMs) with log-link function and Poisson distribution. Both the linear and second-order polynomial models were constructed, and the final model was selected as that with significant coefficients and higher Akaike information criterion (AIC) values. If no model had significant coefficients, then that with the lowest AIC value was adopted. The influence of climatic factors on plant diversity was also analysed using GLMs with log-link function and Poisson distribution. The explanatory variables used in these models were measured as the climatic factors having a stronger correlation with alpha diversity (r > 0.5). Beta diversity was evaluated using the βsin index, considering that this metric excellently performs under various criteria (Koleff, Gaston, & Lennon, 2003). The βsin index was calculated between adjacent plots as follows:
βsin =\(1-\frac{a}{\left(\min\left[b,\ c\right]\ +\ a\right)}\)(1)
where, a is the total number of species found in both plots;b is the number of species found in the focal plot; and cis the number of species found in the other plot.
The elevational patterns associated with alpha and beta diversity were further discussed in relation to changes in plant functional types. Plant functional types are groups of species that respond similarly to environmental and biotic changes (Duckworth, Kent, & Ramsay, 2000). These responses were used to characterize the elevational patterns of plant groups (Bruun et al., 2006; Sánchez-González & López-Mata, 2005; Zhou et al., 2019). This study classified trees, shrubs, herbs, and bryophytes into the following functional types: evergreen and deciduous trees, evergreen and deciduous shrubs, forbs and graminoids, and mosses and liverworts, respectively. The dominance of plant functional groups was calculated as the ratios of the species richness of each functional type to the total species richness of the plant group. The dominance was then plotted against elevation.
To test the applicability of the mid-domain effect to elevational distribution, the discrepancy between the observed results and those predicted by the mid-domain effect was determined using the null model, which was based on the discrete mid-domain effect model (Colwell & Hurtt, 1994). The predicted mean species richness was calculated by 9999 Monte Carlo simulations with the RangeModel software version 5.0 (Colwell, 2006). The predicted values were plotted against elevation and correlated with the observed alpha diversity using Pearson’s correlation.
Finally, the applicability of Rapoport’s elevational rule to elevational distribution was examined based on the elevational range of each plant group. The elevational range was defined as the mean difference between the highest and lowest elevations of all the recorded species in each plot and was calculated as follows:
Elevational range = \(\frac{\sum_{i=1}^{n}{(H_{i}\ -\ L_{i})}}{n}\)(2)
where, n is the total number of species recorded in a plot;Hi is the highest elevation where the i th species was recorded; and Li is the lowest elevation where the i th species was recorded. The highest and lowest elevations were based on herbarium specimens (Nagoya University Museum; NUM-Bt) collected in central Japan (Chubu, Kinki, and Kanto regions), plant diversity databases (Biodiversity centre of Japan, 2018), and plant survey reports from the studied region (Akiyama, 1983, 1984; Hattori, 1958; Inoue, 1981; Kodama, 1971, 1972; Masuzaki & Katagiri, 2010; Takaki, Amakawa, Osada, & Sakuma, 1970).