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).