FIGURE 2 Independent environmental variables used to model the
potential geographical distribution of each species in Northwest Yunnan
2.3.2 Construction of the GWR
model
Fotheringham et al. (1996) proposed the GWR model based on the thought
of local smoothing and the summary of local regression analysis and
variable parameter research. GWR is an extension and improvement of the
traditional global linear regression (e.g., OLS) which adds geographical
locations (i.e., Spatial factors) to the regression parameters, and also
considers the spatial weights of adjacent points (Han et al., 2016). In
addition, GWR model is a local regression model, which can profoundly
explain the spatial non-stationarity relationship between response
variables and explanatory variables by decomposing global parameters
into local parameters (Tripathi
et
al., 2019a).
The
regression equation can be developed as (Han et al., 2016; Tripathi et
al., 2019b):
\begin{equation}
\mathrm{y}_{\mathrm{i}}\mathrm{\ }\mathrm{=}\mathrm{\ }\mathrm{\beta}_{\mathrm{i}\mathrm{0}}\mathrm{\ }\mathrm{(}\mathrm{u}_{\mathrm{i}}\mathrm{,}\mathrm{v}_{\mathrm{i}}\mathrm{)}\mathrm{\ }\mathrm{+}\mathrm{\ }\sum_{\mathrm{k}\mathrm{\ }\mathrm{=}\mathrm{\ }\mathrm{1}}^{\mathrm{p}}{\mathrm{\beta}_{\mathrm{\text{ik}}}\mathrm{\ }\mathrm{(}\mathrm{u}_{\mathrm{i}}\mathrm{,}\mathrm{v}_{\mathrm{i}}\mathrm{)}\mathrm{\ }\mathrm{x}_{\mathrm{\text{ik}}}\mathrm{\ }\mathrm{+}\mathrm{\ }\mathrm{\varepsilon}_{\mathrm{i}}}\nonumber \\
\end{equation}Where k = 1, p explanatory variables,εi denotes the random error term at positioni . In addition, (ui ,vi ) represents the geographic coordinate or
spatial location the of each observation,βi 0 (ui ,vi ) is the intercept at position i ,βik (ui ,vi )
denotes
the local regression coefficient at position i . Whenβ 1k = β 2k =
… = βnk , it indicates that the GWR model is
transformed into an ordinary linear regression model. In this study, the
potential species richness within each grid were used as dependent
variables and environmental factors were used as independent variables
to investigate the explanation capabilities of different categories of
environmental parameters on the potential geographical distribution
patterns of species.
According to the Tobler’s first law (TFL) of geography (Tobler, 1970),
the basic principle of the GWR model to calculate the weight is “the
closer the distance, the higher the assigned weight; on the contrary,
the lower the assigned weight (Fotheringham et al., 2002)”. Therefore,
the weight can be calculated by a monotonically decreasing function in
space distance with [0, 1] as the value range. This type of function
is called as kernel function (Lu et al., 2020). The GWR method usually
employs a Gaussian model as a weight function, where bandwidth is a
function that describes the weight and the distance and is considered as
an important control parameter in weight calculation (Gao et al., 2019).
The function is expressed as (Wang et al., 2020):
ωij =
exp\(\left(-\frac{\mathrm{d}_{\mathrm{\text{ij}}}^{\mathrm{\ }\mathrm{2}}}{\mathrm{b}^{\mathrm{2}}}\right)\)
Where ωij denotes the distance weight of
observation location i and j , dijis the Euclidean distance between location i and j , and b
represents the bandwidth. When the distance between location iand j is larger than b, ωij is equal to 0;
when the distance between location i and j is equal to 0,ωij is equal to 1.
2.4 Model evaluation
2.4.1 Evaluation of the MaxEnt
model
We adopted AUC value to evaluate the
fitting accuracy of the MaxEnt model. The
model
fitting precision can be evaluated as failed if AUC value is between
0.50 and 0.60, poor if AUC value is between 0.60 and 0.70, fair if AUC
value is between 0.70 and 0.80, good if AUC value is between 0.80 and
0.90, and excellent if AUC value is
between 0.90 and 1.00 (Phillips et al., 2006; Zhang et al., 2019). In
addition, the suitability maps were calculated employing the logistic
output of the Maxent, and the range of habitat suitability index (HSI)
value we had obtained was [0, 1]. According to a large number of
previous studies and the expert experience method, we reclassified HSI
value into four grades by Natural Breaks in ArcGIS 10.4 software: 0-0.20
is low, 0.20-0.40 is medium, 0.40-0.60 is high, and 0.60-1.00 is optimal
(Convertino et al., 2014; Yi et al., 2017). In order to conservatively
estimate the suitable potential geographical distribution area of
species, we considered grids with the HSI value larger than or equal to
0.40 as the suitable potential distribution area.
2.4.2 Evaluation of the GWR
model
In this study, we used the package ‘spgwr’ of R software to select
bandwidth by adopting Gaussian function and employed Akaike Information
Criterion (AIC) to confirm the optimal bandwidth. Generally, regression
residual is an evaluation value of the fitting goodness of the model,
including residual sum of squares (RSS) and residual standard deviation
(Sigma), and these two values should be as small as possible. In
addition, R 2 and AIC value can also reflect
fitting goodness of the model. The higher R 2,
and the lower AIC value, indicating the better fitting effect of the
model (Li et al., 2017; Liu et al., 2019). When the difference in the
AIC value (∆AIC) of the two models is greater than three, then the model
with smaller AIC value has better fitting effect (Han et al., 2016; Xue
et al., 2020).