Results
For the three matrices, 17 distance classes were defined. In the first
distance class, the W Global, W Basin and the W FEOW matrix presented an
autocorrelation of 0.459 (Moran’s I = 0.459, p=0.005; Table 1), 0.495
(Moran’s I = 0.495, p=0.005; Table 2) and 0.569 (Moran’s I = 0.569,
p=0.005; Table 3), respectively. The Moran’s I index considering the W
Global matrix presented a positive autocorrelation pattern in the first
distance classes, no autocorrelation in the intermediate classes and a
negative autocorrelation in the last few classes (Table 1, Figure 2a).
The GWR’s considering the distance classes of the: i) W Global matrix
displayed a R² between 0.095 and 0.677 (Table 2) and a maximum ∆AIC
equal to 1,782.488 (Table 2, Figure 2a). Considering the relationship
between the Moran’s I index and the AIC (Table 2, Figure 2a) a fourth
distance class was selected as the optimum radius to investigate the
spatial heterogeneity in relationships; ii) W Basin matrix presented
R-squared varying from 0.195 to 0.376 (Table 3) and a maximum ∆AIC equal
to 119.107 (Table 3, Figure 2b), the fourth distance class was also
selected as the optimum radius for the GWR, based on the relationship
between Moran’s I index and AIC (Table 3, Figure 2b); and iii) When
considering the W FEOW matrix (Table 4, Figure 2c), the Moran’s I index
presented positive autocorrelation for the first distance class and an
absence of autocorrelation in classes two to four, reaching negative
values in the following classes and a sinusoid behavior in the last few
classes (Table 4, Figure 2c). W FEOW matrix distance classes presented a
R² varying from 0.180 to 0.250 (Table 4) and a maximum ∆AIC equal to
59.112 (Table 4, Figure 2c), the sixth distance class was selected after
observing the existing relationship between the Moran’s I index and AIC
(Table 4, Figure 2c). The three GWR models selected as the optimum model
in each connectivity matrix do not present spatial autocorrelation in
the selected distance classes (Figure 3).
The comparison between the three best GWR models (according to the
relationship of AIC and Moran’s I index; Table 4) presented a W Global
matrix associated to a radius of 664.053 km as the best way to verify
the spatial heterogeneity present in the relationships (Table 5). The
GWR of the W Global matrix shows an absence of spatial autocorrelation
in all distance classes (Figure 4) as well as presenting a prediction
power of 40% (r² = 0.400; p = 0.000) for observed richness (Figure 5a).
When we consider each of the hydrographic units separately, most basins
show a correlation greater than the global (Amazonian basin, 45.6%, r²
= 0.456, p = 0.000, Figure 5b; Tocantins, 59.4%, r² = 0.594, p = 0.000,
Figure 5d; São Francisco, 72.9%, r² = 0.729, p = 0.000, Figure 5e; east
transect of the Atlantic basin, 59.6%, r² = 0.596, p < 0.001,
Figure 5f; Paraná, 56.8%, r² = 0.568, p = 0.000, Figure 5g; Southeast
transect of the Atlantic basin, 87.3%, r² = 0.873, p = 0.000, Figure
5h) except for the North/Northeast transect of the Atlantic basin, which
presented a prediction pattern of 21.2% (r² = 0.212; p = 0.005; Figure
5c).
The model revealed an absence of stationarity in the relationships
between the ichthyofauna and the tested hypotheses (Water-Energy,
Terrestrial Primary Productivity and Climatic Temporal Heterogeneity;
Figure 6). The GWR showed that stream ichthyofauna richness was mainly
related to annual temperature oscillation (Figure 6a), June’s
evapotranspiration (Figure 6b) and terrestrial primary productivity
(Figure 6c). The average precipitation (Figure 6d), precipitation
variation (Figure 6e) and the evapotranspiration of January (Figure 6f)
show weak relationships with the richness.
The temperature oscillation-fish richness relationship displayed two
gradients: i) from east (positive values) to west (negative values); and
ii) from northwest (negative) to southeast (positive; Figure 6a). The
June’s evapotranspiration also presented a northwest-southeast
(positive) gradient, with neutral relationships in the coastal area,
Amazonian-Tocantins transition and the northwestern extreme of the
Amazonian region (Figure 6b). The terrestrial primary production
displayed the inverse gradient of June’s evapotranspiration, with
positive values in the Amazon basin, north/northeastern transect of the
Atlantic region and the Tocantins region, with neutral values in the
Paraná hydrographic basin, São Francisco and Southeast transect of the
Atlantic region, and negative values in the east and southeast transect
of the Atlantic basin, demonstrating a north-south gradient, where the
northern portion (closer to the equator) is more associated to the
quantity of water (average annual precipitation; Figure 6c). The
precipitation oscillation (Figure 6e) showed positive values in the
Amazon basin and the extreme West of the north/northeast transect on the
Atlantic basin. January’s evapotranspiration (Figure 6f) presented some
positive values in the Amazon and the north/northeast transect of the
Atlantic basin.
Three regions with distinct characteristics were determined by the
analysis: i) the Amazonian region formed by sites located in the central
and the extreme western border of the Amazon basin; ii) the transition
one composed by the sites situated in the eastern border of the Amazon
basin; and iii) the central region formed by sites from the Tocantins,
São Francisco and Paraná River basin (Figure 6). All regions are
organized in a gradient, with the transition region displaying an
absence of fish richness-environmental variables relationship (Figure
6). The Amazonian region presented a negative relationship of fish
richness with the temperature oscillation (Figure 6a) and June’s
evapotranspiration (Figure 6b), and a positive one with terrestrial
primary productivity (Figure 6c), average precipitation (Figure 6d) and
precipitation variation (Figure 6e). The Brazilian central region
presented inverse relationship compared with the Amazonian one, that is,
a positive relationship of the fish richness with temperature
oscillation (Figure 6a) and June’s evapotranspiration (Figure 6b) and a
negative one with terrestrial primary productivity (Figure 6c). The
average precipitation (Figure 6d) presented positive correlation to fish
richness in the Tocantins basin and no correlation in the São Francisco
and Paraná basins. The precipitation variation (Figure 6e) did not
present any relationship with the fish richness in the Brazilian central
region. This suggests that higher fish richness in streams of the
Amazonian region is associated to areas that present constant
temperature and energy input, with abundant rain homogeneously
distributed throughout the year in areas with denser vegetation (greater
terrestrial primary productivity). In contrast, for Brazilian central
region the greatest fish richness is in areas where temperature and
water input are more heterogeneous, with abundant rain and less dense
vegetation (less terrestrial primary production).