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).