Diversity gradients are observed in various groups of organisms. For fishes in streams, the Water-Energy, Productivity and Temporal Heterogeneity hypotheses are considered the best combination to explain richness patterns. The relationship between species diversity and the variables that represent the hypotheses are generally considered linear and stationary, that is, there is equal relation of cause and effect along an entire geographical extension. The assumption of stationarity has not been tested or even observed in diversity gradients, thus producing imprecise models. Therefore, our goal is to quantify stationarity in the existing relationships between the ichthyofauna of streams and the Water-Energy, Productivity and Temporal Heterogeneity hypotheses using a Geographically Weighted Regression – GWR. In the proposed model, there is conspicuous absence of stationarity between fish species richness and the tested hypotheses. Furthermore, water-energy dynamics were observed as a possible metabolic restriction mechanism acting on the community structuring of stream fishes. This mechanism divides the fish fauna from the studied Brazilian watercourses in two regions: i) Amazonian, characterized by a stable climate and populations with little resistance to thermal variation; and ii) Central, featured by greater ranges of temperature and fish populations resistant to thermal variation.