Hypothesized feedbacks between climate and tectonics are mediated by the relationship between topography and long-term erosion rates. While many studies show monotonic relationships between channel steepness and erosion rates, the degree of nonlinearity in this relationship is geographically variable. There is a critical need to mechanistically explain controls on this relationship in natural settings because highly nonlinear relationships imply low sensitivity between climate and tectonics. To this end, we present a carefully coordinated analysis of cosmogenic 10Be concentrations in river sands paired with topographic, hydro-climatic, and tectonic data for the Greater Caucasus Mountains where topography is invariant along-strike despite large gradients in modern precipitation and convergence rates. We show that spatial patterns in erosion rates largely reflect regional tectonics with little influence from mean precipitation or runoff. The nonlinearity in the erosion rate – steepness relationship to arises from very low runoff variability characteristic of snowmelt hydrology. Transitioning from rainfall- to snowmelt-driven runoff as mean elevation increases is common to many mid-latitude mountain ranges and the associated decrease in runoff variability may represent important, unrecognized dynamics inhibiting the sensitivity of tectonics to climate more broadly.