Understanding functional trait-environment relationships (TERs) may improve predictions of community assembly. However, many empirical TERs have been weak or lacking conceptual foundation. TERs based on leaf venation networks may better link individuals and communities via hydraulic constraints. We report measurements of vein density, vein radius, and leaf thickness for more than 100 dominant species occurring in ten forest communities spanning a 3,300 m Andes-Amazon elevation gradient in Peru. We use these data to measure the strength of TERs at community scale and to determine whether observed TERs are similar to those predicted by physiological theory. We found strong support for TERs between all traits and temperature, as well weaker support for a predicted TER between maximum abundance-weighted leaf transpiration rate and maximum potential evapotranspiration. These results provide one approach for developing a more mechanistic trait-based community assembly theory.