<p>We investigate the one-loop renormalization group evolution in four dimensions of the leading operators in the effective field theories of shift-symmetric scalars, photons, and gravitons. We show that certain non-minimal three-point interactions induce a negative running of the corresponding Wilson coefficients, with beta-functions suppressed by the Planck scale. The decrease of the coefficients toward the infrared prompts us to revisit their dispersive bounds, in particular accounting for graviton loops. Gravitational interactions generate positive infrared contributions which, after smearing over the momentum transfer, are argued to dominate over the negative running, provided the number of non-minimally coupled particles is bounded from above according to the species bound.</p>