The relation between the trace and R-current anomalies in supersymmetric theories implies that the U(1)(R)F-1, U(1)(R), and U(1)(R)(3) anomalies which are matched in studies of N=1 Seiberg duality satisfy positivity constraints. Some constraints are rigorous and others conjectured as four-dimensional generalizations of the Zamolodchikov c theorem. These constraints are tested in a large number of N=1 supersymmetric gauge theories in the non-Abelian Coulomb phase, and they are satisfied in all renormalizable models with unique anomaly-free R current, including those with accidental symmetry. Most striking is the fact that the flow of the Euler anomaly coefficient a(UV)-a(IR) is always positive, as conjectured by Cardy.