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Polycrystalline (Mg_0.9,Fe_0.1)SiO₃ post-perovskite was plastically deformed in the diamond anvil cell between 145 and 157 gigapascals. The lattice-preferred orientations obtained in the sample suggest that slip on planes near (100) and (110) dominate plastic deformation under these conditions. Assuming similar behavior at lower mantle conditions, we simulated plastic strains and the contribution of post-perovskite to anisotropy in the D″ region at the Earth core-mantle boundary using numerical convection and viscoplastic polycrystal plasticity models. We find a significant depth dependence of the anisotropy that only develops near and beyond the turning point of a downwelling slab. Our calculated anisotropies are strongly dependent on the choice of elastic moduli and remain hard to reconcile with seismic observations.