In order to test the hypothesis that seismic anisotropy in the lowermost mantle is caused by the development of a post-perovskite lattice preferred orientation, and that anisotropy can thus be used as a probe of the dynamics of the mantle's lower boundary layer, an integrated model of texture generation in D″ is developed. This is used to predict the elastic anisotropy of the lowermost mantle as probed by global anisotropic tomographic inversions. The model combines the current 3D mantle flow field with simulations of the deformation of post-perovskite polycrystalline aggregates. Different descriptions of single crystal plasticity can lead to model results which are anti-correlated to each other. In models where post-perovskite deformation is accommodated by dislocations moving on (010) or (100), patterns of anisotropy are approximately correlated with the results of tomographic inversions. On the other hand, in models where dislocations move on (001) patterns of anisotropy are nearly anti-correlated with tomographic inversions. If all the seismic anisotropy in D″ extracted from global anisotropic inversions is due to the presence of a lattice preferred orientation in post-perovskite in the lowermost mantle, and if the results of the tomographic inversions are not strongly biased by the sampling geometries, these results suggest that, in contrast to ideas based on the 1D anisotropic signal, deformation of post-perovskite in the lowermost mantle may be accommodated by dislocations moving on (010) or (100). Alternatively, a significant portion of the anisotropic signal may be caused by mechanisms other than the alignment of post-perovskite crystals.