We study systematically the relationship between olivine lattice preferred orientation and the mantle flow field that produces it, using the plastic flow/recrystallization model of Kaminski and Ribe <2001>. In this model, a polycrystal responds to an imposed deformation rate tensor by simultaneous intracrystalline slip and dynamic recrystallization, by nucleation and grain boundary migration. Numerical solutions for the mean orientation of the a axes of an initially isotropic aggregate deformed uniformly with a characteristic strain rate $dot{epsilon}$ show that the lattice preferred orientation evolves in three stages: (1) for small times $t leq 0.2 dot{epsilon}^{-1}$, recrystallization is not yet active and the average a axis follows the long axis of the finite strain ellipsoid; (2) for intermediate times $0.2 dot{epsilon}^{-1} leq t leq 1.0 dot{epsilon}^{-1}$, the fabric is controlled by grain boundary migration and the average a axis rotates toward the orientation corresponding to the maximum resolved shear stress on the softest slip system; (3) for $1.0 dot{epsilon}^{-1} leq t leq 3.0 dot{epsilon}^{-1}$, the fabric is controlled by plastic deformation and average a axis rotates toward the orientation of the long axis of the finite strain ellipsoid corresponding to an infinite deformation (the infinite strain axis.) In more realistic nonuniform flows, lattice preferred orientation evolution depends on a dimensionless grain orientation lag parameter Π(x), defined locally as the ratio of the intrinsic lattice preferred orientation adjustment timescale to the timescale for changes of the infinite strain axis along path lines in the flow. Explicit numerical calculation of the lattice preferred orientation evolution in simple fluid dynamical models for ridges and for plume-ridge interaction shows that the average a axis aligns with the flow direction only in those parts of the flow field where Π ≪ 1. Calculation of Π provides a simple way to evaluate the likely distribution of lattice preferred orientation in a candidate flow field at low numerical cost.