The interpretation of seismic anisotropy in the mantle requires a knowledge of the relationship between the lattice preferred orientation (LPO) of crystals and the convective flow field. In order better to understand this link, we present a model for the evolution of LPO in olivine aggregates that deform by both intracrystalline slip and dynamic recrystallization. Dynamic recrystallization depends on the dislocation density of the grains, which is a function of the applied local stress. Grains with a large density of dislocations lower their bulk strain energy by nucleating strain-free sub-grains at a rate proportional to a dimensionless nucleation parameter λ*. Grains with high energy are then invaded by grains with low energy by grain-boundary migration, at a rate proportional to a dimensionless grain-boundary mobility M*. The value of λ* is constrained by observed LPO patterns in experimentally deformed olivine aggregates, and M* is constrained by the temporal evolution of the strength of the LPO. For M*=125±75 and λ*>3, the model predictions agree well with the experimental results. Numerical calculations of LPO using our model are significantly faster than those based on viscoplastic self-consistent or equilibrium-based theories, making the model especially suitable for applications for complex convective flows.