Vegetation is the most common and most reliable stabilizer of loose soil or sand. This ancient technique is for the first time cast into a set of equations of motion describing the competition between aeolian sand transport and vegetation growth. Our set of equations is then applied to study quantitatively the transition between barchans and parabolic dunes driven by the dimensionless fixation index theta which is the ratio between the dune characteristic erosion rate and vegetation growth velocity. We find a fixation index theta(c) below which the dunes are stabilized, characterized by scaling laws.
