Motivated by the physical picture of shape-dependent air resistance and, consequently, shape-induced differential sedimentation of dust particles, we searched for and found evidence of dust particle asphericity affecting the evolution and distribution of dust-scattered light depolarization ratio (d). Specifically, we examined a large data set of Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) observations of Saharan dust from June to August 2007. Observing along a typical transatlantic dust track, we find that (1) median d is uniformly distributed between 2 and 5 km altitudes as the elevated dust leaves the west coast of Africa, thereby indicating uniformly random mixing of particle shapes with height; (2) vertical homogeneity of median d breaks down during the westward transport: between 2 and 5 km d increases with altitude and this increase becomes more pronounced with westward progress; (3) d tends to increase at higher altitude (>4 km) and decrease at lower altitude (<4 km) during the westward transport. All these features are captured qualitatively by a minimal model (two shapes only), suggesting that shape-induced differential settling and consequent sorting indeed contribute significantly to the observed temporal evolution and vertical stratification of dust properties. By implicating particle shape as a likely cause of gravitational sorting, these results will affect the estimates of radiative transfer through Saharan dust layers.