[1] Recent efforts to empirically measure and numerically simulate biogenic ocean mixing have consistently observed low mixing efficiency. This suggests that the buoyancy flux achieved by swimming animals in the ocean may be negligible in spite of the observed large kinetic energy dissipation rates. The present letter suggests that vertical migration across isopycnals may be necessary in order to generate overturning and subsequent mixing at length scales significantly larger than the individual animals. The animal-fluid interactions are simulated here using a simplified potential flow model of solid spheres migrating vertically in a stably stratified fluid. The interaction of successive solid bodies with each parcel of fluid is shown to lead, under certain conditions, to vertical displacement of the fluid parcels over distances much larger than the individual body size. These regions of displaced fluid are unstably stratified and, hence, amenable to large-scale overturning and efficient mixing.