The transport and mixing properties of the isentropic flow in the lower and middle stratosphere are analyzed by using observed winds to advect a tracer on isentropic surfaces in the range 400--850 K. The effective diffusivity diagnostic introduced by Nakamura and collaborators is applied to the tracer field in order to identify barriers to transport and mixing regions, and to follow their seasonal evolution. Large effective diffusivity corresponds to strong mixing, and small effective diffusivity corresponds to weak mixing, i.e., to barriers. The effective diffusivity shows, in the winter stratosphere of each hemisphere, the evolution of the vortex-edge barrier and the midlatitude surf zone, and also the extent of any mixing within the vortex. At low latitudes in the stratosphere there is a region of low effective diffusivity whose latitudinal width varies with height, broadening substantially from 400 K to 550 K. The low values of effective diffusivity in this tropical-reservoir region imply little isentropic transport into or out of it. There is a strong seasonal cycle to the reservoir, which has different forms at 400 K, 450--600 K, and above 650 K, determined by the relative influences of tropospheric synoptic eddies and stratospheric planetary waves. Comparison of effective diffusivity between the Northern Hemisphere winters 1996/1997 and 1997/1998 shows strong differences at low latitudes according to the phase of the quasi-biennial oscillation (QBO). When there are QBO easterlies, there is a broad region of very low effective diffusivity at low latitudes. When there are QBO westerlies, there are very low values of effective diffusivity at low latitudes within the westerlies themselves but larger values at their edges. ¿ 2000 American Geophysical Union