  Outward migration of low-mass planets has recently been shown to be a
possibility in non-barotropic disks. We examine the consequences of this result
in evolutionary models of protoplanetary disks. Planet migration occurs towards
equilibrium radii with zero torque. These radii themselves migrate inwards
because of viscous accretion and photoevaporation. We show that as the surface
density and temperature fall, the planet orbital migration and disk depletion
timescales eventually become comparable, with the precise timing depending on
the mass of the planet. When this occurs, the planet decouples from the
equilibrium radius. At this time, however, the gas surface density is already
too low to drive substantial further migration. A higher mass planet, of 10
Earth masses, can open a gap during the late evolution of the disk, and stops
migrating. Low mass planets, with 1 or 0.1 Earth masses, released beyond 1 AU
in our models, avoid migrating into the star. Our results provide support for
the reduced migration rates adopted in recent planet population synthesis
models.
