The zone of polarizing activity (ZPA) in the posterior limb bud produces Sonic Hedgehog (Shh) protein, which plays a critical role in establishing distinct fates along the anterior-posterior axis. This activity has been modeled as a concentration-dependent response to a diffusible morphogen. Using recombinase base mapping in the mouse, we determine the ultimate fate of the Shh-producing cells. Strikingly, the descendants of the Shh-producing cells encompass all cells in the two most posterior digits and also contribute to the middle digit. Our analysis suggests that, while specification of the anterior digits depends upon differential concentrations of Shh, the length of time of exposure to Shh is critical in the specification of the differences between the most posterior digits. Genetic studies of the effects of limiting accessibility of Shh within the limb support this model, in which the effect of the Shh morphogen is dictated by a temporal as well as a spatial gradient.