The 20,000 ephemeral ponds, the playas of the southern high plains of the United States, were thought to have experienced a prolonged drought ending approximately 5000 years ago, during which amphibians and other aquatic residents would have died out. A few permanent ponds are conjectured to be the source of repopulation of the entire region since then. We develop a series of mathematical models based on the tiger salamander, Ambystoma tigrinum, on rainfall data, and on field data, to test this hypothesis. We show that, under reasonable assumptions, the region could have been repopulated through migration within this time frame.