Modern horses, zebras, and asses belong to the genus Equus, the only surviving genus in a once diverse family, the Equidae. Based on fossil records, the genus appears to have originated in North America about 4 million years ago and spread to Eurasia (presumably by crossing the Bering land bridge) 2 to 3 million years ago. Following that original emigration, there were additional westward migrations to Asia and return migrations back to North America, as well as several extinctions of Equus species in North America.
The last prehistoric North American horses died out between 13,000 and 11,000 years ago, at the end of the Pleistocene, but by then Equus had spread to Asia, Europe, and Africa.
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Thanks. The article goes on to make a solid case that our Western wild horses should be considered native, not feral. Of course that has broad wildlife management policy implications.