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Mules are of such ancient origin in the Middle East that their exact beginnings are murky.
Strictly speaking, a mule is the offspring of a male ass, or jackass, and a female horse, or mare. They are an example of hybrid vigor, or heterosis, an increase in size and strength resulting from a mixing of species. The same phenomenon appears in plants, and hybrid plants are often sterile, too. And one male foal produced by breeding a mare mule and a stallion was later able to sire some colts. The same mare mule foaled a female fathered by a jackass, but this female never produced any offspring.