Now researchers from Hungary and Sweden claim to have solved the mystery.
The stripes, they say, came about to keep away blood-sucking flies.
They report in the Journal of Experimental Biology that this pattern of narrow stripes makes zebras "unattractive" to the flies.
They key to this effect is in how the striped patterns reflect light.
"We started off studying horses with black, brown or white coats," explained Susanne Akesson from Lund University, a member of the international research team that carried out the study.
"We found that in the black and brown horses, we get horizontally polarised light." This effect made the dark-coloured horses very attractive to flies.
It means that the light that bounces off the horse's dark coat - and travels in waves to the eyes of a hungry fly - moves along a horizontal plane, like a snake slithering along with its body flat to the floor.
Dr Akesson and her colleagues found that horseflies, or tabanids, were very attracted by these "flat" waves of light.
"From a white coat, you get unpolarised light [reflected]," she explained. Unpolarised light waves travel along any and every plane, and are much less attractive to flies. As a result, white-coated horses are much less troubled by horseflies than their dark-coloured relatives.
Having discovered the flies' preference for dark coats, the team then became interested in zebras. They wanted to know what kind of light would bounce off the striped body of a zebra, and how this would affect the biting flies that are a horse's most irritating enemy.
To continue reading click - Zebra stripes evolved to keep biting flies at bay. by Victoria Gill Science reporter, BBC Nature
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