How a single dog manages to help shepherds herd a flock of sheep so efficiently has been a mystery for many years but researchers have apparently finally solved this puzzle.

In a study published in the Journal of the Royal Society Interface on Aug. 27, Daniel Strömbom, from the Department of Mathematics of the Uppsala University in Sweden, and colleagues used GPS data to unravel the mathematical secrets behind how sheepdogs are able to control an unruly flock of over 100 sheep.

Strömbom and colleagues fitted GPS tracking device to a trained sheepdog and on a flock of 46 sheep and then used the GPS data to come up with a computer model of what prompts the dog to move and how the animal responds.

It appears that sheepdogs do their job efficiently by following two simple rules. The first causes the dog to close any gap that it sees when herding the flock. Sheepdogs, in fact, do not actually see the sheep but the gaps between them. When these gaps get too big, the dog weaves them from side to side forcing the sheep to pack closer together. The second rule results in the dog pushing the sheep forward once they are closely packed.

"At every step in the model, the dog decides if the herd is cohesive enough or not," Strömbom explained. "If not cohesive, it will make it cohesive, but if it's already cohesive, the dog will push the herd towards the target."

Study researcher Andrew King, from the Department of Biosciences of the Swansea University in the U.K said that sheepdogs utilize the "selfish herd theory". He said that sheep work with their neighbors when responding to threats.

"It's the selfish herd theory: put something between the threat and you," King said. "Individuals try to minimize the chance of anything happening to them, so they move towards the center of a group."

The researchers said that knowledge of how sheepdogs control a group of sheep can have several applications. Robots, for instance, could be programmed using the same algorithm to control crowds, herd livestock and even clean up the environment albeit some farmers are skeptical about replacing sheepdogs with robots when it comes to herding sheep.

"Our algorithm reproduces key features of empirical data collected from sheep-dog interactions and suggests new ways in which robots can be designed to influence movements of living and artificial agents," the researchers wrote.