The badger is chubby but strong, with short legs, a long body and endearingly goofy gait. It has become a cultural icon to children who grew up reading “The Wind in the Willows,” or more recently, “Harry Potter,” in which the badger is the symbol of the Hufflepuffs. Once tortured by dogs in a blood sport called badger baiting, it is now a protected species in Britain.

But the beloved creatures also carry bovine tuberculosis, a disease that has killed hundreds of thousands of cows across Britain since at least the 1970s. For that reason, the omnivorous mustelids have been targeted in bloody culls to control the disease’s spread.

In some instances the effort worked; in others, it didn’t. All along, Britons who love badgers have questioned the effectiveness and necessity of the culls.

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In a new study, researchers simulated different badger-culling scenarios, and discovered that culling can help reduce the spread of wildlife disease. But to work, the efforts must fall within a “Goldilocks zone,” wherein the number of animals killed, the ground covered and the duration of the cull all must be just right. The study’s results, published in Journal of the Royal Society Interface on Tuesday, help explain some of the mystery over the varied effectiveness of the culls, which has driven decades of dispute in Britain. The results also provide a framework for understanding culling efforts to stop the spread of wildlife diseases in other animals, and suggest that on-the-ground realities often make a successful cull unattainable.