BUNGO-ONO, Japan—For Yusuke Hashimoto, mayor of this small hamlet in southwestern Japan, desperate times call for desperate measures. The town is one of the country's top producers of shiitake mushrooms, but they are also popular with local deer. And that's the rub.

"Deer are encroaching on farmers' ability to make a living," said Mr. Hashimoto, who has become part of a growing movement to reinstate four-legged carnivores to control the herd.

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