Obesity is linked to prostate cancer, scientists know, but it’s not clear why. On Monday, researchers reported a surprising connection.

When prostate cancers lose a particular gene, they become tiny fat factories, a team at Beth Israel Deaconess Medical Center in Boston reported in a paper published in Nature Genetics.

Then the cancers spread from the prostate, often with deadly effect. Prostate cancers that have not lost that gene also can spread, or metastasize — in mice, at least — but only if they have a ready source of fat from the diet.

That finding suggests that dietary fat can substitute for the loss of the gene, fueling prostate cancer. Moreover, the investigators found, an obesity drug that blocks fat production can make metastatic prostate cancers regress in mice and prevent them from spreading.