When it comes to memory loss and dementia, your genes play a powerful role. But as new research shows, what you eat—and how your body processes that food—can make a surprising difference, even for people with the highest inherited risk.

A study using data from more than 5,700 people gathered over 34 years found that the participants who stuck to the Mediterranean diet were less likely to wind up with dementia. But the biggest benefit cropped up in the people who had the highest genetic risk for Alzheimer’s disease—those with two copies of the apolipoprotein E4 (APOE4) variant.