PREDIMED diet from Spain is the Mediterranean diet that is evidence based

Do you lose weight on Mediterranean Diet? link

"A total of 7,447 persons in Spain were randomized to either
1- a Mediterranean diet with increased extra virgin olive oil,
 2-a Mediterranean diet with increased nut intake, or 
3-a control diet where the participants received low fat diet advice. 

The high extra virgin olive oil group ingested an average of
 3.6 tablespoons/day (51 grams/day equal to 459 calories/day) 
of olive oil with 98% of it being extra virgin olive oil. 

The high nut group ate 8.2% of their total daily calories in the form of nuts, including an additional approximately one ounce packet of nuts (15g of walnuts, 7.5 g of almonds, and 7.5g of hazelnuts) provided by the study coordinators. "