http://www.mdpi.com/2072-6643/9/8/822/htm
conclusion:
In conclusion, the findings of the present review indicate that of all the current popular diets, the Atkins Diet was tested in the greatest number of clinical trials and had the most evidence in producing clinically meaningful short-term (≤six months) and long-term (≥one year) weight loss. There was limited evidence supporting the effectiveness of other popular diets in producing clinically meaning short- and long-term weight loss.
I came across this paper in this presentation by the lead author of the above paper.
Steve Anton - Lifestyle Interventions to Preserve Function During Aging
From the same presentation I learned of this interesting paper
Flipping the Metabolic Switch: Understanding and Applying the Health Benefits of Fasting