I keep trying to write the same post, over and over, so I'm just going to spit out a short dense version and get it over with.
Those who live long healthy lives tend not to have excess amounts of body fat, nor continuously high blood sugar.
Fasting causes one to deplete one's stores of sugars and burn stored fat. It obviously is not a sustainable practice.
Intermittent fasting, eating every other day, tends to have the same effect as continued fasting, as one cannot compensate for the deficits by gorging.
Diets with low amounts of carbohydrate attempt to mimic starvation.
The most recent fad is intermittent low-carbohydrate (e.g. here), attempts to mimic intermittent fasting.
Except in unusual circumstances, running depends upon utilizing fat and sugar.
High mileage training causes the body to keep blood sugar low by frequent depletion and body fat gets lowered because of the difficulty of eating enough to maintain stores.
Long runs burn a large number of calories that are not easy to replenish in a short time, lowering fat stores.
Anaerobic running burns only sugars.
A fast run will deplete stored sugars which are difficult to restore in one day, so they should not be attempted more than every-other day.
In short, one can accomplish the same things by exercise that people attempt with fad diets: Exercise frequently. Occasionally exercise for a much longer time than average. Sometimes exercise anaerobically, but no more than every-other day.
But you already knew that. It's common sense.