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In 2004, Stephen Spindler won the first Methuselah Foundation MPrize (the Methuselah Mouse prize) for rejuvenation based on research into the idea that by restricting calories (not nutrition), you can extend a life.
The study applied CR to a group of mice that were aged 19 months. Within two months, the mean time to death started increasing (the mice died off slower than normal). By the end of the experiment, it was showed that the average mouse lifespan had been increased by 42%. For a mouse, that's 4.7 months. The mouse was a special breed that was known to have an average lifespan of exactly 1000 days. The oldest mouse in the trial died six months later than a non-CR mouse would be expected to die. CR delayed the onset of tumours until much later than in the control mice, which may partly explain the effect.
The equivalent in human terms of that mouse life extension is an increase of about 10 years.
It's important to note that calorie restriction is not the same as eating less. Your food is much more than just calories. If restricting calories, you need to make sure that your nutrition stays correct.
Human trials have been undertaken a few times since then. We live much longer than mice, though, so it’s hard to measure the longevity benefits, but a two year test of CR showed a marked decrease in tumour incidence, which is similar to what we see in mice. The 2015 report by the Gerontological Society of America concluded that CR was a tool worth using for non-obese humans.
In 2017, a review of the current literature concluded that properly nutritional calorie restriction in humans promotes metabolic an d molecular health in humans, age-associated biomarkers (signs of aging) in humans were reduced, and there were no adverse effects noted on quality of life or eating behaviour.