There is research that if you do not keep your insulin levels low enough that your body can access your fat stores, than your body will respond to calorie restriction by reducing your metabolic rate. – (See Biggest Loser research).
So to me the issue of strategy revolves around how long a period of cal counting when not in ketosis will the body tolerate before reducing metabolic rate. – I haven’t seen any research on this topic. – So my view is that if someone will loose enough weight in an single round of 8 weeks of eating 800 calories to make it possible to move on to 5:2 afterwards, then Dr MM has effectively sanctioned this as being a workable option and there is no evidence that he is incorrect.
But for those who have enough weight to loose that they ask the advice of members of the forum about repeated rounds we should advise them to play safe and ensure they are in ketosis if they are going to eat 800 calories a day.
If you consider the example of the Biggest Loser, people were evicted each week and even the winners were only on the show for 30 weeks. The majority of participants regained more weight than they lost, Dr Fung points to research that their metabolic rates dropped by 600 calories a day. – I have just come across a different piece of research that says it was 500 calories a day, but that there were some people who did not regain weight but only by maintaining higher levels of exercise. https://www.today.com/health/new-study-biggest-loser-contestants-finds-exercise-not-diet-key-t118250
The other issue is about adaption to eating patterns such as one meal a day. – That is something Dr Fung talks about. I wonder if the issue is again that without either the personal resolve to stay under 20g of carbs or using some mechanism to monitor so you remain in ketosis having one meal a day causes a spike in insulin which is enough to push your body into reducing metabolic rate. Whereas if you fast for 36 hours 3 times a week and then eat without counting calories between each fast you have a long enough period low insulin so that you enter ketosis, and at the same time have periods of refeeding so the body is not triggered into reducing metabolic rate. – If you are having no cals one day, and two meals the next then you will be probably averaging less than 800 calories a day, and Dr Fung says it isn’t important to eat low carb (but it is easier to fast).
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I recently posted a link on the take a look at this thread about a podcast by Dr Bikman, where he explained how burning ketones increases metabolic rate, because it encourages fat cells to be decoupled and burn extra fuel that you may find interesting.