: Does BMR adjust and decrease in response to calorie restriction diets? Is it possible for your Basal Metabolic Rate (BMR) to adjust in response to dieting for long periods of time? If this does happen how much can it go down?

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Yes it can. As a general statement, I'm not sure how much it can go down before it's a problem, which is what I think you are asking as your second question. Starving to death might be seen as this taking the BMR close to zero (though I don't think you would get to zero before death).

I think a good reference for this is Peter Emery's review article "Metabolic changes in malnutrition." There may be more appropriate references when concerning elective reductions in caloric intake, but I suspect the results are similar on a smaller scale.

There are a few sections of the review that are worth quoting and discussing here:

First the general trend and cause:

The basal metabolic rate actually increases during the first few days
of starvation, under the influence of catecholamines that are secreted
in response to decreasing blood glucose concentrations. This
probably reflects the high rate of gluconeogenesis that occurs at this
time. As fasting progresses, however, metabolic rate decreases as free
T3 and catecholamine levels decrease and the rate of gluconeogenesis
decreases.

In essence, when you first start to fast (the references [1,2] that the review sites are from 1-4 days in this section) the body looks to other sources of energy (gluconeogenesis). That is not sustainable over time, and then the BMR begins to drop. How it begins to drop is largely through the lost of lean tissue, with a focus on muscle mass, which is probably a good evolutionary choice over more important systems such as the brain:

The response to a less severe degree of food restriction can also be
seen as a series of adaptive processes with the same priorities, that
is to maintain the supply of glucose to the brain and to minimise the
loss of lean tissue. Basal metabolic rate decreases to minimise the
negative energy balance. This is achieved partly by loss of
metabolically active tissue, but there is also some evidence that the
efficiency of energy metabolism increases leading to a decrease in
energy expenditure per unit cell mass.

Again, the referenced review article is also worth a read, especially as it deals with otherwise healthy individuals and people "dieting" in the common sense of the word (but in no means the medical). Again body composition and physical activity take a leading role here, but changes in efficiency are certainly noted if not understood. A conclusion reached on efficiency calculation (ibid) is also worth quoting:

It would thus appear that the generally used indicator of metabolic
efficiency in humans, that is a reduced oxygen consumption per unit
fat free mass, is fraught with problems since it does not account for
variations in contributions from sub-compartments of the fat free mass
which include those with high metabolism at rest such as brain and
viscera and those with low metabolism at rest such as muscle mass.

When in your life span you start on your low caloric diet can effect the outcome of the diet. A commonly understood example is a shorter stature/smaller skeletal frame will develop under limited nutritional intake. It's probably worth noting that on an evolutionary scale, having too many calories is an exceedingly new problem. In other words, even if we wouldn't see it as preferential in the developed world today, it is probably an adaptive response to lose lean body mass or not develop additional skeletal structure (with goals of efficiency).

I will end returning Dr. Emery's coverage of the same topic:

The main response in chronically malnourished populations is slow
growth rate, delayed maturity, and small adult stature. Small stature
can be seen as a successful adaptation to low-energy intake because
overall basal metabolic rate will be low. However, when metabolic rate
is adjusted for fat-free mass there is no significant difference
between those who are most malnourished and those who are well
nourished. The reason for this is that the main deficit in lean
tissue mass is in muscle, which has a relatively low metabolic rate,
while the size of the visceral organs, which are much more
metabolically active, is much less affected. Hence these changes in
body composition may cancel out any increase in the efficiency of
cellular metabolism.

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First of all, the 1000-2500 calorie statement from the answer to this question is not due to formula inaccuracies (only 0.5% of the variation were attributed to that), but is the actual measured BMR in a study within Scottish population.

Second, we know from the above mentioned question in SE that the BMR is dependent, amongst others, of fat-free body mass (FFM), i.e. muscle mass. In the forementioned study, 63% of BMR variation could be attributed to variations in FFM. And we also know that diets can lead to a loss of this mass, if they aren't overcompensated by exercise; thus the logical deduction can be made that a diet can lead to BMR decrease, if it's not compensated for, e.g. by exercise or high-protein-intake diets.

I couldn't find any other evidence on direct changes to BMR by a diet, so this connection (diet - FFM decrease - BMR decrease) may just be it for now.