The paper, "Constrained Total Energy Expenditure and Metabolic Adaptation to Physical Activity in Adult Humans", aimed to explore why it is that exercise's impact on energy expenditure doesn't appear to be linearly "additive" - meaning that studies on energy expenditure suggest that increases in exercise, don't come with a comparable increase in total daily calories burned. In part this is because with increasing exercise comes increasing exercise efficiency, but the remainder is less clear. Is there an "exercise" thermostat in our bodies that effectively dials down our activity levels outside of our workouts whereby if you workout hard in the gym in the morning you'll sit more and fidget less for the rest of the day?
Here the authors put forward their theory of "Constrained Total Energy Expenditure" to explain the phenomenon I've covered here a few times - that objectively measured energy expenditures don't seem to vary much the world over. From the first world to the third world, as a species we seem to share the same total daily energy expenditures each and every day. This fits with the authors' constrained hypothesis.
To test their constrained model they objectively evaluated energy expenditures, in 332, mixed-sex, adults drawn from Ghana, South Africa, Seychelles, Jamaica, and the United States. The measures they tracked were total energy expenditure by way of doubly labeled water method, resting metabolic rate by way of respirometry, and physical activity by way of wearable tri-axial accelerometers.
What they sought to learn was which model would be best represented by the subjects' objective measurements - additive or constrained? If additive you'd expect a linear increase in energy expenditure with activity. If constrained you'd expect adaptations to blunt increasing energy expenditure even as activity levels rose.
Also worth noting, the authors point out that regardless of which model you choose to believe in, their findings had physical activity accounting for only 7%–9% of the variation in total energy expenditure after controlling for anthropometric variables and population location. Translated this means that when it comes to energy balance, what you eat matters a hell of a lot more than how much you exercise regardless of how exercise contributes to energy balance. It also means that you're not likely to be able to outrun your forks.
Of course you shouldn't take this as a license not to exercise, as exercise is probably the single most important modifiable determinant of your health. Putting this another way, you lose weight in the kitchen, you gain health in the gym.
(Below is my keynote presentation for PHE Canada where I make the case for rebranding exercise)