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Let's say someone lives at sea level and then stays at an altitude of 2'500 m for three weeks. Her body will adapt by increasing the amount of red blood cells. In the end, her stamina will be as good as it was at sea level (given comparable amount of exercise etc.).

When returning back to sea level, will she have increased stamina for a while?

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    Are you certain her stamina will be as good as it was at sea level? Can you clarify why you say that? Your question is based on some potentially dangerous presuppositions. – anongoodnurse Sep 30 '15 at 2:32
  • @anongoodnurse While some of those assumptions are flawed, "Are you certain that she will not die of acute mountain sickness on going from sea level to 2500 m" is orthogonal to the question. If it isn't, we have to make sure every question on here includes the caveat that you don't otherwise die from falling space debris. – Fomite Oct 1 '15 at 0:38
  • @Fomite - you're absolutely correct. I'll correct that. – anongoodnurse Oct 1 '15 at 1:42
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I could not find a report where this has been formally studied but it is highly likely that persons coming to plains after staying at high altitude will feel more energetic, for a few days at least. This is even used by many sports organizations. Quoting from "Human Biological Adaptability: Adapting to High Altitude":

On returning to sea level after successful acclimatization to high altitude, the body usually has more red blood cells and greater lung expansion capability than needed. Since this provides athletes in endurance sports with a competitive advantage, the U.S. maintains an Olympic training center in the mountains of Colorado. Several other nations also train their athletes at high altitude for this reason. However, the physiological changes that result in increased fitness are short term at low altitude. In a matter of weeks, the body returns to a normal fitness level.

Following figure accompanies above description:

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A number of factors may be responsible for this:

  • Increased hemoglobin level stimulated by lower oxygen level in air at high altitude

  • Bartsch & Gibbs (http://circ.ahajournals.org/content/116/19/2191.full) have documented a number of changes in the body that occur on high altitudes exposure from 1 to several days or weeks as in tourists or trekkers. These changes indicate that several systems (especially heart, lungs, muscles and other tissues) are under stress. There are many other reports also documenting these changes. The relief of this stress on returning to plains will give a sense of greater energy and stamina.

  • The paths in hilly areas are commonly going up and down and it is more exertional than moving around in the plains. Hence, a stay at high altitude often builds exercise capacity. It is like gentle trekking most of the time.

  • Hilly areas generally have lesser pollution than cities in the plains.

  • The temeperature and humidity conditions are generally more pleasant in hilly areas.

  • Psychological factors including relief from anxiety and stress of routine life. It is like one feels rejuvenated after having been on a holiday.

Because of above factors one may feel better stamina, at least for some time, after returning from a sojourn at high altitude.

You may also be interested in my answer on how to avoid acute mountain sickness and its complications (Avoiding acute mountain sickness, high altitude pulmonary & cerebral edema).

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I am going to answer this purely anecdotally based on personal experience having lived in Boston, but spending winter holidays in Colorado, ranging in altitude from ~5000 to 9000 ft.

Assuming our hypothetical persons conditioning remains the same, yes, they'll have a short period of time when they return to sea level when they've got greater stamina due to greater oxygenation. It's a particularly pleasant sensation - for example, I was able to sprint up the large hill that separated the lower and upper part of my campus, while this was manifestly not possible in my "normal" shape.

That being said, it tapers off quickly.

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