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At first glance, higher altitudes equal lower temperatures, which would likely slow down cellular metabolism. However, while backpacking in New Mexico in ~90 degree weather, I experienced the same thing -- the flies were slow enough I was able to catch them easily in my hand, as well as with chopsticks.

Is this related to air density? Why are these flies so much slower to react and move about in the mountains.

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The atmospheric density may not be the only factor, but from a physics standpoint, flying animals should in general move more slowly at high altitude.

As an example, New Mexico's Wheeler Peak is at an altitude of ~4 km above sea level. For a back-of-the-envelope air density calculation, a good estimate of scale height is 10 km, i.e. $\rho(h) = \rho_{sea}*e^{-h/10km}$ , which means the air density at Wheeler Peak is about $2/3$ the density at sea level (other air conditions being equal).
For wing-flapping animals, the power required to maintain flight is inversely proportional to the air density. I'm not confident about how flies' wing movements would be affected (this is where an entomologist should step in), but in any case their air speed should be reduced at high altitude.

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It may be influenced by inter-species differentiation in characteristics. Were the flies larger or smaller than other flies? If there were flies of different sizes present in the same location and under the same temperatures, how did their relative speeds compare?

To know the species of fly which one is examining is quite difficult. It can come down to counting hairs on the fly's body under a microscope--literally. But some species may simply have different habits when compared to another species.

Mosquitoes are in the same order as flies (Diptera), and in Southeast Asia there are many species of mosquitoes. Some make a noise or hum while flying; some fly silently. Some are quite fast; others are much slower to take off, making them easier to slap. Some have an uncanny ability to sneak in and bite while one is otherwise occupied/absorbed in something, while others seem too eager and land in plain sight while one is watching. Some are larger, with more painful bites; others are smaller and their bites itch longer after their deed has been done.

A consideration of these simple variables leads to the obvious conclusion that more information about the flies in question might be needed before a determination could be made as to why they seem slower.

Air densities might be a factor, in addition to gravitational forces. I'm not knowledgeable about the relative impact of thinner air versus the amount of gravity to be overcome in flight, but I know large jet airplanes fly faster and with less drag (resistance) at higher altitudes, making high-altitude flight more efficient.

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