High altitude: an exploration of human adaptation

Natural selection, a fundamental concept in evolutionary biology, is the mechanism by which evolution is driven, favoring organisms that are best adapted to their environments. This process enhances their chances of survival and reproduction. Adaptation, a key outcome of this process, involves genetic modifications that optimize an organism's functionality under specific environmental challenges, such as extreme cold or thinner air at high altitudes.
Beyond physical adaptations, psychological...

Respiration is a crucial physiological function involving exchanging oxygen (O2) and carbon dioxide (CO2) between an organism and its environment. Various factors can impact this essential process:

The Earth and its atmosphere have provided humans with air, water, and food, but these are not the only requirements for survival. Humans also require a specific range of temperature and pressure that the Earth and its atmosphere provides.
Oxygen
Atmospheric air is only about 20 percent oxygen, but that oxygen is a key component of the chemical reactions that keep the body alive, including the reactions that produce ATP. Brain cells are susceptible to a lack of oxygen because they require a...

Animal organs and organ systems constantly adjust to internal and external changes through a process called homeostasis ("steady state"). Examples of these changes include regulation of the level of glucose or calcium in the blood or internal responses to external temperatures. Homeostasis requires  maintaining an internal dynamic equilibrium:

Hypertrophy is the increase in the size of individual cells, resulting in the enlargement of a tissue or organ. Unlike hyperplasia, which involves an increase in cell number, hypertrophy is characterized by an increase in cell volume. This process often occurs in response to higher functional demand or hormonal stimulation, leading to the production of more structural proteins and organelles, thereby enhancing the cells' work capacity.There are two primary types of hypertrophy: physiological...

Change in atmospheric pressure with height is particularly interesting. The decrease in atmospheric pressure with increasing altitude is due to the decreasing gravitational force per unit area as we move away from the surface of the earth.
Assuming the air temperature is constant at a given altitude and that the ideal gas law of thermodynamics describes the atmosphere to a good approximation, one can find the variation of atmospheric pressure with height.
Let p(y) be the atmospheric pressure at...