Last Word on Viewpoint: Premature birth: a neglected consideration for altitude adaptation

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:

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:

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...

Besides the pressure difference between the external environment and the lungs, the airflow rate and ease of pulmonary ventilation are also influenced by three other factors: surface tension of the fluid in the alveoli, compliance of the lungs, and airway resistance.
Alveolar Surface Tension
The alveolar fluid lines the luminal surface of the alveoli and exerts a force called surface tension. This force is caused by the polar water molecules in the liquid being more strongly attracted to each...

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...