It depends on what type of carb you have.
Float carbs are limited by the fact they meter fuel by volume of air that enters the engine. But as we know the power produced by the engine is dependant upon the mass flow of air through the engine.
An engine will take in the same mass of air at sea level as it will at altitude , but the mass of air will be less at altitude as the air is less dense. If the same amount of fuel is metered into this less dense air we create a rich mixture and therefore lose power. So we grab for the red lever and lean off the mixture, as the mixture is leaned temperature is allso increased, temperature has an effect on air densitiy, warmer air is less dense than cooler air, hence the leaning proccess is a balence between creating the correct mixture for a given mass of air and the cylinder (combustion) temperature.
The 15:1 ratio is the stoichiometric ratio of gasolene, this is a purely theoretical figure. The engine manufacture will state best mixture ratios for bes power based od their analysis taking many factors into consideration.
Hope this is of some help, im not an engine person really
im avionics
Cheers
Stu.