How do limiting factors affect the population of the arctic tundra?
Limiting factors place restrictions on how quickly an organism can grow to maturity, and how many offspring it can produce
First of all we should be talking here about communities; 'populations' refers only to individuals of the same species.
In the tundra, the main limiting factors are:
Because it is so cold for much of the year, plants and cold-blooded organisms hibernate or become dormant. They don't grow, so productivity is very low. Warm-blooded animals (eg birds, bears, wolves, etc) migrate away to warmer climates.
And then again, because it is very cold, this also means water is frozen for much of the year, so tundra is effectively a cold desert. No water - another reason why growth is so slow.
And for much of the year, there is little light and short days -- so very little photosynthesis, so very little food is available.
Low productivity means less amount of solar energy is getting trapped. Thus less number of animals can live in the area, carrying capacity being low.