Immigration and Emigration:
If a population of snow leopards decided to immigrate out of their current habitat, they would have to find a place where their coats blend in. Their ability to camouflage helps them hunt and find food that they need to survive.
If the leave a population and go to a place where they can blend, they will have a higher chance of surviving and thriving. They could also benefit if there are better food sources.
When they move to a different habitat they might get benefits and have an increase on their population making them have a higher fitness and survival rate.
Usually when snow leopards leave their habitat, it's because their habitat was not helping them or allowing them to have a high fitness which made it hard to survive in that particular environment.
Births and Deaths:
Typically, a mother snow leopard will have two or three cubs per litter. The mating season is typically January to mid-March. The cubs will stay with their mothers for about 18 to 22 months until they are old enough to go out on their own.
If they weren't endangered, they would typically increase because they are the top predators in their environment. They are not preys to another organism in the area. Which makes them reproduce more, but because they are endangered, their population has been decreasing mostly due to the fact that humans are letting their livestock graze more which damages grass which is a primary source for a snow leopard's prey.
Because humans have such a great impact on the population of snow leopards, their population has been rapidly decreasing a little bit more each year.
If their food supply starts to go down such as a gazelle, then their population will have a sudden decrease like an s curved graph. So, they would need to find a different resource such as deer which will make their population increase again and they will discover different species to feed on. Eventually their population will reach carrying capacity.
Snow Leopards are an example of commensalism, because they benefit from other organisms such as other prey. They typically have no competition but their population could decrease because of diseases.
Humans play a big role on the snow leopard population. If their was an avalanche, because they live in the mountains, a lot of them could die. If they lived in warm weather, they wouldn't be able to camouflage into their surroundings making it harder to catch their prey and hide from humans.