What would increase or decrease a population?
There is an entire branch of mathematical ecology that is devoted to modeling populations. If we consider a simple model of a population, we can say the population is made up of individuals that reproduce at a certain rate, die at a certain rate, immigrate at a certain rate (move into the population) and emigrate at a certain rate (move away from the population). So the most basic factors to affect the population are birth rate, death rate, immigration rate and emigration rate. You can make more complicated models that take into account the age structure of the population (which would change the birth rate), or consider a population under predation (which would change the death rate) etc etc. Your question is general enough that it gets the catch all answer to biology questions: it depends.
