How the following could influence the population:
Immigration and emigration- Organisms coming into the populations increases the population, but then organisms leave the population at the same time to level out the population. Immigration is coming into the population an emigration is leaving the population.
Births and deaths- Having animals born into the population again helps the population grow, but then other organisms die, and it makes it so that it is hard to exceed the carrying capacity, unless the birth rate is way higher than the death rate.
Logistic growth- When the population first started out, they had an abundance of resources and not many organisms in the population. Because of this, they reproduced as much as possible to get the population started, and then they grow exponentially, until they start to run low on their resources, so they slow down the reproduction and reach their carrying capacity.
Density-dependent factors- In the populations there can be sickness that goes around, or even worse if another species that is bigger and more aggressive moves into the same community and starts liking them off the populations will go down immensely. They also would lose a lot of their resources to whatever species is sitting in on their community.
Density-independent factors- These duck live in fairly urban areas, and can have to deal with a lot of different natural disasters and weather. The weather where most ducks live is completely unpredictable. There can be snow, and then extreme heat. There can also be tornadoes and earthquakes. All of these things bring the population down in numbers, and make them suffer in resources.