Density-independent population growth. Population ecology is a subdiscipline of ecology dealing with the growth and decline of populations. It is closely related to community ecology, conservation, and population genetics. Aside from the issue of human population size, understanding population growth is important in conserving species, in controlling and predicting outbreaks of pests and diseases, in understanding evolution, and in gauging the effects of various environmental factors on wild species. You can probably think of some additional reasons to understand population growth.
Models play an important role in population ecology.
Usually these models are mathematical. This introduction won't involve any heavy mathematics, but you should be familiar with the major ideas involved. There are at least two rather different uses of models in ecology. One is to make specific predictions, like the change in concentration of a toxin in response to a change in the environment. The other is as an aid to clear thinking.