A classic ecology problem for these exams traces the cyclical fluctuations in the population densities of two species intertwined in a predator-prey relationship, that is, the snowshoe hare (prey) and the Canadian lynx (graph copied from the Encyclopedia Brittanica Blog: http://www.britannica.com/blogs/2011/06/rise-fall-canada-lynx-snowshoe-hare/).
The data makes several suggestions. First of all, one can see that maxima in hare population densities are consistently simultaneous with, or slightly preempt, lynx population maxima. The strongly correlated data suggest the hare is a key source of food for the lynx, such that higher hare population densities provide lynx populations with the energy necessary to grow in size. However, the hare population minima which always follow maxima suggest that once lynx populations increase past a critical threshold, hares cannot maintain their populations due to the presumed ubiquity of the predator (the lynx), and hence hare populations crash. Clearly, the data seems to suggest that a key limitation to each species' carrying capacity in this ecosystem is each other!