The graph above represents a typical carrying capacity graph, or the maximum population size a certain environment can support for an extended period of time, for a population of a particular species. Under ideal conditions, a population naturally increases until it overshoots the carrying capacity.  At this point, the environment can no longer provide for the species, due to a number of different environmental resistances, including food, crowding, competition, etc. The population, due to lack of resources, will begin to die out, allowing the environment to recover. As the environment recovers, the species population is able to flourish once more. This leads to a fluctuation between the prosperity of the species and the prosperity of the environment (hence the fluctuations in the graph). This type of growth is called logistic growth.