Population and basic community ecology are commonly presented to students through a set of distinct models, such as those for exponential growth, logistic growth, competition, predation, and so forth. This approach mirrors the historical development of the field, but it has several shortcomings as a way to present ecological theory. First, the classical equations can appear disconnected from one another. Second, differences in the parameters and styles of the equations do not lend themselves to comparison in a common graphical form. And third, the set of equations as they are commonly presented provides no easy way to see whether any concepts are left out. In fact, something is left out that is not commonly taught: the concept of faster-than-exponential growth approaching a singularity, which is important for understanding rapidly growing systems. In the present article, we demonstrate a unified approach that simplifies the traditional equations of ecology, expands their scope, and emphasizes their interconnections.

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