A reproduction curve is the size of a population in a given generation plotted against its size in the preceding generation. Here I introduce its utility as an analytical tool in the study of animal population processes. As an example, I apply it to re-interpret the US census data to which Pearl and Reed fitted their logistic model. My analysis reveals some problems in the way Pearl and Reed envisaged the logistic nature of the US population. In particular, I reveal that the iconic sigmoid curve of the logistic model has no ecological significance but a mere consequence of the mathematical attribute that a population is a non-negative entity. I show an alternative way to conceive the actual nature of the logistic law and reinterpret the US census data. In particular, I introduce the notions of endogenous process (as intrinsic to the population) and exogenous (environmental) influences on it.

This well-known law of ecology serves as the basis and the starting line for studying and understanding animal population processes at higher levels of complexity. However, the classical logistic curve, as originally conceived by Verhulst and later by Pearl and Reed, was an empirical law without theoretical bases, and the conventional interpretations of the model’s attributes, i.e. the iconic sigmoid curve and the ‘carrying capacity of the environment’, are misleading. Here I develop a theoretical model on the basis of ecological first principles to critically examine and reinterpret the classical law.

Mathematics (elementary algebra, calculus, or statistics) is an essential part of this chapter. However, I show in an easy-to-follow manner how to construct the original logistic differential equation and how to solve it so that even those students without an adequate background in mathematics would understand the ecological meaning of the logistic law.