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.