Application of population-based theoretical models to the study of real world populations requires the relationship between the real and theoretical populations to be defined. Otherwise, it is not possible to take a representative field sample or census of a population. I demonstrate that the concept of a biological population is based on a circular definition and is logically untenable. A population is composed of a number of individuals whose membership of the population is determined by their relationship to the rest of the population. This has serious implications for common practice in a range of ecological and evolutionary disciplines.