ABSTRACT
A model describing the land distribution patterns of a system in demographic equilibrium is developed. The model is derived from three postulates: a) the existence of a quantum of individual area; b) the inevitable occupation of all habitable land; and c) the fundamental distinguishability among individual members of a large population, and indistinguishability of the quanta of individual area. The fundamental theorem of this model states that the available land will be distributed among the members of the population so as to maximize the degree of disorder (entropy) in the system. Real systems that have not achieved demographic equilibrium will proceed in time seeking the state of greatest disorder. Land occupation patterns in the USA are matched successfully with theoretical predictions. Demographic stabilization of two previously demographically isolated systems is described. Some implications of this process to urban planning and development are discussed. Within the tolerance of the predicted fluctuations when the model is applied to small systems, comparisons are made of the equilibrium conditions with the observed clustering effect of small animal groups. An extension of the theorem of greatest disorder predicts an optimum population size, and this prediction is compared with the observed population leveling of confined clusters of animals.
