The application of mathematical theory and technique to ecology. The earliest studies in ecology were by naturalists interested in organisms and their relationships to the environment. Such investigations continue to this day as an active and central part of the subject, and have focused attention on understanding the ecological and evolutionary relationships among species. A large mathematical literature has arisen as an aid to the formalization of concepts and ideas; the underlying goal has been to understand patterns of nature. For the most part, such approaches are retrospective, designed to help in understanding how current ecological relationships developed, and to place that development within appropriate evolutionary context.