Mathematical ecology

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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 a central part of the subject, and have focused attention on understanding the ecological and evolutionary relationships among species. 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. The second major branch is applied ecology, and derives from the need to manage the environment and its resources. Here the necessity for rigorous mathematical treatments is obvious, but the goals are quite different from those in evolutionary ecology. Management and control are the objectives, and the relevant time horizon lies in the future. The focus is no longer simply to derive understanding and explanation; rather, one seeks methods for prediction and algorithms for control.

There has been a dramatic increase in mathematical activity concerning the modeling and control of epidemics, and an increasing recognition of the need to view such problems in their proper ecological context as host-parasite interactions. Researchers are using mathematical models to help to understand the factors underlying disease outbreaks, and to develop methods for control such as vaccination strategies. See also Epidemiology.

Finally, the need for environmental protection in the face of threats from such competing stresses as toxic substances, acid precipitation, and power generation has led to the development of more sophisticated models that address the responses to stress of community and ecosystem characteristics, for example, succession, productivity, and nutrient cycling. See also Ecology; Ecology, applied; Environmental engineering.