2.1.1 Analytic Equation

Ecology is the study of organisms in relation to their environment. In the course of this study, ecologists have developed mathematical models to describe these relationships. In general, these models are systems of differential equations that describe the average case changes in populations. As these models address average case behavior, they are applicable only to large populations.

Ecological models include the Volterra-Lotka model [LOG] as discussed in Section 1.1.1, a more in depth description can be found in Lotka-Volterra Two Species Model. Other models include the logistic equation, habitat selection models, diease vector models, and more.

To solve this equation we can either use techniques for solving systems of differential equations or we can use a continuous simulation. In either case, these simulations give us a prediction about population growth and decline based on some measurable quantities.

To get an idea of how these equations behave, it might be worth examining Simulation Server again.

For an interesting example an application of a complex analytical model and the prediction accuracy can be found in [SWART1].

• [LOG] Logofet, Dmitrii, Matricies and Graphs: Stability Problems in Mathematical Ecology, CRC Press, Boca Raton, 1993, p 103
• [SWART1]Swartzman, G.L. and Kaluzny, S.P. Ecological Simulation Primer, Macmillan, New York, 1987 pp 112-122.