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Abstract
Until the early 1970s, ecologists generally assumed that erratic fluctuations observed in natural populations were a product of stochastic noise. It is now known that extremely complex dynamics can arise from basic deterministic processes. This field of study is generally called chaos theory. Here, a computer program, SLAC (Stability, Limits, And Chaos), is described, which facilitates the study of a simple deterministic model known as the logistic difference equation. It is designed to familiarize the biology student, who may not be mathematically inclined, with the fundamental concepts of population dynamics, especially the not-so-intuitive notion that complexity can evolve from deterministic mechanics. In addition to the program, pedagogically significant issues associated with the derivation of the equation and its parameters, and population dynamics in general, are highlighted.
Notes
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Strictly speaking ‘sigmoidal’ only applies to continuous models, not discrete ones. This is also the case for ‘exponential’, and thus here the terms ‘sigmoidal-like’ and ‘exponential-like’ are used.