Applications of Algebra and Coalgebra in Scientific Modelling: Illustrated with the Logistic Map

In computer science, the algebra–coalgebra duality serves as a formal framework for connecting the perspectives of state-based and behavior-based models. In other sciences such as ecology, these perspectives are seemingly harder to reconcile. We explore modelling paradigms, in the sense of philosophy of science, as an intermediate step in translating the (co)algebraic framework from computer science into applications in ecology. We illustrate the application potential of this approach with a simple model from theoretical ecology: the logistic map. Several versions of algebraic models with progressively more sophisticated carriers and operations are introduced and finally contrasted with a corresponding coalgebraic model. We illustrate two modelling paradigms with these examples. Only one of these has traditionally been used in ecology. The second one, which is based on a coalgebraic dualisation, offers new modelling perspectives in ecology and environmental science.