Jeffrey Dambacher:
Qualitative Mathematical Modelling

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Qualitative mathematical modelling will be introduced as a means to understand and predict the dynamics of complex systems. The technique poses the question: if all we know of a system is the general nature of the relationships between species and environmental or human variables, but not the precise intensity of these interactions, then what do we know? It turns out that we know not everything, but quite a lot. Qualitative mathematical modelling describes complex systems through only the sign (0, +, -) of the effect or interaction between variables, and thus can easily include variables and processes that are important, yet difficult to measure. Calculations of system stability and predictions of perturbation response proceed through analysis of the feedback properties of a system. While model predictions are imprecise, there are nonetheless rigorously derived and readily testable. This approach leads to many interesting, practical, multidisciplinary, and surprisingly overlooked applications to complex dynamical systems. This talk will provide a brief introduction to the basic approach and include example applications and extensions to a Bayesian interpretation of results.

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Dr Jeffrey Dambacher's background was originally in the ecology of stream fishes. A desire to understand the complex relationships of fish communities, rivers and watersheds led him to the method of qualitative mathematics as a tool to address complex systems. With CSIRO this work has been expanded to address problems of integrated monitoring and management of socio-ecological systems such as the Great Barrier Reef, marine ecosystems of Australia’s exclusive economic zone, Mediterranean fisheries and aquaculture systems in Tasmania, Chile and France.