Organization of specialized course from 24th to 28th February 2020 about Qualitative Mathematical Modelling of Complex Socio-Ecological Systems at the Institute of Marine Science (ICM-CSIC), Barcelona, Spain.
Teacher: Dr. Jeffrey Dambacher (CSIRO, Hobart, Tasmania).
The course was an event of MarCons COST Action.
Qualitative mathematical modelling was introduced as a means to understand and predict the dynamics of complex biological and socio-economic 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 interactio
n 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.
Coursework was divided between lecture and use of modelling software (provided); students will need access to computer laptops (or share with a partner) and at times will work in groups on applied problems.
Topics covered in the course included:
- Introduction, history and philosophy
- Derivation of community (Jacobian) matrix & defining relevant subsystem
- Modified (nonlinear) interactions & split variables
- Model building examples (Yellowstone Park wolves & urchin barrens)
- Press perturbation analysis
- Socio-economic & biophysical systems
- Qualitative measures of Lyapunov stability
- Predicting change in life expectancy
- Application to Bayes nets