Modeling is a way of understanding phenomena that occur in the real world which is applied when experimentation is difficult or impossible. There are analytical models which can be typically implemented in a simple spreadsheet by setting input variables and immediately obtaining a result. Simulation models require multiple iterations and are more relevant where the dynamics of the problem are important - how the solution develops over time.

Popular paradigms include System Dynamics (SD), Discrete Event Simulation, Probabilistic Graphical Models (PGM) or Agent Based Modeling (ABM). While SD and discrete event simulation have been taught at universities in various disciplines, ABM has only recently received increased interest. ABM is a decentralized approach which, compared to SD, has no central definition of the global system behavior (dynamics). Instead, the model defines the behavior of individual agents and the global behavior emerges from their interaction over time. PGMs leverage probabiity and graph theory to allow dealing with large amounts of evidence data and can dynamically adjust beliefs as new facts become available.

### Thinking about oil depletion

In the following model, adapted from World Energy-Economy Scenarios with System Dynamics Modeling by Carlos de Castro et al., you can see a basic SD model from the paper which shows the essence of peak oil theory. This simple example is further enhanced in the paper with additional effects including technology, population and GDP adding further feedback loops and dynamic effects to the overall system.

### More examples

Below are further examples of models found on the web which help thinking of sustainability issues in interesting ways.

- Prey-Predator
- Sustainable Forestry
- Climate Change
- Greenhouse Effect
- Distribution of Urban Populations
- Sugarscape
- Cheese Slicer
- Climate Bathtub
- Urban Dynamics
- World Dynamics
- MayaSim

### Pointers to some modeling tools

- R Project and its many libraries on CRAN
- Forio
- Vensim
- Stella
- NetLogo
- Mimosa
- AnyLogic
- PowerSim
- InsightMaker and Systems Wiki
- Mental Modeler
- SamIam
- Hugin