Model Behavior and the Strengths of Causal Loops: Mathematical Insights and a Practical Method

Quantifying the strength of causal loops on a stock can help bring insights into the relationship between model structure and behavior. This paper uses mathematics to derive loop strengths in a number of generic small models using the relationship between the second and rst derivative from the Pathway Participation Metric method. The loop strengths are plotted in a System Dynamics (SD) simulator together with the stocks to help explain behavior in the Limits to Growth, Predator-Prey, Diusion and SIR models among others. Issues such as loop dominance, ow dominance and the change of polarity of higher order loops are used to explain behavior. In particular the identity of the causal loops in the Diusion and SIR models are discussed and compared with previous work. Finally a numerical method for computing loop strengths and identifying dominant loops within an SD simulator is presented and applied to the Yeast Model. It is hoped that the paper will inspire others to use loop strengths in their analysis and understanding of SD models.

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