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Translating Causal Loop Diagrams to Stock & Flow Diagrams
From SystemsWiki
After spending a number of hours laboring over several of the concepts put forth in Reinterpreting Generic Structures[1] I started toying around with some of the Archetype Stock & Flow models I had previously created. After tinkering with several Archetype implementations the conclusion was that the relation between Systems Thinking Diagrams (STDs), or Causal Loop Diagrams (CLDs), and Stock & Flow simulation models was so loose as to be almost meaningless. It was very easy to make the Stock & Flow diagram look very much like one of the Archetypes, while altering the embedded equations one could make it produce behavior patterns similar to any one of several other Archetypes. So what's the implication?
Being able to construct diagrams from which one could infer essentially very little should be most disconcerting. If one is to make any sense out of this there would have to be a rigorous method of translating Causal Loop Diagrams into Stock & Flow models that would provide a level of confidence in the translation. What follows is a method for doing this which should provide an appropriate level of confidence.
Contents |
[edit] Causal Loop Diagrams (CLDs)
Causal Loop Diagrams are composed of only two components, elements and influences. An influence also has a direction, indicated by an arrow, and an indicator as to whether the influenced element is added to (+) or subtracted from (-) by the influencing element. The simplest diagram I could come up with containing these elements is:
From this diagram there are only a couple things which are implied:
- E1 and E2 are elements of the model.
- E1 adds to E2.
Note that if E1 decreases it still adds to E2, just not so readily. And, the diagram doesn't indicate that E2 has any influence on E1.
[edit] Stock & Flow Diagrams (SFDs)
Stock & Flow Diagrams are composed of four different components: Stocks, Flows, Variables, and Links. I understand the labels may vary slightly in different arenas. In iThink the variables are referred to as converters and in Vensim they are referred to as auxiliary variables.
There are several conventions for Stock & Flow diagrams:
- Stocks are only changed by Flows
- Flows add to, or subtract from, Stocks, or
- originate or terminate in clouds when the source or destination is outside the boundaries of the model
- Stocks influence Flows or Variables
- Variables influence Flows, or other Variables (Variables are used to disaggregate a model; it is possible to have a valid model made up of nothing but stocks and flows. The equations in the flows would be undecipherable; hence the use of variables to increase model clarity and understanding.)
- Parameters do not influence Stocks (except to set their initial value)
Fig. 2 is a diagram containing the four elements, though not all the valid relations:
From this diagram, which just happens to be a Reinforcing Loop, there are several things which are implied:
- The flow adds to the Stock to increase it. Because it is one directional flow It would be inappropriate to create a negative flow without making the arrow bi-directional.
- The Stock determines the var.
- The var determines the flow.
Any understanding beyond this would require an understanding of the actual equations within the individual items.
[edit] Translating CLDs to SFDs
Fig. 3 is a simple Causal Loop Diagram (CLD) to use for this purpose, though it is not considered to be a rigorously developed diagram so don't get too hung up on its completeness or validity, for it most definitely neither.
This is a CLD for some service business that bills out employee services to clients, and yes, there's no service quality identified in the diagram. It's just an example.
The translation of this diagram to a SFD will be performed based on several assumptions:
- Assumption # 1: CLDs contain no flows!
- Assumption # 2: If Assumption # 1 is correct then all the elements on the above diagram must be either Stocks or Parameters.
- Assumption # 3: Stocks represent things that accumulate, or decline, over time, and don't reflect instantaneous change.
From these assumptions it would seem to make sense that Employees, Cash, and pct Billing are Stocks.
The part that is likely to be confusing has to do with when there are two or more influences for a single Stock as in Fig. 4.
It would seem that this could be implemented in one of two ways:
or as:
Mathematically the two are identical, i.e, (B+A-C) = (B+(A-C)), and when both the inflow and outflow originate from and terminate in clouds which one is is used depends on which one makes the model easier to understand. If the model is such that flows are between Stocks then there is a very substantial difference in terms of the effect there is on the model.
Based on the above assumptions the Causal Loop Diagram of Fig. 3 would readily translate into the following Stock & Flow Diagram.
This diagram simply takes Fig. 3, changes employees billing to a Stocks, creates flows, add to billing and remove from billing, and moves the influences that were to the Stock to the appropriate Flows. If this method is used to translate CLDs to SFDs it should consistently produce the same results.
[edit] References
- ↑ Lane, David C. and Smart Chris (1996) Reinterpreting Generic Structure: Evolution, Application and Limitations of a Concept. Sys Dyn Rev 12(2): 87-120.
- Lane, David D. (web) Can We Have Confidence in Generic Structures?
- [tcld.msys] MapSys Model Source
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