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Thinking in Diagrams

Stock & flow diagram

Systems & feedbackField guide · Systems & feedback · 4 of 6

What would still be there if everything stopped?

Over variables and effects, a stock & flow diagram shows stocks, the flows that fill and drain them, clouds, and signals carrying readings to flows and to other variables.

  • Stock & flow diagram: water in tub Stocks: water in tub (liters). Auxiliaries: tap opening; drain blockage. Flows: filling, from a cloud to water in tub (liters per minute); draining, from water in tub to a cloud (liters per minute). Signals: tap opening to filling, +; drain blockage to draining, −. filling draining + − literswater in tub tap opening drain blockage
    polarity
  • Stock & flow diagram: beans in warehouse Stocks: beans in warehouse (kilograms). Auxiliaries: beans ordered. Flows: deliveries, from a cloud to beans in warehouse (kilograms per week, with a delay). Signals: beans ordered to deliveries, +, with a delay. deliveries + kilogramsbeans in warehouse beans ordered
    delay
  • Stock & flow diagram: dirty dishes; clean dishes Stocks: dirty dishes (dishes); clean dishes (dishes). Flows: washing up, from dirty dishes to clean dishes (dishes per day). Signals: clean dishes to washing up, −. Loop B1 cupboard full, balancing: clean dishes, washing up, which fills clean dishes. washing up − dishesdirty dishes dishesclean dishes B1cupboard full
    loop
  • Stock & flow diagram: rabbits in warren Stocks: rabbits in warren (rabbits). Flows: births, from a cloud to rabbits in warren (rabbits per month). Signals: rabbits in warren to births, +. Loop R1 breeding, reinforcing: rabbits in warren, births, which fills rabbits in warren. births + rabbitsrabbits in warren R1breeding
    reinforcing loop
  • Stock & flow diagram: water in tub Stocks: water in tub (liters). Flows: draining, from water in tub to a cloud (liters per minute). Signals: water in tub to draining, +. Loop B1 draining down, balancing: water in tub, draining, which drains water in tub. draining + literswater in tub B1draining down
    balancing loop
  • Stock & flow diagram: water in tub Stocks: water in tub (liters). Flows: filling, from a cloud to water in tub (liters per minute). Boundary bathroom contains: water in tub. bathroom filling literswater in tub
    boundary
  • Stock & flow diagram: water in barrel Stocks: water in barrel (liters). Auxiliaries: rainfall (external driver). Flows: collecting, from a cloud to water in barrel (liters per day). Signals: rainfall to collecting, +. collecting + literswater in barrel ‹rainfall›
    external driver
  • Stock & flow diagram: water in tub Stocks: water in tub (liters). Auxiliaries: liters short of full. Flows: filling, from a cloud to water in tub (liters per minute). Signals: liters short of full to filling, +. filling + literswater in tub liters short of full
    gapdrawn as an ordinary variable
  • Stock & flow diagram: goats Stocks: goats (goats). Auxiliaries: goats per hectare. Flows: goats dying, from goats to a cloud (goats per year). Signals: goats per hectare to goats dying, +, nonlinear. goats dying + goatsgoats goats per hectare
    nonlinear effect
  • Stock & flow diagram: members Stocks: members (people). Auxiliaries: posters up. Flows: joining, from a cloud to members (people per month). Signals: posters up to joining, +, hypothesis. joining + peoplemembers posters up
    evidence coding
  • Stock & flow diagram: water in tub Stocks: water in tub (liters). Auxiliaries: tap opening (leverage point). Flows: filling, from a cloud to water in tub (liters per minute). Signals: tap opening to filling, +. filling + literswater in tub ????tap opening
    leverage point
  • Stock & flow diagram: water in tub Stocks: water in tub (liters). Flows: filling, from a cloud to water in tub (liters per minute). Behavior note: full in about ten minutes. filling literswater in tub full in about ten minutes
    behavior note
  • Stock & flow diagram: water in tub Stocks: water in tub (liters). Behavior-over-time graph of water in tub: rises toward a value and flattens. literswater in tub water in tub (liters)time
    behavior-over-time graph
  • Stock & flow diagram: water in tub Stocks: water in tub (liters). literswater in tub
    stock
  • Stock & flow diagram: water in tub Stocks: water in tub (liters). Flows: filling, from a cloud to water in tub (liters per minute). filling literswater in tub
    flow
  • Stock & flow diagram: water in tub Stocks: water in tub (liters). Flows: draining, from water in tub to a cloud (liters per minute). draining literswater in tub
    cloud
  • Stock & flow diagram Auxiliaries: tap opening. tap opening
    auxiliary
  • Stock & flow diagram: water in tub Stocks: water in tub (liters). Auxiliaries: tap opening. Flows: filling, from a cloud to water in tub (liters per minute). Signals: tap opening to filling, +. filling + literswater in tub tap opening
    signal
  • Stock & flow diagram: water in tub Stocks: water in tub (liters). Flows: filling, from a cloud to water in tub (liters per minute); draining, from water in tub to a cloud (liters per minute). Stock equation: change in water in tub = filling − draining. filling draining literswater in tub change in water in tub = filling − draining
    stock equation

How each mark is drawn and read: chapter 6, What the notation expresses.

A flow’s double line moves material from one stock or cloud to another. A signal, a single thin line, is an effect carrying a reading to a flow’s valve or an auxiliary, which it changes; no signal ends at a stock.

Stock & flow diagram: water in tub Stocks: water in tub (liters). Auxiliaries: tap setting; drain opening. Flows: filling, from a cloud to water in tub (liters per minute); draining, from water in tub to a cloud (liters per minute). Stock equation: change in water in tub = filling − draining. Signals: tap setting to filling, +; drain opening to draining, +; water in tub to draining, +. filling draining + + + literswater in tub tap setting drain opening change in water in tub = filling − draining

Filling runs from a cloud into water in tub and draining out to another; signals from tap setting and drain opening set the flows, and the water’s + signal to draining makes deeper water drain faster (chapter 6’s bathtub).

Draw one when something builds up or runs down, when cutting what comes in hasn’t stopped a total rising, or when something leaving one place has to turn up in another (chapter 6’s signals).

When nothing accumulates, a sentence does, or a causal loop diagram for effects running in a circle; how much there is now is a list of amounts. The diagram holds no numbers (chapter 6, what stays informal).

  • Reasoning5 of 5
  • Polish4 of 5bathtub sketch → simulation model
  1. One stock with an inflow and outflow
  2. Transfers between stocks, signals and delays
  3. Units, nonlinear effects, constraints and behavior-over-time graphs
  • A causal loop diagram is redrawn by hand as a stock & flow diagram, what accumulates becoming stocks, filled and drained by flows that signals set.
  • Where the controlled variable accumulates, it is drawn on a feedback control diagram with a stock & flow diagram’s stock, flows and signals, the roles written above them.
  • Chapter 6, What Accumulates: stocks, flows, clouds, units, transfers, auxiliaries, signals, the stock equation, delays on flows and behavior-over-time graphs; exercises SF 01–05.
  • Chapter 7, Stocks Inside Feedback: loops through stocks, conservation, aging chains, material and signal delays, and capacity limits; exercises SF 06–10.
  • Donella H. Meadows, Thinking in Systems: A Primer (Chelsea Green, 2008), chapter 1, The Basics, on stocks, flows, clouds as sources and sinks, and the bathtub.
  • John D. Sterman, Business Dynamics: Systems Thinking and Modeling for a Complex World (Irwin/McGraw-Hill, 2000), chapter 4, Structure and Behavior of Dynamic Systems, on the shapes behavior over time takes; chapter 6, Stocks and Flows, on the notation and on telling a stock from a flow by freezing a system in time; chapter 7, Dynamics of Stocks and Flows, on reading a stock’s path from its net flow; chapter 11, Delays, on delays in material and in information; and chapter 12, Co-Flows and Aging Chains.
  • Linda Booth Sweeney and John D. Sterman, “Bathtub Dynamics: Initial Results of a Systems Thinking Inventory”, System Dynamics Review 16, no. 4 (2000), on how well students with no training in system dynamics read stocks and flows.
  • isee systems, Working with Building Blocks (Stella help), on the parts of a model in Stella, a modeling program.