Forming a Dynamic Hypothesis: Causal Loop Diagrams

Todd BenDor Associate Professor Department of City and Regional Planning bendor@unc.edu 919-962-4760 Course Website: http://todd.bendor.org/datamatters

We have already been thinking about feedback…

populationbirths deaths

birth rate death rate

populationbirths

birth rate

deaths

death rate

+

++

-

++

(+) (-)

A Representation of more than one feedback loop

Guidelines for labeling an arrow as positive (+) or negative (-)

AB+

XY-

XC

BA

?- +

Why Draw These Diagrams?

• To see the feedback loops

• Causal Loop Diagrams (CLD) are for thinking and discussion (not for simulation) – “soft” system dynamics – systems thinking

Drawing the diagrams

• Pencil and paper • Drawing the loops in Vensim • PowerPoint

The classic case of a “bad HVAC” system

energy contentin BTU

airtemperaturethermostat's target

temperature

furnace heatproduction inBTU per hour

heat loss in BTUper hour

outdoortemperature

+

+-

-

+ -+

(-)

(-)

Also two feedback loops – this time both negative loops

Positive Feedback Loops

• Can often lead to exponential growth • Or they can lead to rapid decline • If change is “good”, sometimes called “virtuous

circles” • If not so good, sometimes called “vicious circles” • The loop acts to magnify the effect of outside

disturbances • 0, 2, 4,6 (any even number) of – arrows in the loop

R

Negative Feedback Loops

• Can often lead to exponential decline • Or they may serve as control loops

– with an explicit goal (i.e., engineered like a thermostat) – or with an implicit goal (a natural system)

• The loop acts to negate the effect of outside disturbances

• 1, 3, 5, 7 (any odd number) of (–) negative arrows in the loop

• Tend to be much more common than positive feedback loops

C

Supply & Demand: Example of Coupled Loops

Negative Loops: How do they deal with the effect of outside disturbances?

Inventory of cars atdealers

retail car sales

market price

car production

-

-

-+

+

--

Portion of a typical model of a “Boom Town”

constructionworkers atproject site

total workersother

workershousing demand

housingconstructionstock of houses

++

+

+

+

-(-)

cost ofconstruction

cumulative costof project

++

Look for the Feedback and you will see the “Big Picture”

constructionworkers atproject site

totalworkers

other workers inthe town

housingdemand

housingconstruction

stock ofhouses

++

+

+

+

-

(-)

cost ofconstruction

cumulative costof project

+ +

vacancy rate

-

+

constructionworker

satisfaction +

other factors such aspublic infrastructure

constructionworker productivity

normal need forconstruction

workers-

+

(-)

(+) the housing

problem is alsoa company

problem

constructionworker turnover

-

-

Drawing Diagrams

• Previous examples start from scratch – the goal is to get started thinking about the key feedbacks in the system

• Next example: We have a model and we are wondering about its feedback loops

A Familiar Population Model

young population mature population elderly populationbirths maturation aging deaths

maturation rate aging rate death rate

+

total population

mature femalesfraction female

births per mature female per yr

young population

births

maturation

mature population

aging

elderly population

deaths

+

- + - +-

Start with the stocks and flows

Explain the easy flows

young population

births

maturation

mature population

aging

elderly population

deaths

+

- + - +-

++

+maturation rate

aging rate death rate

+ +

+

(-) (-)(-)

Explain the births

young population

births

maturation

mature population

aging

elderly population

deaths

+

- + - +-

++

+maturation rate

aging rate death rate

+ +

+

(-) (-)(-)

mature females

fraction female

births per mature female per year

++

+

+(+)

S-Shaped Growth

• Flowers Model

• Sales Company Model

• Epidemic Model

Loops in the Flowers Model

suitable area

(-)

(-)

(+)

fraction occupiedgrowth rate decay rate

decaygrowth

area of flowers

--

++

+

-

+

+

+

Loops in the Sales Model

number ofsales

persons

departures

exit rate

new hires

budgetednumber of

sales persons

average salary

sales deptbudget

fraction tosales annual

revenues

widget sales

widget price

effectiveness

+--

+

+

-

++

+

++

+

+

+

-

SalesGrowth(+)

saturation(-)

(-)hiringcontrol

(-)

Loops in the Epidemic Model

InfectedPopulation

SusceptiblePopulation

infections

recoveries

RecoveredPopulation

FrSusceptible

fr of contacts that arewith a susceptible

person

dangerouscontacts per

day

total contactsper day

contacts per day perinfected person

duration ofinfection

-+

-

++

+

+

+

infectivity

+

+

++

-

contagion (+)

depletion (-)

recovery (-) +

Beginners Difficulties

• Avoid “too many arrows” – Your goal is to show the loops, not the clutter

• Avoid “action words” – The action is in the arrows, not in the words

car sales go down becauseof higher prices

market price isgoing up

inventories go up becauseof higher production andbecause of lower sales

car production goes upbecause of higher prices

-

-+?

+

Good

Bad

Inventory of cars atdealers

retail car sales

market price

car production

-

-

-+

+

--

Find the Errors

AB

CD

+-

+

+

(+)

AB

CD

++

+(+)

+

How Many Loops?

A1A2

A3

A4A5A6A7

A8

A9

A10A11 A12

ATotal

AB

C

DE

F

Homeostasis

• Refers to our remarkable capability to maintain a relatively stable physiological state even when the outside environment is varying dramatically.

Homeostasis

• Walter Cannon, Professor of Physiology, Harvard Medical School

• The Wisdom of the Body (1932)

• Higher organisms had “learned” this ability over eons of time through gradual evolution

The Wisdom of the Body

• Control of Blood Pressure • Control of Blood Sugar • Control of Food Intake • Control of Water Intake • Control of Salinity

These systems are fundamentally the same when we think of their homeostatic properties.

External Disturbance to the Body

size of initial cut orrupture

size of thewoundopening

trauma tolocal vessels

+ vascularspasm+ - blood

loss

++

Feedback loops controlling clot formation

size of initial cut orrupture

size of thewound opening

trauma tolocal vessels

size ofthe clot

+vascularspasm

+

--

+

amount ofthrombin

formation ofprothrombin

activator

+

+

formation offibrin fibers

+

+

+

bloodloss

++

-

+

A dangerous (+) loop forms

• Once a critical amount of thrombin [coagulant] is formed, a vicious circle develops that causes still more blood clotting and more thrombin to be formed; thus, the blood clot continues to grow until something stops its growth. -- Guyton & Hall (1996)

How does the body control blood pressure while a clot is forming?

size of initial cut orrupture

size of thewound opening

trauma tolocal vessels

size ofthe clot

+vascularspasm

+

--

+

amount ofthrombin

formation ofprothrombin

activator

+

+

formation offibrin fibers

+

+

+

bloodloss

++

-

+

volume ofblood in

circulation

bloodpressure

-

++-

contraction ofthe encircling

muscles

contractionof the spleen

capacity ofthe vascular

system

-

-

-

-

blood storedin the spleen

--

-

-

Clot formation Blood Pressure

Topic of Cannon (1932): The Wisdom of the Body

Should We Try to Extend Homeostasis Beyond Physiology?

• Cannon: Yes – his concluding section

• Cannon’s Advice: homeostasis is “not a special gift” bestowed upon the highest organisms but is the consequence of gradual evolution

Webster’s Defines Homeostasis:

Tendency toward maintenance of a relatively stable internal environment in the bodies of higher animals through a series

of interacting physiological processes

Tendency toward maintenance of relatively stable social conditions among groups with respect to various factors

(such as food supply and population among animals) and to competing tendencies and powers within the body politic, to

society, to culture among men.

OK

Say What?

Extending Cannon’s Ideas

• Homeostatic responses may be extremely difficult to detect (as in 98 degrees body temperature)

• Look for both Positive as well as Negative Feedback

• Can think of a “Span of Control”

Stability Concepts discussed so far

• Stability around equilibrium

The Span of Control

Body Temperature Control

Runaway behavior? When the body is too hot, runaway behavior takes over. This runaway feedback (if not stopped) leads to death.

Home Heating System

Could you envision runaway behavior?

Loss of Blood

What is the run-away behavior here?

Application to my field - urban systems

• Urban resilience • How can we think about homeostasis with regards

to local or regional economies? • Transport

• What about environmental systems? • Applications to your fields?