Basics of Causal Loop Diagrams: Structure & Behavior

(1)

Basics of Causal Loop Diagrams:

Structure & Behavior

Nathaniel Osgood

([email protected])

(2)

Causal Loop Diagram

Food Ingested

+

-• Focuses on capturing causality and

Hunger

• Focuses on capturing causality – and especially feedback effects

I di t i f l i t ( )

• Indicates sign of causal impact (+ vs. –)

0 y ∂ – x →+_{y indicates} – x →-_{y indicates} 0 y x > ∂ 0 y x ∂ _< ∂ y _∂_x

(3)

Meaning of A

Î

B

Meaning of A

Î

B

• We are reasoning here about g causal influences: The

changes on B caused by changes in A

• We are interested in causal influence because we want to be able to reason about “what if” counterfactual situations

able to reason about what if counterfactual situations

– This should not merely be

• An associational relationship (e g correlation absentAn associational relationship (e.g. correlation absent causation)

– If unsure, remember that models are useful as capturing dynamic hypotheses about how things work – and generally work well as long hypotheses about how things work and generally work well as long

as we keep these limits in mind

• A matter of definition

– e g the larger the # afflicted by conditione.g. the larger the # afflicted by condition XX, the smaller the number the smaller the number

(4)

Identifying Link Polarity

• Within a causal loop diagram, all linkages should be associated with a polarity (+ vs -)

• Tips for identifying X→Y link polarity

– Reason about this link in isolationReason about this link in isolation

• Do not be concerned about links preceding X or following Y

– Ask “if X were to INCREASE, would Y increase or

decrease compared to what it would otherwise

h b ”?

have been”?

• Increase in Y implies “+”,decrease in Y implies “-”

• If answer is not clear or depends on value of X need to • If answer is not clear or depends on value of X, need to

think about representing several paths between X and Y

(5)

Critical: Notion of “Y Increases”

Critical: Notion of Y Increases

• Must Clearly DistinguishMust Clearly Distinguish

• Correct interpretation for causal loop diagrams: “if X were to

INCREASE, would Y increase or decrease compared to what it

would have otherwise been ”?

• Different notion (common misunderstanding of link polarities): “if X

were to INCREASE would Y increase or decrease over time”?

were to INCREASE, would Y increase or decrease over time ?

(6)

Polarity

• AÎ+_{B Does}_not_{mean that if A rises then B}

will rise over time

– Just says that B will be higher than it would otherwise have been

– B may still be declining over time – but is larger

than it would otherwise have been, w/o increasing A

• AÎ-_{B Does}_not _{mean that if A rises then B will}

decline over time

– Just says that B will be lower than it would otherwise have been

– B may still be rising over time – but is higher than it otherwise would have been without increasing A

(7)

Causal Pathways

• We can reason about the influence of one

variable and another variable by examining the y g signs along their causal pathway

• Two negatives (whether adjacent or not) will actTwo negatives (whether adjacent or not) will act to reverse each other

– Consider AÎ-_B_Î-_C

– Consider AÎ BÎ C

• An increase to A leads B to be less than it otherwise would have been

• B being lower than it otherwise would have been causes C to be higher than it otherwise would have been

• (compared to what it otherwise would have been)

(8)

Tips

• Variables will often be noun phrases • Variables should be at least ordinal • Variables should be at least ordinal

• Links should have unambiguous polarity • Indicate pronounced delays

• Avoid mega-diagramsg g • Label loops

• Distinguish perceived and actual situation • Distinguish perceived and actual situation • Incorporate targets of balancing loops

• Try to stick to planar graphs

(9)

Ambiguous Link

• Ambiguous Link: Sometimes + sometimes -Ambiguous Link: Sometimes +, sometimes

Rate of Weight G i

Food intake _{Energy Surplus}

• Replace this by disaggregating causal

Gain e gy Su p us

+

pathways by showing multiple links

Rate of Weight G i

Food intake Energy Surplus Calories Taken in + + Gain Basal Metabolism e gy Su p us Calories Burrt + ₊ -+

(10)

Example 2

• Ambiguous Link: Sometimes + sometimesAmbiguous Link: Sometimes +, sometimes – _Overtime Work Accomplished

per Day

+

th b h i lti l li k

Fatigue

+

Overtime

Greater Incorporation of Outside Tasks at Work

Efficiency + + --Work Accomplished per Day + + More Time Working +

(11)

Example 3

• Ambiguous Link: Sometimes + sometimes -Ambiguous Link: Sometimes +, sometimes

Proportion of Fat

Calories Ingested

in Foods Calories Ingested

Proportion of Fat in Foods

Diet Caloric

Density _{Calories Ingested}

+ ₊

+ in Foods

Satiety Amount of Food

Eaten

+

(12)

Feedback Loops

• Loops in a causal loop diagram indicate

f db k i th t b i t d

feedback in the system being represented

– Qualitatively speaking, this indicates that a

i h ki k ff t f h th t

given change kicks off a set of changes that cascade through other factors so as to either amplify (“reinforce”) or push back against

amplify ( reinforce ) or push back against (“damp”, “balance”) the original change

• Loop classification: product of signs in • Loop classification: product of signs in

loop (best to trace through conceptually)

Balancing loop: Product of signs negative – Balancing loop: Product of signs negative – Reinforcing loop: Product of signs positive

(13)

Example Vicious/Virtuous Cycles

• Positive (“reinforcing” “amplifying”) feedbackPositive ( reinforcing , amplifying ) feedback can lead to extremely rapid changes in situation

# of Infectives # New Infections + + Weight Perceived Individual Target Weight + # of Activated g as Normal Mean Weight in Population + + Prevalence of Ob i Prevalence of GDM + + # of Activated Memory Cells + + Obesity Prevalence of Macrosomic Infants + # of Clonal Expansions

(14)

Example “Balancing Loops”

Example Balancing Loops

• Balancing (“regulatory”, “negative

feedback”) loops tend to be self regulating feedback ) loops tend to be self-regulating

# New Infections # of Susceptibles -+ Food Ingested Policy

Mistakes Learning from Mistakes + Food Ingested + -Policy Reevaluation Adaptation + -Hunger + Policy Effectiveness +

(15)

-Best Practice:

Incorporating Thresholds

• Balancing loops tend to be self-regulatingBalancing loops tend to be self regulating

ad to Threshold Hunger to Motivate Eating Policy Reevaluation + Food Ingested Reevaluation Policy Adaptation -+ -Policy Effectiveness + T h ld f P li Hunger

Treshold for Policy Dissatisfaction to Lead to

(16)

Best Practice:

Indicating (Pronounced) Delays

• Balancing loops tend to be self-regulatingBalancing loops tend to be self regulating

Policy Reevaluation + Threshold Hunger to Motivate Eating Policy Policy Adaptation + - Food Ingested Policy Effectiveness Treshold for Policy

+

-y Dissatisfaction to Lead to

(17)

Elaborating Causal Loops

Prevalence of GDM + Creation of Nutrition Prevalence of Obesity G + Creation of Nutrition and Exercise Programs

+ -# of Infectives + Prevalence of Macrosomic Infants + Study of Obesity + # N I f ti + + # New Infections -+ # of Susceptibles +

(18)

More Elaborate Diagrams

(19)

More Elaborate Diagrams 2

(20)

Causal Loop Structure : Dynamic Implications

• Each loop in a causal loop diagram is

associated with qualitative dynamic behavior

behavior

• Most Common Single-Loop Modes of

D i B h i

Dynamic Behavior

– Exponential growth

– Goal Seeking Adjustment – Oscillation

• When composed, get novel behaviors due

to shifting loop dominance

– Behaviour of system more than sum of parts

(21)

CL Dynamics: Exponential Growth

(Fi t O d R i f i L )

(First Order Reinforcing Loop)

• Example # of Infectives _{Individual Target}

+ Example + + Weight Perceived as Normal g Weight + + +

# New Infections Mean Weight inPopulation

+

(22)

CL Dynamics: Goal Seeking (B l i L ) (Balancing Loop) • Example: _d _d ad to Threshold Hunger to Motivate Eating

Example: _{Food Ingested}

• Dynamic behavior Hunger

+

(23)

-Causal Loop Dynamics: Oscillation

(B l i L ith D l )

(Balancing Loop with Delay)

• Causal StructureCausal Structure

(24)

Growth and Plateau

• Loop structure: Potential Existing Users

Likelihood of Cross Listing and Listing on Search

Engines +

Loop structure:

– Reinforcing Loop

Balancing Loop Word of

Customers -+ -Engines New Users Discovering Site + + – Balancing Loop D i B h i Mouth Sales Customers + + +

Internet Users Yet to Discover Site

-• Dynamic Behavior:

Graph for Customer 100,000 75 000 75,000 50,000 25,000 From Tsai 0 0 10 20 30 40 50 60 70 80 90 100 Time (Month) Customer : Current

(25)

Complexities & Regularities

Department of Computer Science

(26)

Feedbacks Driving Infectious

Disease Dynamics

S u s c e p t ib le s + C b + -N e w I n f e c t io n s C o n t a c t s b e t w e e n S u s c e p t ib le s a n d I n f e c t iv e s + I n f e c t iv e s + + -N e w R e c o v e r ie s

(27)

Example Dynamics of SIR Model

(No Births or Deaths)

SIR Example 2,000 people 600 people 10,000 people 1,500 people 450 people 9,500 people 1,000 people 300 people 9,000 people 500 people 150 people 8,500 people 0 people 0 people 0 people 8,000 people 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 Time (days)

Susceptible Population S : SIR example people

Infectious Population I : SIR example people

(28)

Shifting Feedback Dominance

SIR Example 2,000 people 600 people 10,000 people S u s c e p t ib le s + 1,500 people 450 people 9,500 people N e w I n f e c t io n s o n t a c t s b e t w e e n S u s c e p t ib le s a n d I n f e c t iv e s I n f e c t iv e s + + + -+ -1,000 people 300 people 9,000 people S u s c e p t ib le s N e w I n f e c t io n s C o n t a c t s b e t w e e n S u s c e p t ib le s a n d I n f e c t iv e s + -+ N e w R e c o v e r ie s S u s c e p t ib le s N e w I n f e c t io o n t a c t s b e t w e e n S u s c e p t ib le s a n d I n f e c t iv e s + -+ 500 people 150 people 8,500 people 0 people I n f e c t iv e s I n f e c t iv e s + + N e w R e c o v e r ie s + -I n f e c t iv e s I n f e c t iv e s + + N e w R e c o v e r ie s + -0 people 0 people 8,000 people 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 Time (days)

(29)

Shifting Feedback Dominance

SIR Example 2,000 people 600 people 10,000 people S u s c e p t ib le s + 1,500 people 450 people 9,500 people N e w I n f e c t io n s o n t a c t s b e t w e e n S u s c e p t ib le s a n d I n f e c t iv e s I n f e c t iv e s + + + -+ -1,000 people 300 people 9,000 people S u s c e p t ib le s N e w I n f e c t io n s C o n t a c t s b e t w e e n S u s c e p t ib le s a n d I n f e c t iv e s + -+ N e w R e c o v e r ie s S u s c e p t ib le s N e w I n f e c t io o n t a c t s b e t w e e n S u s c e p t ib le s a n d I n f e c t iv e s + -+ 500 people 150 people 8,500 people 0 people I n f e c t iv e s I n f e c t iv e s + + N e w R e c o v e r ie s + -I n f e c t iv e s I n f e c t iv e s + + N e w R e c o v e r ie s + -0 people 0 people 8,000 people 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 Time (days)

(30)

Common Phenomena In Complex Systems

• Counter-intuitive behaviour

(Often the result of interactions between feedbacks [fb])

• Snowballing: When things go bad, they often go very bad very

q ickl quickly

– “Vicious cycles” lead to “cascading” of problems

(Due to positive feedback) (Due to positive feedback)

– “Path dependence”: Different starting points can lead to divergence in project progress

(Due to positive feedback interacting w/ mult. negative fb)

• Policy resistance: Situation can be unexpectedly difficult to change

change

(Typically due to negative feedbacks that resist change)

• Lock-in: Waiting raises barriers to improvementLock in: Waiting raises barriers to improvement

(31)

Issues with Causal Loop

Diagrams

• Unclear variablesUnclear variables

• Diagrams can become very large

C f i di l it

• Confusion regarding polarity • Non-causal relationship

• Conservation not captured

• Behavior not always same as archetypeBehavior not always same as archetype • Missing causal factors

Mi i li k

• Missing links

(32)

Unclear Variables

Variables Lacking Clear

Polarity Implicit Polarity Polarity

• Gender • Ethnicity

Implicit Polarity

• Population (size)

• Revenue (amount of) Ethnicity

• Shape

Often categorical &

non-Revenue (amount of) • Sound, Color (more of) • Socioeconomic status

ordinal

A k h th “ X” i

(greater, lesser) • Ask whether “more X” is

– Meaningful – Unambiguous

(33)

Very Large Diagrams

http://kim.foresight.gov.uk/Obesity/Obesity.html

Still useful for getting “big picture”

(34)

(35)

(36)