Modeling Causal Interaction Between Human Systems and Natural Systems Sara Friedman Sara Friedman Santa Fe Institute 2002 REU Program University of California,

Modeling Causal Interaction

Between Human Systems and

Natural Systems

Sara FriedmanSara Friedman

Santa Fe Institute 2002 REU ProgramSanta Fe Institute 2002 REU Program

University of California, BerkeleyUniversity of California, Berkeley

Motivation:

• Fundamental natural processes are cyclic (e.g. topsoil maintenance)

• Acyclic or unidirectional causal models are unrealistic in terms of describing our interaction with natural systems

• How can we represent cyclic causal chains, and predict effects of interventions?

Presentation Outline• Existing mathematical causal theories:

Graphical Models and Causal State Theory

• Simulating a mutual causal process:Feedback Between Human Behavior and Environmental

Quality

• Conclusion:Creating Sustainable Causal Cycles

Between Human Systems and Natural Systems

• Related reading and acknowledgements

• No unified theory – large field encompassing many applications, approaches and formalisms

• Definitions and theorems rely on DAGs for underlying structure (no recursion or feedback)

Graphical Models of Causality

Causal State Theory

• Mathematically embodies Occam’s Razor: causal states are minimally complex while maximally predictive

• Very abstract – doesn’t use intuitive notion of “causal factors”, role of interventions is unclear – BUT

• Innovative, rigorous, still in early stages of development

Summary of Causal Theories

• Lots of insights, clever discovery algorithms and useful applications to everything from machine learning to epidemiology

• At present, no unified general approach to mathematically describing causation

• Need: Rigorous theory to analyze real world policy issues involving cyclic causal chains

Back to the issue at hand…

• Interaction between human and natural systems is complex and involves factors which mutually affect each other (human behavior and environmental quality).

• How to model this type of process?

• What insights can the model give us regarding effects of interventions?

Simulate Feedback EffectsHuman Culture

(Prosociality/Restraint)

Ecosystem Function

(Renewable resource base)

Question: Under what conditions do the altruists take over and maintain patch productivity?

Model Definitions and Equations• Patch Productivity: K• Altruists: A’s• Nonaltruists: N’s• Frequency of A’s: P• Average Payoff: W

Initial Patch Productivity: Kzero = 100Direct Dependence of W on K: B=1Exploitation factor of an N: X=0.05Growth increment of patches: k=0.3Number of patches/groups: m=10Individuals per group: n=10Global updating percentage: g=0.8Idiosyncratic updating rate: mut=0.5Number of time steps: time=200

• Payoff of an N on patch j:

WNj = B Kj (1 + X)

• Payoff of an A on patch j:

WAj = B Kj (1 + 0)

• Productivity of Patch j at time t:

Kj(t) = Kj

(t-1) [1– (Nj(t-1) X)](1+k)

Note: Nj(t-1) is the number of N’s in j at t-1

• Replicator Dynamic for t t+1:

Pj = Pj (1-Pj) (WAj – WNj) / Wj

Notice: since X > 0, ΔPj < 0 for all j

How will the A’s ever survive?!

Without global updating or other group-level effects:

Nearly Inevitable Crashes Problem! How to fix this?…

Group-Level Effects

Random assortation with colonization

• Extinctions: If megapatch is degrading, extinctions become very likely on the least productive patches. Dead patches revitalize to prevailing megapatch average productivity, and colonization occurs, probably by a group with relatively high average payoff.

Consequence:

N-dominant patches will be replaced by the offspring of A-dominant groups, and between-group variance will increase

• Institutions: Individuals in group j decide to do global updating or not en masse at each time step.Consequence: the replicator dynamic could actually increase the A’s: (WA – WN) >? 0

ResultsThis run with default parameters and group-level effects shows how feedback can create homeostatic-like dynamics. Also, stochasticity (i.e. luck) had major effects on outcomes; the initial distribution of altruists set important conditions for the degree of between-group variance relative to within-group variance.

Did it work? Will the A’s (and the megapatch) survive?…

Group Size and Global Updating were Key Parameters

• Small n increased between-group variance relative to within-group variance, augmenting the influence of both group-level effects: extinctions and global updating.

• Global updating worked especially well when there were “ideal patches” (mostly altruists, high patch productivity) to copy, and additionally when most of the A’s lived on ideal patches. The “ideal patch” effect is an outcome of high between-group variance, relative to within-group.

Correlation of Total Altruist Frequency with Average Patch Productivity, Varying g & n

Each histogram represents 200 runs, under default parameter conditions, except global updating and group size varying as stated.

How do we know g and n were such important parameters?…

Conclusion: Altruists can do well with group level effects, when the differences between groups are more significant than the differences within the groups. Small groups who can see how people in other patches are doing will protect their resource base, more than large groups who don’t look globally as much.

But what does this really tell us?

• The model is extremely simple; the simulation was written in R. It is not spatial or agent-based, and fails to capture realistic patch-boundary or group-size dynamics.

BUT

• The process of simulating gives heuristic insights into dealing with causal cycles…

Cybernetic View of Model

And now for the big picture…

Creating Sustainable Causal Cycles Between Human & Natural Systems

• Interventions in cyclic causal chains have different effects over time (the nth time around) than they do initially. Directly applying interventions deduced from acyclic causal models to cyclic socio-ecological processes can potentiate maladaptive decisions.

• In a cyclic model, to control runaway or autocatalytic effects, look for links where the driving deviations are being amplified. Try to correct or compensate for the deviations rather than exaggerating them.

Related Reading• Sam Bowles & Astrid Hopfensitz, The Co-evolution of Individual Behaviors

and Social Institutions

• Jung-Kyoo Choi, Play Locally, Learn Globally: The Structural Basis of Cooperation

• Cosma Shalizi & Jim Crutchfield, Computational Mechanics: Pattern and Prediction, Structure and Simplicity

• Marcus Feldman & Kevin Laland, Gene-Culture Coevolutionary Theory

• Donald Grayson, The Archaeological Record of Human Impacts on Animal Populations

• Judea Pearl, Causality: Models, Reasoning, and Inference

• Peter Spirtes et al, Causation, Prediction, and Search

• Robert Edgerton, Sick Societies: Challenging the Myth of Primitive Harmony

• Simon Levin, Fragile Dominion: Complexity and the Commons

Thanks to: Sam Bowles

Jeff Brantingham

Cosma Shalizi

Jim Crutchfield

Paolo Patelli, Bae Smith, and Dave Krakauer

Santa Fe Institute

Dan Friedman

The End