Sara Friedman

1
Modeling Causal Interaction Between Human Systems
and Natural Systems

• Sara Friedman
• Santa Fe Institute 2002 REU Program
• University of California, Berkeley

2
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?

3
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

4
Graphical Models of Causality

• No unified theory large field encompassing
  many applications, approaches and formalisms
• Definitions and theorems rely on DAGs for
  underlying structure (no recursion or feedback)

5
Causal State Theory

• Mathematically embodies Occams Razor causal
  states are minimally complex while maximally
  predictive
• Very abstract doesnt use intuitive notion of
  causal factors, role of interventions is
  unclear BUT
• Innovative, rigorous, still in early stages of
  development

6
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

7
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?

8
Simulate Feedback Effects
Ecosystem Function (Renewable resource base)
Human Culture (Prosociality/Restraint)
Question Under what conditions do the altruists
take over and maintain patch productivity?
9
Model Definitions and Equations

• Patch Productivity K
• Altruists As
• Nonaltruists Ns
• Frequency of As P
• Average Payoff W
• Initial Patch Productivity Kzero 100
• Direct Dependence of W on K B1
• Exploitation factor of an N X0.05
• Growth increment of patches k0.3
• Number of patches/groups m10
• Individuals per group n10
• Global updating percentage g0.8
• Idiosyncratic updating rate mut0.5
• Number of time steps time200

• 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)?(1k)
• Note Nj(t-1) is the number of Ns in j at t-1
• Replicator Dynamic for t ? t1
• ?Pj Pj ? (1-Pj) ? (WAj WNj) / Wj
• Notice since X 0, ?Pj
• How will the As ever survive?!

10
Without global updating or other group-level
effects
Nearly Inevitable Crashes ? Problem! How to fix
this?
11
Group-Level Effects

• 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
Random assortation with colonization
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
As (WA WN) ? 0
12
Results
Did it work? Will the As (and the megapatch)
survive?
This 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.
13
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 As lived on ideal patches. The
  ideal patch effect is an outcome of high
  between-group variance, relative to within-group.

14
Correlation of Total Altruist Frequency with
Average Patch Productivity, Varying g n
How do we know g and n were such important
parameters?

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

15
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
dont look globally as much.
16
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

17
Cybernetic View of Model
And now for the big picture
18
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.

19
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

20
Thanks to
Sam Bowles Jeff Brantingham Cosma Shalizi Jim
Crutchfield Paolo Patelli, Bae Smith, and Dave
Krakauer Santa Fe Institute Dan Friedman
21
The End