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Modeling Causal Interaction Between Human Systems and Natural Systems. Sara Friedman Santa Fe Institute 2002 REU Program University of California, Berkeley. Motivation:. Fundamental natural processes are cyclic (e.g. topsoil maintenance)
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Modeling Causal Interaction Between Human Systems and Natural Systems
Santa Fe Institute 2002 REU Program
University of California, Berkeley
Graphical Models and Causal State Theory
Feedback Between Human Behavior and Environmental Quality
Creating Sustainable Causal Cycles Between Human Systems and Natural Systems
(Renewable resource base)
Question: Under what conditions do the altruists take over and maintain patch productivity?
Frequency of A’s: P
Average Payoff: W
Initial Patch Productivity: Kzero = 100
Direct Dependence of W on K: B=1
Exploitation factor of an N: X=0.05
Growth increment of patches: k=0.3
Number of patches/groups: m=10
Individuals per group: n=10
Global updating percentage: g=0.8
Idiosyncratic updating rate: mut=0.5
Number 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?!Model Definitions and Equations
Nearly Inevitable Crashes Problem! How to fix this?…
N-dominant patches will be replaced by the offspring of A-dominant groups, and between-group variance will increase
Random assortation with colonization
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.
Each histogram represents 200 runs, under default parameter conditions, except global updating and group size varying as stated.
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.
And now for the big picture…
Paolo Patelli, Bae Smith, and Dave Krakauer
Santa Fe Institute