1. Introduction Management model: fisheries Decision Theory Resilience Thinking
UNKNOWN UNKNOWNS:
MANAGEMENT
UNDER UNCERTAINTY
& ALTERNATE
STABLE STATES
@cboettig
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 1/33

2. Introduction Management model: fisheries Decision Theory Resilience Thinking
Decision Resilience
Theory Thinking
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 2/33

3. Introduction Management model: fisheries Decision Theory Resilience Thinking
1 Introduction
2 Management model: fisheries
3 Decision Theory
4 Resilience Thinking
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 3/33

4. Introduction Management model: fisheries Decision Theory Resilience Thinking
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 4/33

5. Introduction Management model: fisheries Decision Theory Resilience Thinking
Building blocks
State Space
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 5/33

6. Introduction Management model: fisheries Decision Theory Resilience Thinking
Building blocks
State Space
Action (Decision) Space
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 5/33

7. Introduction Management model: fisheries Decision Theory Resilience Thinking
Building blocks
State Space
Action (Decision) Space
Ecological model (State
equation)
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 5/33

8. Introduction Management model: fisheries Decision Theory Resilience Thinking
Building blocks
State Space
Action (Decision) Space
Ecological model (State
equation)
Socio-economic model
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 5/33

9. Introduction Management model: fisheries Decision Theory Resilience Thinking
Building blocks
State Space
Action (Decision) Space
Ecological model (State
equation)
Socio-economic model
Value function
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 5/33

10. Introduction Management model: fisheries Decision Theory Resilience Thinking
Building blocks
State Space
Action (Decision) Space
Ecological model (State
equation)
Socio-economic model
Value function
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 5/33

11. Introduction Management model: fisheries Decision Theory Resilience Thinking
State space | Action space
Fish stock size
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 6/33

12. Introduction Management model: fisheries Decision Theory Resilience Thinking
State space | Action space
Fish stock size
x
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 6/33

13. Introduction Management model: fisheries Decision Theory Resilience Thinking
State space | Action space
Fish stock size Fishing harvest intensity
x
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 6/33

14. Introduction Management model: fisheries Decision Theory Resilience Thinking
State space | Action space
Fish stock size Fishing harvest intensity
x h
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 6/33

15. Introduction Management model: fisheries Decision Theory Resilience Thinking
Ecological model | Economic Model
Stock recruitment function
Xt+1 = Zn f (Xn )
Beverton-Holt
Ax
f (x) =
1 + Bx
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 7/33

16. Introduction Management model: fisheries Decision Theory Resilience Thinking
Ecological model | Economic Model
Profit equation
Stock recruitment function
π(x, h) = p min(x, h)
Xt+1 = Zn f (Xn )
h h
− c0 + c1
Beverton-Holt x x
Ax
f (x) = p price of fish
1 + Bx
c0 , c1 costs
Bellman’s Value function
Vt = max Th Vt+1 + π(xt , ht )e−δ(T −t) (1)
h
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 7/33

17. Introduction Management model: fisheries Decision Theory Resilience Thinking
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 8/33

18. Introduction Management model: fisheries Decision Theory Resilience Thinking
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 9/33

19. Introduction Management model: fisheries Decision Theory Resilience Thinking
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 10/33

20. Introduction Management model: fisheries Decision Theory Resilience Thinking
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 11/33

21. Introduction Management model: fisheries Decision Theory Resilience Thinking
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 12/33

22. Introduction Management model: fisheries Decision Theory Resilience Thinking
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 13/33

23. Introduction Management model: fisheries Decision Theory Resilience Thinking
Decision Resilience
Theory Thinking
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 14/33

24. Introduction Management model: fisheries Decision Theory Resilience Thinking
What could go wrong?
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 15/33

25. Introduction Management model: fisheries Decision Theory Resilience Thinking
What could go wrong?
f (x) has some stuctural
uncertainty
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 15/33

26. Introduction Management model: fisheries Decision Theory Resilience Thinking
What could go wrong?
Policy makers don’t listen to
mathematically optimal
strategies
f (x) has some stuctural
uncertainty
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 15/33

27. Introduction Management model: fisheries Decision Theory Resilience Thinking
Resilience thinking approaches
Early warning signals of
tipping points
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 16/33

28. Introduction Management model: fisheries Decision Theory Resilience Thinking
Resilience thinking approaches
Early warning signals of Considering key
tipping points stakeholders
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 16/33

29. Introduction Management model: fisheries Decision Theory Resilience Thinking
Abandon decision theoretic approaches?
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 17/33

30. Introduction Management model: fisheries Decision Theory Resilience Thinking
Abandon decision theoretic approaches?
No! Synthesize resilience concepts with
decision theories. . .
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 17/33

31. Introduction Management model: fisheries Decision Theory Resilience Thinking
Sometimes hard to identify the “increase” signal
Carpenter et al. 2011
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 18/33

32. Introduction Management model: fisheries Decision Theory Resilience Thinking
Decision theory needs probabilities, not possibilities
Boettiger &
Hastings
2012
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 19/33

33. Introduction Management model: fisheries Decision Theory Resilience Thinking
Decision theory needs probabilities, not possibilities
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 20/33

34. Introduction Management model: fisheries Decision Theory Resilience Thinking
Decision theory needs probabilities, not possibilities
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 21/33

35. Introduction Management model: fisheries Decision Theory Resilience Thinking
Policy Costs
Policy makers don’t listen to mathematically optimal strategies?
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 22/33

36. Introduction Management model: fisheries Decision Theory Resilience Thinking
Socio-economic optimum strategy
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 23/33

37. Introduction Management model: fisheries Decision Theory Resilience Thinking
Socio-economic optimum strategy
Reality: typical policy
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 23/33

38. Introduction Management model: fisheries Decision Theory Resilience Thinking
There is a cost to changing policy
we can
model that. . .
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 24/33

39. Introduction Management model: fisheries Decision Theory Resilience Thinking
Adding costs to changing policy
ΠL1 (xt , ht , ht−1 ) = Π0 + c2 abs (ht − ht−1 ) (2)
2
ΠL2 (xt , ht , ht−1 ) = Π0 + c2 (ht − ht−1 ) (3)
Πfixed (xt , ht , ht−1 ) = Π0 + c2 I(ht , ht−1 ) (4)
Πasym (xt , ht , ht−1 ) = Π0 + c2 max (ht − ht−1 , 0) (5)
Where I(a, b) = 0 for a = b and I(a, b) = 1 for a = b.
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 25/33

40. Introduction Management model: fisheries Decision Theory Resilience Thinking
Previous Action becomes part of state-space
s Action
Previou
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 26/33

41. Introduction Management model: fisheries Decision Theory Resilience Thinking
Cost-free
optimum
Optimum
under policy
costs
Cost-free
stock
Stock under
policy costs
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 27/33

42. Introduction Management model: fisheries Decision Theory Resilience Thinking
Cost-free
optimum
Optimum
under policy
costs
Cost-free
stock
Stock under
policy costs
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 27/33

43. Introduction Management model: fisheries Decision Theory Resilience Thinking
Cost-free
optimum
Optimum
under policy
costs
Cost-free
stock
Stock under
policy costs
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 28/33

44. Introduction Management model: fisheries Decision Theory Resilience Thinking
Cost-free
optimum
Optimum
under policy
costs
Cost-free
stock
Stock under
policy costs
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 28/33

45. Introduction Management model: fisheries Decision Theory Resilience Thinking
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 29/33

46. Introduction Management model: fisheries Decision Theory Resilience Thinking
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 30/33

47. Introduction Management model: fisheries Decision Theory Resilience Thinking
Ignoring political realities leads to worse solutions
Reducing policy costs results in better management
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 31/33

48. Introduction Management model: fisheries Decision Theory Resilience Thinking
Conclusions
Decision theory provides a quantitative way to address
policy choices under uncertainty
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 32/33

49. Introduction Management model: fisheries Decision Theory Resilience Thinking
Conclusions
Decision theory provides a quantitative way to address
policy choices under uncertainty
But: traditional framework ignores key possibilities that
aren’t probabilities
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 32/33

50. Introduction Management model: fisheries Decision Theory Resilience Thinking
Conclusions
Decision theory provides a quantitative way to address
policy choices under uncertainty
But: traditional framework ignores key possibilities that
aren’t probabilities
Modeling approaches can sometimes quantify these, and
identify when they matter most
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 32/33

51. Introduction Management model: fisheries Decision Theory Resilience Thinking
Conclusions
Decision theory provides a quantitative way to address
policy choices under uncertainty
But: traditional framework ignores key possibilities that
aren’t probabilities
Modeling approaches can sometimes quantify these, and
identify when they matter most
More synthesis of resilience thinking and decision theory is
needed!
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 32/33

52. Introduction Management model: fisheries Decision Theory Resilience Thinking
Conclusions
Decision theory provides a quantitative way to address
policy choices under uncertainty
But: traditional framework ignores key possibilities that
aren’t probabilities
Modeling approaches can sometimes quantify these, and
identify when they matter most
More synthesis of resilience thinking and decision theory is
needed!
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 32/33

53. Introduction Management model: fisheries Decision Theory Resilience Thinking
Acknowledgements
Image credits
NOAA
Millennium Ecosystem Assessment
flickr users gfpeck, saneboy, tranchis
Boettiger et al 2012
Scheffer et al. 2001
Code, lab notebook, and more:
http://carlboettiger.info/
Carl Boettiger, UC Davis cboettig@ucdavis.edu Management under uncertainty 33/33