Adaptive management

• AM is about learning to manage DYNAMIC systems more effectively

• There are two kinds of AM:– Passive (certainty equivalent): assumes

statistical estimation performance is independent of policy choice

– Active (dual effect of control): assumes estimation performance depends on policy (policy “probes for opportunity”)

Apparently some people never learn: the sad history of the

Cheasapeake Bay oyster fishery

(from Rothschild et al MEPS 1994)

History of AM

• Ecosystem modeling workshops, 1970• AEAM workshop process, 1972-74• Dual control problem (experiments), 1976• Many case studies using AEAM workshop

process 1976-2000• Split in AM definition (experimentation versus

consensus building) 1990• Recognition of very high failure rates for case

studies and the IBM debate (modeling vs experimentation), 1997

The prototype adaptive management problem: Fraser River sockeye salmon

• Limited range of historical experience

• Rationalizer model that “explains” past management (ƞ1)

• Possible opportunity (ƞ2) for improvement, need “probing” management experiment to test

From Walters and Hilborn 1976

Decision tables for stock rebuilding experiments Rationalizer model correct (Ricker)

Opportunity model correct (Beverton-Holt)

Maintain current management policy

Modest harvest value maintained

Modest harvest value maintained

Conduct probing experiment

Loss during experiment, followed

by modest value when experiment ended

Initial loss followed by long term gain in value if experiment done for

long enough

Surprise and opportunity: unexpected results from the Fraser sockeye

experimentKvichak Sockeye

0

5000

10000

15000

20000

25000

30000

1955 1965 1975 1985 1995

spaw

ner

s (m

illi

on

s)

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

Pro

du

ctiv

ity

(lo

g r

ecru

its/

spaw

ner

)Spawning escapement

Productivity (lnR/S)

Quesnel Sockeye

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

1950 1960 1970 1980 1990 2000

Spaw

ners

(mill

ions

)

-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

Prod

uctiv

ity (l

og

Rec

ruits

/Spa

wne

r)

Spawners

Productivity (lnR/S)

Late Shuswap Sockeye

0.00

1.00

2.00

3.00

4.00

5.00

6.00

1950 1960 1970 1980 1990 2000

Sp

awn

ers

(mil

lio

ns)

-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

Pro

du

ctiv

ity

(lo

g

Rec

ruit

s/S

paw

ner

)

Spawners

Productivity (lnR/S)

But these effects are not seen in stocks for which escapement has not increased, i.e. effects are not due to shared environmental factor(s):

Other AM examples

• Hatchery impact on wild coho stocks(alternating hatchery releases)

• Restoration of endangered humpback chub, Grand Canyon(exotic predator control, warm water)

• Impacts of line fishing on Great Barrier Reef fish communities(rotating openings and closures)

Need for actively adaptive policies

• Learning rates generally do depend on policy choice, since responses are generally regression relationships

• Not all “probing” policies are worth testingpolicy

response

Experimental design choices in AM

• Only BA (before-after) comparisons are available for large, unique systems

• For spatially structured systems, “pilot experiments” can be used on representative local areas– CI (control-impact) comparisons assume control sites

are good predictors of how impacted sites would have behaved

– BACI (before-after control-impact) comparisons let us control for time effects that may affect all sites

BACI design treats Control sites as models for how Impacted sites

would have behaved if not treated

Time

Time series measure

Treated site data

Control site data

Predicted treated site data

There is no scientific way to say with certainty how any treated system would have behaved if it had not been treated (we can never both treat and not treat a system at the same time).

We can only gain reassurance that an apparent response was not caused by something besides treatment by repeating the treatment over and over and looking for similarities in responses; that is what is meant by “replication” (replicates are NOT identical experimental units).

Dynamic systems are nasty

• BA experiments ALWAYS lead to debate about effect of treatment versus other changes observed after treatment

• CI comparisons fail when there is selection bias (eg marine protected areas vs nearby fished areas), and/or divergent natural behavior

• BACI designs do not control for time-treatment interactions

Confounding of effects in before-after comparisons: nature does not give

unambiguous contrasts among causal factors

• Native fish abundances in the Grand Canyon have increased dramatically since 2003.

• Was this caused by “mechanical removal” of predatory trout, or by increases in water temperature?

8

9

10

11

12

13

14

15

16

17

18

1990 1995 2000 2005 2010

Year

Te

mp

era

ture

(o

C)

0

0.5

1

1.5

2

2.5

3

Ra

inb

ow

tro

ut

rela

tiv

e c

atc

h

pe

r e

ffo

rt

Temperature

Trout catch per effort

Time-treatment interactions

• If a treated experimental unit shows some undesired response compared to control, should we assume the response was due to treatment?

• Proponent of the policy represented by the experimental treatment can simply argue that treated units respond differently to temporal forcing factors than do untreated units

time

response

C

T

Staircase experimental designs

• Instead of comparing treated to untreated units, compare units treated at different starting times

• Does the “shape” of the treatment response change over time, i.e. does it depend on the time when treatment started?

time

response

C

T

Staircase experimental designs

General Linear Model (GLM) approach to analysis:

Yit=μi + Tt + Rt-ti + eit

Unit effectError

Time since treatment effectTime effect

1 32 4 5 6 7 81 2

13 4 5 6 72 3 4 5 6Unit 4

Unit 3Unit 2Unit 1

1 2 3 4 5 6 7 8 9 Time (t)

Study unit (i)

What is the average effect of time since treatment, over possible times of treatment?

Adaptive management experiments

• Expensive because of need to control for complex time dynamic effects

• Risky because responses may be the opposite of expected

• Require innovative monitoring approaches (e.g. cooperation with stakeholders, use of technologies with high initial capital cost).

Finding optimum adaptive policies

• For simple models, we can do this with “stochastic dynamic programming”

• The basic idea is to represent total value from time t into the future, Vt, as a sum of two components:

Vt = vt + Vt+1

Want highest value of this

Value this year, depends on(1) Stock this year(2) Stock left to breed

Future value, depends on(1) Stock left to breed(2) Natural disturbances(3) Information gained about

effect of breeding stock onproduction

There is a tradeoff among the value components

Stock left to breed this year

Value componentsVt, Vt+1

Vt+1 (future value)

Vt (immediate value)

Dynamic programming tests each possible breeding stock size to find the best choice, with Vt+1 averaged over possible future disturbances

Modeling dynamics of learning using Bayes Theorem

)(

)|()()(

1

1

NP

hypNPhypPhypP

t

tt

hyp

tt hypPhypNPNP )()|()( 11

Where Pt-1(N) is the “probability of the data:

Suppose N fish are observed in year t. Then:

Note that differences in predicted N among the hypotheses are represented by different P(N|hyp) distributions.

In dynamic programming for adaptive management, both N and the probabilities Pt(hyp) are treated as dynamic state variables.