Transcript Uncertainty and Decision Making - School of Environmental and

Uncertainty and Decision Making
 Presence of uncertainty is one of the most
significant characteristics of environmental
management decisions
– Statistical errors and burden of proof (NRC chap. 8, 9)
– Assessing threat and conservation priorities (Todd and
Burgman 1998)
– Managing Kirtland’s warblers in the face of
environmental uncertainty (Marshall et al. 1998)
 Adaptive Management is one way to
increase certainty over time
Uncertainty (Todd and Burgman 1998)
 Statistical uncertainty
 Subjective judgement
 Systematic error
 Incomplete knowledge
 Temporal variation
 Inherent stochasticity
 MOST CONSERVATION DECISIONS
IGNORE IT
Statistical Uncertainty
 Type I error: probability of rejecting Ho
when Ho is actually true
– scientist’s set this low so as to rarely incorrectly
reject hypotheses and therefore slow or confuse
the progress of science (=0.05)
 Type II error: probability of not rejecting
the Ho when it is actually false
– usually high because high precision (large
sample size) is needed to reduce it and as type I
error is reduced type II error increases
Power---the tradeoff between Type I
and Type II error
 Power = 1-  ( = probability of type II error)
– probability of correctly rejecting the Ho
– increases with increasing Type I error
– increases with increasing precision (N)
1.2
High Precision
(cv=.1)
1
Power
0.8
Medium
Precision
(cv=.3)
Low Precision
(cv=.8)
0.6
0.4
0.2
0
0.05
0.2
0.3
0.4
0.5
Probability of Type I error
Trading Off Type I and Type II Error
in Biological Terms (Noss 1992)
 Type I Error
– Reject true Ho
– Claim an effect when
none exists
– Protect more species
than necessary
– Lose scientific
credibility
– Increase
socioeconomic costs
more than necessary
 Type II error
– Accept false Ho
– Claim no effect when
one exists
– Protect species less
than necessary
• may loose species
– Lose practical and
scientific credibility
– Permit activities that
should not have been
approved
Burden of Proof
 Who has to demonstrate convincingly that a
conservation action is needed?
– Minimize type I error means burden of proof is
on the party trying to conserve a species
• cost of incorrectly concluding there is a problem
(Type I) is greater than cost of incorrectly
concluding there is not a problem (Type II)
– Poor Information on status of species reduces
power and increases Type II error
• burden of proof is again on the conservationist
Do We Just Minimize Type II
Error?
 Simple shifting of burden of proof from
conservationists to resource users
– Unnecessary socioeconomic hardship?
 Need to explicitly consider what shifting
burden of proof means for conservation and
then argue the prudent route
 Precautionary Principle
– better to err on side of caution when effect is
not reversible
• EXTINCTION
Formal Evaluation of
Uncertainty
 Kirtland’s warblers (Marshall et al. 1998)
 Want to minimize costs of management
(maximize timber harvest return) while
keeping P(N<S)<
– N is pop size at end of management
– S is population size the manager wants (target)
– 1- = “margin of safety”
• recognizes that management is not certain
– probability quantifies our uncertainty of hitting S
Margin of Safety
 If we want to only undershoot our target 5%
of the time then we have a 95% “margin of
safety”
 Increasing the margin of safety, means
reducing the chances of undershooting our
target
– This costs money!
– For Kirtlands’ warblers it means harvest less
timber so you are sure you wont’t end up with
too few warblers
Costs of “Safety”
 Safety costs because of uncertainty:
– we are not sure what warbler population will do
without management (environmental and
demographic stochasiticity)
– we are not sure what the forest will do (growth
models)
– we are not sure how warblers will respond to
forest management (habitat suitability models)
Quantifying the Costs
Cost (Millions of $)
 Increasing from a 90% to 99%
16
14
12
10
8
6
4
2
0
90
95
Safety Margin
99
margin of safety doubles the
costs (reduces harvest)
 Less certainty means you have
to be especially conservative in
resource management which
costs more (less resource
removed)
 Irreversible effects (extinction)
command greater safety
margins
Including Uncertainty (Todd and
Burgman 1998)
 Rather than using a simple point estimate
for a variable, you can encode variation in
the variable and combine variation among
several variables using FUZZY SET
THEORY
 Estimate of population size
– point is mean of 550
– fuzzy set used to calculate likelihood of
membership in population of 0 - 10,000
• cumulative probability distribution using SE
Fuzzy Sets
Variable
Point =
550
Point=
70
1. Population Size
(a) 0-500
(b) 501-1000
(c) 1001-3000
(d) 3001-10,000
(e) 10,001-50,000
(f) >50,000
3. Range Size (Km2)
(a) <100
(b) 101-1000
(c) 1001-40,000
(d) 40,001-100,000
(e) 100,001-2,000,000
(f) >2,000,000
Points
Degree of
Membership
10
8
6
4
2
0
.526
.379
.091
.003
0
0
10
9
7
4
1
0
.55
.45
0
0
0
0
Fuzzy Sets
define a range
of likely values
rather than
just a point
estimate
Degree of Membership
 Can be from a
cumulative
probability
distribution
1
.526
– Population Size
• SE=300
 Can be assigned by
expert opinion
– Degree of “belief”--Range Size
• could be up to
900km2
0
500
Population Size
Combination of Fuzzy Sets
 Can take unions and intersections just like
with crisp sets
 Intersection gives degree of membership in
both outcomes
Most Likely
given
uncertainty
Point
Estimate
Outcome
1a ∩ 3a
1a ∩ 3b
1b ∩ 3a
1a ∩ 3b
1c ∩ 3a
1c ∩ 3b
1d ∩ 3a
1d ∩ 3b
Degree of Membership
.526
.45
.379
.379
.091
.091
.003
.003
Score
20
19
18
17
16
15
14
13
Adaptive Management
Recognizes That Managers Need to Work
Before Mechanisms are Understood
Solutions for Many of Wildlife Science’s Current Shortcomings
Relevant
Spatial
and Temporal
Scale
Hypotheticodeductive
Methods
Long-term
Research
Validation via
Monitoring
Increased ManagerResearcher Partnerships
Benefits and Compromises of
Adaptive Management
Management
Increase Area for
Humans and
Wildlife Value
Hypothesis
Development
Research
Test
Alternative
Hypotheses
Compromise
Short-term
Performance
by Implementing
Some Poor
Maximize
Alternatives
Wildlife Population
Viability and
Urban
Development
Learn How to
Provide Habitat
Effectively and
Efficiently
Compromise
Statistical Rigor
But Gain Scale
Sensitivity
and Relevance
Summary
 Uncertainty is a certainty
 We usually deal with it by minimizing type I error
 Need to lay out the implications to conservation of
type I versus type II error
 May be able to incorporate uncertainty in the
decision making process by modeling stochasticity
(PVAs and the warbler example) or combining
information with fuzzy set statistics
 Adaptive Management may allow refinement of
management techniques as uncertainty is reduced
References
 Marshall, E., Haight, R. and F. R. Homans. 1998. Incorporating
environmental uncertainty into species management decisions:
Kirtland’s warbler habitat management as a case study. Cons. Biol.
12:975-985.
 Todd, C.R. and M. A. Burgman. 1998. Assessment of threat and
conservation priorities under realistic levels of uncertainty and
reliability. Cons. Biol. 12:966-974.
 Noss, R. F. 1992. Biodiversity: many scales and many concerns. Pp1722 in Kerner, H. F. (ed.) Proceedings of the symposium on biodiversity
of northwestern california.