Evaluation of harvest control rules (HCRs): simple vs. complex strategies
Dorothy Housholder
Harvest Control Rules WorkshopBergen, Norway
September 14, 2004
1. Introduction• Role of Models
2. Project Objective
3. Materials & Methods• Model Structure
4. Results & Discussion• General Simulation of HCRs• Specific Situation Simulation of HCRs
5. Conclusions
6. Future Work
Role of Models in Fisheries:
• Create
• Compare
• Simulate
• Evaluate
StochasticityStochasticity (randomness and uncertainty) needed in needed in fish population dynamicsfish population dynamics
No model can accurately describe a biological process
management strategies in a mathematical
computer environment
Model should be slowly built up to a certain point…
PROBLEM:Need for better
fisheries management
HARVESTCONTROL
RULES!
Clearly specified policy
Definition of Terms:
Spawning Stock Biomass
FishingMortality (F)
Multi-parameter strategy = ‘complex’ HCR–Strategies with more than one parameter
FmaxFmax
B* B*
Type 2 Type 3
One parameter strategy = ‘traditional’ HCR– e.g.: constant harvest rate– Only 1 control parameter
Fconst
Type 1
HCR Performance Criteriahow to judge an HCR
• Average annual yield
Yield
Year
• CV
= (sd/(avg_yield)* 100
– coefficient of variation of mean yield as a %• Risk– Probability of biomass being below a min acceptable level (i.e. 10% of virgin biomass)
Research Questions• Do complex HCR perform better/worse than
the traditional harvesting strategies?Optimization approaches:
• Single criterion optimization (i.e., yield)• Multi-criteria optimization (i.e., yield, CV, Risk)
• Trade-offs among the performance criteria?
• Does performance of the HCR depend on
environmental/fishing mortality uncertainty?
Project ObjectiveObtain a more comprehensive & theoretical
understanding of harvest control rules (HCRs) and their effect on stochastic population dynamics
Materials & Methods
this project in a nutshell:
GENERICFISH STOCK
HCRType1Type2Type3
Average annual yield, CV, Risk
MODEL
Model Components: Parameters
Symbol Description Value Dimension w1 weight of age 1 fish 1 w w2 weight of age 2 fish 3 w M0 natural mortality for N0 2 t-1 M1 natural mortality for N1 0.4 t-1 M2 natural mortality for N2+ 0.2 t-1 f1 fecundity at time 1 proportional to the weight of N1 10 ind. f2 fecundity at time 2 proportional to the weight of N2+ 30 ind. k k used in Beverton-Holt s0 0.0001 ind -1
N0 N0 at year 0 0 ind. N1 N1 at year 0 1 ind. N2+ N2+ at year 0 1 ind. Ey Environmental stochastic multiplier 0.5 or 1.5 p Environmental variability probability 0.1-1.0
Vy Fishing variance 0.00-0.1 R0 net reproductive rate 3.96 ind.
PP
PP
good year bad year
The Model and Simulation Procedures:
N0
N1
N2+
s0
s1
s2+
fecundity1
fecundity2+
M
M0
M1
M2+
Ey
Vy
Vy
F
F
Model Components (cont)
Population equations:
N0 (year) = f1N1 (year) + f2+N2+ (year)N1 (year+1) = s0N0 (year) N2+ (year+1)
= s1N1 (year) + s2+N2+ (year)
Survival equations:
s0 = exp (-M0 * Ey)/ 1+kN0
s1 = exp (-(M1 + F * Vy))s2+ = exp (-(M2+ + F * Vy))
Simulation Procedures
F parameter loop0.0-6.0
Intervals of 0.5
B parameter loop0-800
Intervals of 50
Fish population ‘core’
N1N2+N0
• Search for F and B parameters that optimize the performance criteria
Optimization approaches:
•Single criterion optimization (i.e., yield)
•Multi-criteria optimization (i.e., yield, CV, Risk)
Examining the model:
Spawning Stock Size (N1 + N2+)
0.0 2.0e+4 4.0e+4 6.0e+4 8.0e+4 1.0e+5 1.2e+5 1.4e+5
Rec
ruit
men
t (N
0)
0
1000
2000
3000
4000
Recruitment
P
P
good year bad year
good year
bad year
Results & Discussion
Examining the model: Stochasticity
Year
0 20 40 60 80 100
Sp
awn
ing
Sto
ck S
ize
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
p=0.1 p=0.3 p=0.5 p=0.7 p=0.9 no stochasticity
Year
0 20 40 60 80 100
Sp
awn
ing
Sto
ck S
ize
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
p=0.1 p=0.3 p=0.5 p=0.7 p=0.9 no stochasticity
RESULTS: General Simulation
5,000 years
different levels of environmental and fishing stochasticity
General Simulation
different levels of environmental and fishing stochasticity
1800
2000
2200
2400
2600
2800
0.00
0.02
0.04
0.06
0.08
0.10
0.100.15
0.200.25
0.300.35
0.400.45
Max
Avg
Yie
ld
F V
aria
nce
p
1800
2000
2200
2400
2600
2800
0.00
0.02
0.04
0.06
0.08
0.10
0.100.15
0.200.25
0.300.35
0.400.45
Max
Avg
Yie
ld
F va
rian
ce
p
50
55
60
65
70
75
80
85
0.00
0.02
0.04
0.06
0.08
0.10
0.100.15
0.200.25
0.300.35
0.400.45
CV
F V
aria
nce
p
50
55
60
65
70
75
80
85
0.00
0.02
0.04
0.06
0.08
0.10
0.100.15
0.200.25
0.300.35
0.400.45
CV
F V
aria
nce
p
0
10
20
30
40
0.00
0.02
0.04
0.06
0.08
0.10
0.100.15
0.200.25
0.300.35
0.400.45
RIS
K
F V
aria
nce
p
0
10
20
30
40
0.00
0.02
0.04
0.06
0.08
0.10
0.100.15
0.200.25
0.300.35
0.400.45
RIS
K
F V
aria
nce
p
0
10
20
30
40
0.00
0.02
0.04
0.06
0.08
0.10
0.100.15
0.200.25
0.300.35
0.400.45
RIS
K
F V
aria
nce
p
50
55
60
65
70
75
80
85
0.00
0.02
0.04
0.06
0.08
0.10
0.100.15
0.200.25
0.300.35
0.400.45
CV
F V
aria
nce
p
HCR TYPE 1 HCR TYPE 2 HCR TYPE 3
1800
2000
2200
2400
2600
2800
0.00
0.02
0.04
0.06
0.08
0.10
0.100.15
0.200.25
0.300.35
0.400.45
Max
Avg
Yie
ld
F V
aria
nce
p
BIOMASS
F
Fconst
B* B*
Fmax
Fmax
Type 1 Type 2 Type 3• Best in max avg yield• Lowest CV• Lowest risk
Advantages and inadequacies:General Simulation
• HCR 1, 2 & 3– Similar yield
– Very high CV
– Small tradeoffs between CV and risk
Best HCR dependent Best HCR dependent on levels of the on levels of the
model’s stochastic model’s stochastic noise!noise!
HCR Avg Yield CV RISK 1 2705 (0.1, 0.05) 79.5 (0.2, 0.1) 14 (0.1, 0.008)
2 2584 (0.1, 0.03) 80 (0.1, 0.1) 37.5 (0.2, 0.1)
3 2517 (0.1, 0.0) 82.9 (0.1, 0.1) 22 (0.1, 0.05)
Environmental variabilityFishing variance
RESULTS: Specific Situation Simulation
50,000 years
Environmental variability = 0.25Fishing variance = 0.025
HCR Type 1: Specific Situation Simulation Environmental variability = 0.25Fishing variance =0.025
F Mortality
0 1 2 3 4 5 6 7
CV
& R
isk
0
20
40
60
80
100
120
140
160
180
Ave
rage
Yie
ld
0
500
1000
1500
2000
2500
CV
Risk
Avg Yield
Max Yield= 2348Fmax= 0.4CV= 59.3Risk= 0.01
Specific Situation Simulation (cont)
HCR Types 2&3: Environ. variability =
0.25Fishing variance =0.025
0
20
40
60
80
100
120
140
160
180
01
23
45
6
0100
200300
400500
600700
CV
F Mortality
Thres Biomass
HCR TYPE 2 HCR TYPE 3
0
20
40
60
01
23
45
6
0100
200300
400500
600700
RIS
K
F Mortality
Thres Biomass
0
500
1000
1500
2000
2500
01
23
45
6
0100
200300
400500
600700
Avg
Yie
ld
F Mortality
Thres Biomass
0
500
1000
1500
2000
2500
01
23
45
6
0100
200300
400500
600700
Avg
Yie
ld
F Mortality
Thres Biomass
0
20
40
60
80
100
120
140
160
180
01
23
45
6
0100
200300
400500
600700
CV
F Mortality
Thres Biomass
0
20
40
60
01
23
45
6
0100
200300
400500
600700
RIS
KF Mortality
Thres Biomass
• Clear tradeoffs
• Less risk and CV at lower F levels
• Types 2&3 NOT sensitive to Threshold Biomass (B*)
resilience factor (!)
HCR Type 2 & 3: Environ. variability = 0.25; F variance =0.025
0
500
1000
1500
2000
2500
0 1 2 3 4 5 6
0100
200300
400500
600700
Avg
Yie
ld
F Mortality
Thres Biomass
Max Yield= 2351Fmax= 0.4B*= 350CV= 59.5Risk= 0.0
Max Yield= 2365Fmax= 0.4B*= 750CV= 59.1Risk= 0.0
Specific Situation Simulation: Practicalities of the HCR
BIOMASS
F M
orta
lity
0.4
350 750
0.4 0.4
Type 1 Type 2 Type 3
-Yields very similar-CVs very similar
-Type 1 most practical!
Yield= 2348 Yield= 2351 Yield= 2365
Conclusions (but…we don’t always get it totally right…)
General Conclusions:
1. HCR Type 1 • best overall• practical, “simple”• robust in uncertainty
2. HCR Type 2• best for Risk (conservationists)• More practical than Type 3 (lower B*)
3. HCR Type 3• least practical for fishermen• good for conservationists
BIOMASS
F Fconst
B* B*
Fmax
Fmax
Type 1 Type 2 Type 3
Research “Answers”• Do complex HCR perform better than
traditional harvesting strategies?
• Trade-offs among the performance criteria?
• Does performance of the HCR depend on environmental/fishing mortality uncertainty?
No, not for this model. Simple is best! NOTE: this model was very resilient!!
Higher F gives higher CV and Risk values for all HCR Types
Yes! Need good uncertainty estimates in fisheries management
Future WorkMore realistic model with more age classes
N0N1
N2N3
N4
N5
etc…to a max age
Model should be slowly built up to a certain point…
More extensive simulations–Modelling an HCR after real data (i.e. cod, salmon, herring): different management for different life histories!
Future Work: What works, what doesn’t?? current proposal
to Norwegian Research CouncilOBJECTIVE:• Outline ways of management
that seem recommendable, and highlight rules that fail
• Point out factors for failure or success in worldwide fisheries management test results’ robustness with model simulations
SSB
F mortality
Catch
“I see a major trend…towards simpler rules for setting harvest levels, with the complex models being used primarily to test the robustness of the rules.”
- Ray Hilborn 2003. (emphasis added)
Remember to: K I S S ! Keep It Simple, Stupid!
Acknowledgements Advisors:
Mikko Heino: researcher, Institute of Marine Research; Adaptive Dynamics Network, International Institute for Applied Systems Analysis, Laxenburg, Austria
Øyvind Fiksen: associate professor, Department of Biology, University of Bergen