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