Evaluation of harvest control rules (HCRs): simple vs. complex strategies Dorothy Housholder Harvest Control Rules Workshop Bergen, 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 Stochasticity needed in fish population dynamics Stochasticity (randomness and uncertainty) needed in fish 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 HARVEST CONTROL RULES! Clearly specified policy

Definition of Terms: Spawning Stock Biomass Fishing Mortality (F) Multi-parameter strategy = ‘complex’ HCR –Strategies with more than one parameter F max B* Type 2Type 3 One parameter strategy = ‘traditional’ HCR –e.g.: constant harvest rate –Only 1 control parameter F const Type 1

HCR Performance Criteria how 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 Objective Obtain a more comprehensive & theoretical understanding of harvest control rules (HCRs) and their effect on stochastic population dynamics

Materials & Methods

this project in a nutshell: GENERIC FISH STOCK HCR Type1 Type2 Type3 Average annual yield, CV, Risk MODEL

Model Components: ParametersPP good yearbad year

The Model and Simulation Procedures: N0N0 N1N1 N 2+ s0s0 s1s1 s 2+ fecundity 1 fecundity 2+ M M0M0 M1M1 M 2+ EyEy VyVy VyVy F F

Model Components (cont) Population equations: N 0 (year) = f 1 N 1 (year) + f 2+ N 2+ (year) N 1 (year+1) = s 0 N 0 (year) N 2+ (year+1) = s 1 N 1 (year) + s 2+ N 2+ (year) Survival equations: s 0 = exp (-M 0 * E y )/ 1+kN 0 s 1 = exp (-(M 1 + F * V y )) s 2+ = exp (-(M 2+ + F * V y ))

Simulation Procedures F parameter loop Intervals of 0.5 B parameter loop Intervals of 50 Fish population ‘core’ N1N1 N 2+ N0N0 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:

Recruitment P P good yearbad year good year bad year

Results & Discussion

Examining the model: Stochasticity

RESULTS: General Simulation 5,000 years different levels of environmental and fishing stochasticity

General Simulation different levels of environmental and fishing stochasticity BIOMASS F F const B* F max Type 1Type 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 on levels of the model’s stochastic noise! Environmental variability Fishing variance

RESULTS: Specific Situation Simulation 50,000 years Environmental variability = 0.25 Fishing variance = 0.025

HCR Type 1: Specific Situation Simulation Environmental variability = 0.25  Fishing variance =0.025 Max Yield= 2348 F max = 0.4 CV= 59.3 Risk= 0.01

Specific Situation Simulation (cont) HCR Types 2&3: Environ. variability = 0.25 Fishing variance =0.025 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 Max Yield= 2351 F max = 0.4 B * = 350 CV= 59.5 Risk= 0.0 Max Yield= 2365 F max = 0.4 B * = 750 CV= 59.1 Risk= 0.0

Specific Situation Simulation: Practicalities of the HCR BIOMASS F Mortality Type 1 Type 2 Type 3 -Yields very similar -CVs very similar -Type 1 most practical! Yield= 2348 Yield= 2351Yield= 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 F const B* F max Type 1Type 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 Work More realistic model with more age classes N0N0 N1N1 N2N2 N3N3 N4N4 N5N5 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 Council OBJECTIVE: 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 (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