Operating Model & Control RulesSome progress for Chapter III

2015-05-20

Time Table

Changes in the pathway:

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Chapter III

       

Goal: Impact of misspecification model under a spatially-structured population, the PatagonianToothfish in South-America

                          

Needs:·

Operating Model v/s Assessment Model

Explore some state variables

Implementing a MSE process

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3/25

Outline

Review Operating Model

Candidate Harvest Control Rules and Performance Metrics

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Structure in ADMB

Conditioning operating model

Simple example: Implications of recruitment process error

List TODO

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Designs of harvest control rules

Uncertainties & scenarios

Performance measures

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4/25

Review Operating ModelPotential MSE under spatial population

Annual Cycle

6/25

Projection

7/25

Some Results

Let me show you some scenarios (/home/jcquiroz/Dropbox/utas-aad-research/Chapter%20-%20III/OM_toy_modelling/) to explain the ADMB structure.

8/25

Some statistic for the Toy Mode

Realizations: 1.000 [maybe is too many]

Scenarios: 2 [low sigmaR / high sigmaR]

Control Rules: 1 [constant catch rate]

Number of assessment (fit) per realization: 30 [yrs projection]

Total of assessment: 60.000

Functions per assessment: 43 [real model > 200]

Total functions evaluated: 2.580.000

Runtime in my laptop: 3 hours, 13 minutes, 44 sec

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9/25

TODO in MSE

Thinking in Chapter III (the Chilean case):

Thinking in Chapter II (the Kerguelen case):

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Identify toothfish conservation or management objectives

Define operating model requirements (e.g. spatial population)

Conditioning of hte operating model on the available data and knowledge

Set up the management strategies or posible candidates

Evaluate alternative performance measures

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Build an operating model according with the feedback from Phil and Paul

Apply the same rational of Chilean case

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10/25

Harvest Control RulesPerformance Metrics

Current knowledge

Actual harvest Policy·

Reference points (rp) defined following a Tier system (May, 2014)

Four Tier categories based on quality and quantity data (1a > 1b > 2 > 3)

Patagonian Toothfish (TOP) was clasified in Tier 1b

rp biomass-based |     Target: ;     Limit:

rp mortality-based |     Target: ;     Limit:

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Method: Proxies for MSY, taking account of uncertainty in the stockassessment model and resilience of the specie

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- SB40% SB20%

- Fspr45% Fspr30%

12/25

Gaps & potential contributions

No HCRs are explicitly defined for the fishery of TOP in Chile

Although several methods exist for estimating rp, it is unclear which performsbest.

No stock management objectives: example at oversimulated period

No clear prejection period (objectives short - medium - long term)

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· SB > SB40% P > 0.8

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13/25

Operating Model

The reference points are calculated by finding the value of that results in the zero derivative of catchequilibrium equation. This is accomplished numerically using a Newton-Raphson method where aninitial guess for is set equal to .

where spawning biomass per recruit.

Fe

Ce

Fmsy M

Fe+1

∂Ce

∂Fe

∂C2e

∂F 2e

= −Fe

∂Ce

∂Fe

∂C2e

∂F 2e

= + +Reϕq Feϕq

∂Re

∂FeFeRe

∂ϕq

∂Fe

= +ϕq

∂Re

∂Fe

Re

∂ϕq

∂Fe

ϕq

14/25

HCRs F-based

15/25

HCRs Catch-based

Numerically solve the Baranov catch equation

Time-consuming simulation

Always better option stakeholders

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16/25

Simple formulation

Fishing Mortality - Based ( : linear; : non-linear )

Catch - Based

γ = 0 γ ≠ 0

=F~

y

⎧⎩⎨⎪⎪⎪⎪

0,

,( )βB0

By

γ / −αBy B0

β−αFmsy

,Fmsy

/ < αBy B0

α <= / < βBy B0

/ >= βBy B0

=C~

y

⎧⎩⎨⎪⎪⎪⎪

0,

C( ,βB0

By

/ −αBy B0

β−αFmsy)y

C( ,Fmsy)y

/ < αBy B0

α <= / < βBy B0

/ >= βBy B0

17/25

Performance HCR F-based (images_hcr/fig1.png)

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Trend depletion (images_hcr/fig2.png)

19/25

Risk depletion (images_hcr/fig3.png)< SBlim

20/25

Get close target: (images_hcr/fig4.png)

P(SB >= 0.9 ⋅ S )Btarget

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Fishing Mortality (images_hcr/fig5.png)

22/25

Trade offs (images_hcr/fig7.png)

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TODO in HCR

Explore quantitatively the interactions between performance measuresEvaluate the trade offs following some explicative modelling:

for example:

where, : process error; : implementation error; : estimation error; steepness and is anyperformance measure.

= α + + + +PMi β1

⎡

⎣⎢⎢⎢⎢⎢

hi1

hi2

⋮hi

n

⎤

⎦⎥⎥⎥⎥⎥ β2

⎡

⎣⎢⎢⎢⎢⎢

σ ir1

σ ir2

⋮σ i

rn

⎤

⎦⎥⎥⎥⎥⎥ e

+

⎛

⎝⎜⎜⎜⎜⎜⎜β3

⎡

⎣⎢⎢⎢⎢⎢⎢

σic1

σic2

⋮

σicn

⎤

⎦⎥⎥⎥⎥⎥⎥ β4

⎡

⎣⎢⎢⎢⎢⎢⎢

σiE1

σiE2

⋮

σiEn

⎤

⎦⎥⎥⎥⎥⎥⎥

⎞

⎠⎟⎟⎟⎟⎟⎟

εi

σr σc σE h PM

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Slides in progress

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