Date post: | 25-Jul-2015 |
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Science |
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Operating Model & Control RulesSome progress for Chapter III
2015-05-20
Time Table
Changes in the pathway:
2/25
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)
18/25
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
21/25
Fishing Mortality (images_hcr/fig5.png)
22/25
Trade offs (images_hcr/fig7.png)
24/26
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
25/26
Slides in progress
26/26