Transcript Stock assessment of yellowfin tuna in the Indian Ocean

Stock assessment of yellowfin tuna in
the Indian Ocean using MULTIFAN-CL
(IOTC-2011-WPTT13-36).
Adam Langley, Miguel Herrera and Julien
Million
Introduction
• Preliminary assessment using MFCL in 2008;
refined during WPTT 10.
• Assessment updated and revised during
WPTT-11 and WPTT-12 (2009 & 2010).
• Starting point for WPTT-13 assessment.
MFCL model dynamics
• Regional structure. Spatially disaggregated,
age structure population model.
• Model fitting to catch, size data (length freq),
and tag release/recovery data.
• Fishery data (catch, effort, lf) by time step.
• Movement between regions (can be age
specific).
• Tag dynamic similar to overall population
dynamics. Reporting rates, mixing phase.
WPTT-12 assessment
•
•
•
•
•
Commence model 1972.
Fixed growth (Fonteneau 2008).
Longline selectivity cubic spline.
Down-wt LF data (Sample size 10).
PS 2 fisheries: three time blocks. Different
selectivity.
• Low age-specific natural mortality (M).
• SSR steepness options 0.60, 0.70, 0.80, 0.90.
• Additional spatial aggregated model (one-region).
WPTT-13 revisions
• Additional year of data – all fisheries.
• LL CPUE indices: JP updated (CPUE2010) and
alternative indices with lat*long (R2-5); revised TW
indices (R1).
• Revised catch data. Major revision to TR 5 and OT 5
catch history.
• Segregated distant-water (LL 5) and fresh tuna
longline fleets (LF 5) in R5. 25 fisheries.
• Range of steepness values (consistent with BET)
0.55,0.65,0.75,0.85, 0.95.
• Single region, region 2 models.
Spatial stratification
Relatively homogeneous
areas wrt species
population dynamics
(size, fishing mortality,
fishery distribution).
25N
R1
15N
5N
R2
R5
5S
Consistent with spatial
distribution of tag
releases.
15S
R3
R4
25S
35S
20E
40E
60E
80E
100E
120E
Catch distribution
150
50
0
0
50
150
250
Most of catch within
regions 1, 2 and 5. PS and
GN dominate total catch.
Region 4
250
Region 1
1980
2010
1990
2000
2010
2000
2010
2000
2010
Year
250
150
LL
LS
OT
TR
50
BB
FS
GI
HD
LF
0
0
50
150
250
Region 5
1990
2000
2010
1980
Year
1990
Year
IO Total
50
0 100
150
300
250
500
Region 3
0
2010 catch 294,000 t.
1980
Region 2
1980
High catches 2004/2005.
PS free schools sets. Log
sets dominate last few yrs.
2000
Year
Total catch (1000s mt)
Purse-seine catch largely
restricted to region 2.
Gillnet R1 and R5.
Handline R1.
LL fresh R5.
1990
1980
1990
2000
2010
1980
1990
Model structure
• 5 regions. 28 age classes. 1972-2010.
• LL CPUE index (1972 onwards) – shared
(constant) catchability and selectivity among
regions (LL 1-5).
• Age-specific natural mortality (fixed).
• Growth (fixed).
• Common biol pars for male and female.
• Movement dynamics (estimated).
• Recruitment: overall regional proportion,
temporal trend, regional deviates.
• SRR steepness fixed (0.55,0.65, 0.75, 0.85,0.95).
Fishery configuration
Fishery
Nationality
Gear
Region
1. GI 1
All
Gillnet
1
2. HD 1
All
Handline
1
3. LL 1 post 1972
All
Longline
1
4. OT 1
All
Other
1
5. BB 2
All
Baitboat
2
6. PS FS 2 2003-06
All
Purse seine, school sets
2
7. LL 2 post 1972
All
Longline
2
8. PS LS 2 2003-06
All
Purse seine, log/FAD sets
2
9. TR 2
All
Troll
2
10. LL 3 post 1972
All
Longline
3
11. LL 4 post 1972
All
Longline
4
12. GI 5
All
Gillnet
5
13. LL 5 post 1972
All
Longline (distant water)
5
14. OT 5
All
Other
5
15. TR 5
All
Troll
5
16. PS FS 3
All
Purse seine, school sets
3
17. PS LS 3
All
Purse seine, log/FAD sets
3
18. TR 3
All
Troll
3
19. PS FS 5
All
Purse seine, school sets
5
20. PS LS 5
All
Purse seine, log/FAD sets
5
21. PS FS 2 pre 2003
All
Purse seine, school sets
2
22. PS LS 2 pre 2003
All
Purse seine, log/FAD sets
2
23. PS FS 2 post 2006
All
Purse seine, school sets
2
24. PS LS 2 post 2006
All
Purse seine, log/FAD sets
2
25. LF 5
All
Longline (fresh tuna)
5
0.10
0.05
Fonteneau & Hallier (IOTC2010-WPTT-27).
fix low M
estimated
0.00
Maturity at age.
Natural mortality
Growth parameters.
0.15
M-at-age fixed.
0.20
Key inputs – biol.
parameters
0
5
10
15
Age class
20
25
200
Growth
Fonteneau 2008
100
50
0
Length (cm)
150
Variation of length at age.
1
5
10
15
Age (quarters)
20
25
2000
2000
15000
2500
0 5000
1000
0
15000
5000
15000
1980
2000
24. PS LS 2 2007-10
5000
1500
0
2000
2000
25. LF 5
0
5000
1000 2000
1980
15000
1980
20. PS LS 5
2000
2000
0
1000
0
2000
0
1980
1980
23. PS FS 2 2007-10
0 500
40
0
1980
1980
15. T R 5
2000
22. PS LS 2 Pre 2003
18. T R 3
2000
400
800 1200
1980
1980
2000
19. PS FS 5
120
1980
1980
2000
0
0
0
2000
4000
20 40 60 80
10. LL 3 Post 1972
2000
2500
100
60
0 20
1980
2000
0 5000
1000
0
20
0
5000
0
2000
80
1500
200 400 600
5. BB 2
1980
14. OT 5
0 500
1980
15000
2000
60
40
40000
20000
400
0
2000
21. PS FS 2 Pre 2003
17. PS LS 3
200
15000
2000
13. LL 5 Post 1972
9. T R 2
2000
16. PS FS 3
12. GI 5
1980
8. PS LS 2 2003-06
1980
4. OT 1
1980
Increasing TR, GI, HD catches.
11. LL 4 Post 1972
1980
2000
10000
800
1980
2000
0
High PS FS 2 catch in 2004/05.
7. LL 2 Post 1972
0
2000
0
1980
Recent drop in LL2 catch. Drop
in LL 4 and 5 catches.
2000
100
4000
0
1980
3. LL 1 Post 1972
Expressed in tonnage for all
fisheries, except LL.
1980
300
2. HD 1
Catch data complete to 2010.
6. PS FS 2 2003-06
0
2000
20000
15000
5000
0
1980
8000
Key inputs –
catch data
1. GI 1
1980
2000
1980
2000
8 10
4
2
0
2000
1980
10
0
2000
23. PS FS 2 2007-10
2000
0
-1.0
2
4
6
18. T R 3
1980
8
6
4
2000
2
0
1980
20. PS LS 5
8
15. T R 5
2000
1980
0.0 0.5 1.0
1980
2000
25. LF 5
1980
2000
1980
2000
-1.0
0
0.0
-1.0
2
0.4
0.8
10. LL 3 Post 1972
2000
24. PS LS 2 2007-10
0
-1.0
2000
1980
19. PS FS 5
15
14. OT 5
2000
5
0.03
0.00
5
1980
0.0 0.5 1.0
0.06
15
10
1980
5. BB 2
2000
10
2000
9. T R 2
0
0.00 0.04 0.08 0.12
PS effort not separated by set
type. Effort data for many
fisheries considered unreliable.
0.0 0.5 1.0
0.4
1980
2000
13. LL 5 Post 1972
1980
6
2000
2000
0.8
8. PS LS 2 2003-06
4. OT 1
1980
1980
0.0
0.10
0.00
1980
Standardised CPUE indices for
JP LL fleet (in regions 2-5). TW
CPUE index in region 1.
2000
0 1 2 3 4 5 6
3. LL 1 Post 1972
Effort data not available for
several fisheries (“missing”).
-1.0
1980
2000
22. PS LS 2 Pre 2003
4
2000
0.0 0.5 1.0
1980
1980
17. PS LS 3
5
0.4
1980
0 1 2 3 4 5 6
12. GI 5
0.0
-1.0
CPUE plotted for each fishery.
21. PS FS 2 Pre 2003
6
20
5 10
7. LL 2 Post 1972
2000
15
1980
0.8
2. HD 1
2000
0.0 0.5 1.0
1980
16. PS FS 3
0
0
2000
11. LL 4 Post 1972
0.00 0.10 0.20 0.30
10
15
6. PS FS 2 2003-06
5
0.0 0.5 1.0
-1.0
1980
0.0 0.5 1.0
Key inputs –
effort data
1. GI 1
1980
2000
1980
2000
1980
2000
GLM standardised CPUE index of
JP and TW LL data. JP indices incl.
lat*long.
0.6
0.0
0.00
0.2
0.10
0.4
0.20
Key inputs – LL
CPUE
1980
2000
2010
1980
1990
1.0
0.5
1990
2000
2010
1980
1990
2000
2010
LL IO
4
LL 3
CPUE latlong
CPUE 2010
CPUE IO
3
1.5
2
1.0
1
0.5
0
1980
LL IO for single region model.
2010
LL 5
0.0
Sharp decline in LL2 from 2005.
Steady decline in LL5.
2000
0.0 0.2 0.4 0.6 0.8 1.0
1.5
LL 2
1980
Standardised effort series (effort
= catch/CPUE).
1990
0.0
CPUE
Regional scaling (0.21, 1.00, 0.55,
0.15, and 0.85).
LL 4
0.30
LL 1
1990
2000
2010
1980
1990
2000
2010
Key inputs –
size data
Length frequency data from
most of the key fisheries.
No/limited data for some
minor fisheries.
Effective sample size 10 (n =
1000/100.
Key inputs –
size data
LL2 length data, recent period.
Contraction of the LF
distribution.
Uncertainty in the
comparability of data over
entire time period.
Longline length frequency data, region 2 and region 5.
Longline length frequency data.
Key inputs – tag
data
Tag release/recoveries IO RT.
54,393 releases, 9961 recoveries
(corrected). Not including recent
small scale tag releases.
Reporting rate information for PS
fishery from tag seeding. Used to
correct recoveries.
Overall RR for PS fishery fixed at
0.81 (retention 90%, PS catch
sampled = Seychelles landings
90%).
PS recoveries aggregated within
region.
Key inputs – tag
data
Tag recoveries by
release/recovery region.
Mostly within region 2.
Some movement of tags
1 > 2, 2 > 1, 2 > 5
(3 > 2, 2 > 3)
Model runs
• Approximate final 2010 model (WPTT 12)
(CPUE2010).
• New JP CPUE indices (CPUElatlong) (BASE).
• New LL R5 structure and new JP CPUE indices
(newLL).
• Single region model (IOregion).
• Region 2 model (region2).
• 5 values of steepness.
• Sensitivity. Tag mixing period (1-4 Q).
Model
diagnostics catch
Good fit to the catch data
for all fisheries.
High catch penalty.
Model
diagnostics –
CPUE indices
Effort deviates.
Principal LL fisheries –
no strong trend in
edevs with the
exception of LL1.
High penalty assoc
with LL edevs (cv
10%).
Model diagnostics
– CPUE indices
Principal LL fisheries.
Good fit to CPUE data.
Strong recent decline
in LL 2 CPUE.
Model diagnostics –
size data
Selectivity functions
(cubic spline ).
Shared between LL
fisheries.
Shared between
fisheries where size
data not available.
PS 2 – temporal split
esp. LS.
Model
diagnostics –
length data
Overall fit to the
length data
(aggregated over
time).
Related to fixedgrowth assumption?
Model
diagnostics –
length data
Overall fit to the
length data
(aggregated over
time).
Model
diagnostics –
length data
Some lack of fit for some
fishery/periods:
HD 1 recent Maldives data.
LL 2 and 5. Smaller fish in
1990s.
Model
diagnostics –
length data
Sampling error in some
fisheries e.g. PS FS 3, TR 5.
Model diagnostics –
tag data
Fixed tag reporting rate for
PS fishery.
PS grouped for tag returns.
All other fisheries have
uninformative priors on RR.
LL in R2 reporting rate
about 15%.
5e+01
5e+00
Reflects size of fish
tagged, fishery selectivity,
fishery RR.
5e-01
First 4 quarters not in LL
(mixing period).
Returns per quarter
Recoveries by period at
liberty.
5e+02
Model diagnostics –
tag data
5
10
15
Quarters at liberty
20
0 2 4 6 8
0.0
0.8
0.0
0 5
0.4
15
8
4
0.8
PS 2 Post 2006
0.0
0
2008
2011
25. LF 5
100
0.4
0.8
250
0.8
0.4
0
0.0
40
2005
PS 3
0.0
0
4
0.4
8
0 400 1000
0.8
12
0.0
0.4
0.8
0.4
0.0
20
0
1
0
10
PS 2 Pre 2003
15. TR 5
11. LL 4 Post 1972
80
5. BB 2
0
Reasonable fit to some of
the other main fisheries
recovering tags (except
OT2).
PS 5
14. OT 5
10. LL 3 Post 1972
15
4. OT 1
5
Good fit to the PS tag
recoveries, except for a
couple of quarters.
13. LL 5 Post 1972
9. TR 2
40
60
0
0.0
4
3
3. LL 1 Post 1972
18. TR 3
0.4
1000
0 400
4
2
0
7. LL 2 Post 1972
1.0
2.0
2. HD 1
2
Tag recoveries by fishery
and by quarter.
12. GI 5
0.8
PS 2 2003-2006
6
Model
diagnostics – tag
data
1. GI 1
2005
2008
2011
2005
2008
2011
2005
2008
2011
Improved fit with longer
mixing rate (Q4).
Figure includes mixing
period.
PS 2 fishery recoveries by
age class.
Figure excludes mixing
period.
Tag fits to diffusion
rates (and tag
recovery rates).
Model pars/outputs – movement
Max. 12.8% per quarter, 4 > 5 in Q2.
Model
pars/outputs
– catchability
Constant LL
catchability.
Dependent on effort
data series.
Increasing PS q ??
Free temporal q for
fisheries with missing
effort.
Model
pars/outputs
– recruitment
R2 and R5 account for
most of the recruitment.
Temporal trends in
recruitment (initial and
long-term).
Low recruitment in R2
during 2000s.
Recent recruitment 80%
of long-term average.
Model
pars/outputs
– recruitment
Comparison of
runs.
Model
pars/outputs
– biomass
Total and adult
biomass.
R2 and R5 (and 3)
account for most of
the biomass.
Model
pars/outputs
– biomass
Comparison of
runs.
Model
pars/outputs
– biomass
1000
2000
3000
4000
5000
Base case
CPUE latlong
CPUE 2010
Region2
0
REGION 2 Biomass (thousands mt)
6000
Comparison of
runs REGION2.
1980
1990
2000
2010
Comparison with 2010
Differences in LL CPUE
data set, LL5 fishery
configuration and catch
history for some key
fisheries.
Reconciliation of
differences.
Comparison with 2010
Run1.
2010 tag, LL CPUE 2010
approach, old LL 5 fishery, new
catch/effort.
Run10
2010 fishery catch/effort, 2010
year.
Run12
Ex 2010 year
Model
pars/outputs
– fishing
mortality
F for the “current”
(2006-2009) period.
F highest in R1, R2 and
R5.
Model
pars/outputs
– fishery impact
Total biomass
Model
pars/outputs
– fishery impact
Main fishery impact occurring
within R1, 2 and 5.
Fishery impact lower in region
4.
Overall, 45% reduction in
biomass.
Stock Status - SRR
Fixed steepness = 0.75
(intermediate value
from range).
Uninformative about
appropriate value for
steepness.
400
300
200
100
0
Equilibrium yield (1000 mt per year)
Stock Status –
equilibrium
conditions
0.0
0.5
1.0
1.5
2.0
1.5
2.0
6000
4000
2000
0
Equilibrium total biomass (1000 mt)
0.0
0.5
1.0
7000
Fishing mortality multiplier
3000
5000
Steepness 0.55
Steepness 0.65
Steepness 0.75
Steepness 0.85
Steepness 0.95
0 1000
Steepness = 0.75
Fmult = 1.37
Ycurrent = 364,000 mt
Beq = 0.462 * B0
BMSY = 0.315 * B0
Equilibrium adult biomass (1000 mt)
Fcurrent = F2006-2009
8000
Fishing mortality multiplier
0.0
0.5
1.0
Fishing mortality multiplier
1.5
2.0
Overfishing
2.0
1.0
F=Fmsy
F/Fmsy
1.5
Overfishing
1.0
F=Fmsy
2008
2010
2009
2008
2010
2009
1990
0.5
1.0
B<Bmsy B=Bmsy
1.5
2.0
2.5
B>Bmsy
B/Bmsy
3.0
2000
1995
1990
1985
1980
0.0
2005
0.5
1995
3.5
1975
1985
1980
0.0
2000
F<Fmsy
0.5
2005
0.0
F<Fmsy
F/Fmsy
F>Fmsy
2.0
Overfished
1.5
F>Fmsy
Overfished
0.0
0.5
1.0
1.5
SB<SBmsySB=SBmsy
2.0
2.5
B>Bmsy
SB/Bmsy
STEEPNESS = 0.75
F/Fmsy = 0.73; B/Bmsy = 1.41; SB/SBmsy = 1.54
F2009/Fmsy = 0.79; B2009/Bmsy = 1.17; SB2009/SBmsy = 1.21
3.0
3.5
Stock Status –
reference
points
Management
quantity
~
YFcurrent
~
YFMSY (or MSY)
~
B0
~
BFcurrent
~
BMSY
~
SB0
~
SBFcurrent
~
SBMSY
Units
2009 and 2010
progressively more
pessimistic.
Total catches in 2010
about 294,000 mt.
Lower recent
recruitment.
h 0.65
h 0.75
h 0.85
h 0.95
mt per year
298,160
338,920
364,080
380,560
392,440
mt per year
298,600
343,520
383,000
418,400
452,800
mt
7,769,000
7,665,000
7,595,000
7,517,000
7,464,000
mt
2,894,000
3,271,000
3,507,000
3,649,000
3,755,000
mt
3,039,000
2,818,000
2,615,000
2,405,000
2,177,000
mt
7,037,000
6,942,000
6,879,000
6,809,000
6,761,000
mt
2,467,000
2,786,000
2,988,000
3,107,000
3,197,000
mt
2,598,000
2,372,000
2,164,000
1,950,000
1,719,000
Bcurrent
mt
3,772,942
3,746,533
3,737,290
3,717,375
3,708,526
SBcurrent
mt
3,423,649
3,397,606
3,388,139
3,368,676
3,359,825
2,637,868
2,618,445
2,612,008
2,596,823
2,590,180
6,431,602
6,406,138
6,398,318
6,378,312
6,369,848
0.486
0.489
0.492
0.495
0.497
1.304
1.145
1.066
1.019
0.988
1.221
1.307
1.405
1.520
1.675
0.587
0.585
0.584
0.583
0.582
0.487
0.489
0.493
0.495
0.497
0.375
0.377
0.380
0.381
0.383
1.388
1.220
1.134
1.084
1.051
1.295
1.408
1.539
1.698
1.921
0.373
0.427
0.462
0.485
0.503
0.351
0.401
0.434
0.456
0.473
0.391
0.368
0.344
0.320
0.292
0.369
0.342
0.315
0.286
0.254
1.045
0.861
0.730
0.628
0.537
0.952
1.161
1.341
1.517
1.725
0.950
1.175
1.381
1.593
1.860
0.999
0.987
0.951
0.910
0.867
Bcurrent B2000
0.673
0.674
0.674
0.674
0.674
SB2009 SB2000
0.535
0.535
0.535
0.536
0.536
SB2009
Based on current (20062009) conditions.
h 0.55
Bcurrent, F  0
~
Bcurrent B0
~
Bcurrent BFcurrent
~
Bcurrent BMSY
Bcurrent Bcurrent, F 0
~
SBcurrent SB0
SB2009
~
SB0
~
SBcurrent SBFcurrent
~
SBcurrent SBMSY
~
~
BFcurrent B0
~
~
SBFcurrent SB0
~
~
BMSY B0
~
~
SBMSY SB0
~
Fcurrent FMSY
~
~
BFcurrent BMSY
~
~
SBFcurrent SBMSY
~
YFcurrent MSY
mt
Other model options
• Higher/lower values of steepness; more/less
optimistic stock status; higher/lower yields.
• New LL5 fishery config slightly less optimistic.
• New CPUE (lat*long) slightly more optimistic
than old LL CPUE approach.
• Region 2 stock status comparable to 5-region
base case.
• Single region IO model considerably more
pessimistic.
Overfished
Overfishing
2.0
1.5
F>Fmsy
20102008
2009
1.0
F=Fmsy
F/FmsyOverfishing
2.0
1.0
F=Fmsy
2008
2010
2009
2005
2000
1995
1990
1985
1980
0.0
0.5
1.0
B<Bmsy B=Bmsy
1.5
2.0
B>Bmsy
B/Bmsy
5 Region
2.5
3.0
3.5
0.5
1995
1990
1985
1975
0.0
2000
F<Fmsy
0.5
2005
0.0
F<Fmsy
F/Fmsy
1.5
F>Fmsy
Overfished
1980
0.0
0.5
B<Bmsy
1.0
B=Bmsy
1.5
2.0
B>Bmsy
B/Bmsy
Single region
2.5
3.0
3.5
Comparison with 2010
2010 model
run1
run10
run12
2010 tag data set
exclude 2010 length data F24
run10.frq with 2010 excluded
run30
refit 2010 model
steepness current YRS
0.7 2005-2008
0.7 2005-2008
0.7 2005-2008
0.7 2005-2008
0.7 2005-2008
MSY
323,480
418,000
452,800
366,640
SB2SBMSY
1.50
1.64
1.67
1.67
Fmult
1.03
1.43
1.56
1.21
Neg LL
290504.6
363,880
1.53
1.21
290522.7
Convergence problems with 2010 final model – local minima.
Differences in the selectivity of PS LS 2 fishery resulting in differences in F-at-age.
Degree of confounding between R0 and PS LS selectivity parameters.
Inclusion of 2010 data influential resulting in higher Fmult and MSY.
Differences in selectivity for PS FS 2 (2007-2010) and TR fisheries.
Stock status
• Five values of steepness – stock status varies
accordingly.
• Stock status sensitive to regional structure.
• Five region. F (2006-09) less than FMSY. B and SB
(2006-09) well above BMSY and SBMSY. MSY 350-450 K
mt.
• Single region. F (2006-09) exceeds FMSY. B and SB
(2006-09) approaching BMSY and SBMSY. MSY 250-350
k mt.
• Current equilibrium yields comparable to MSY.
• Stock status in 2009 and 2010 considerably more
pessimistic than 2006-09 average.
Preliminary conclusions 1
• Update and refinement of 2010 MFCL
assessment. Complex model (spatial structure,
fisheries).
• Trends in SA model driven by CPUE indices
(esp R2, 3, 5). Temporal trends in recruitment.
• Fishing mortality at an historically high level.
• Recent recruitment (last 10 years) lower (70%)
than long term average.
• High fishery impacts in most regions. Overall
impact reducing biomass by 45%.
Preliminary conclusions 2
• BRPs sensitive to SRR and conclusions on (MSY
based) stock status dependent on steepness
assumption and regional structure.
• Stock biomass above or approaching BMSY (all
options).
• Exploitation rates above or below FMSY depending
on regional structure.
• Current catches at lower range of MSY estimates.
• MSY dependent on equilibrium recruitment
(recent low recruitment).
• Management advice (projections, etc).
Key issues 1
• Longline CPUE indices, including temporal trends
in LL catchability.
• Spatial structure.
• Reliability of most recent data (2010 year).
• Growth (sex specific?), maturity, natural mortality.
• SRR steepness (meta analysis).
• Size data lacking for some important fisheries.
Representativeness of size data.
• LL length data; smaller fish 1990s.
• LL selectivity – logistic, cubic spline.
Key issues 2
• Time blocks for PS 2 fisheries (pre 2003, 2003-06,
post 2007). Later period sensitive to most recent
data.
• Possible temporal trends in selectivity for key
fisheries.
• Definition of effort. Limited effort data for many
fisheries.
• Express uncertainty of current stock status
(probability surface on Kobe plot).
Stock projections
• Kobe 2 strategy matrix.
• The K2SM summarises potential management
actions, for example TAC and time-area
closures, that correspond to specific
probabilities of reducing over fishing or
rebuilding the stock within specific
timeframes.
Projections
• Deterministic or stochastic.
• Uncertainty. MFCL recruitment only (other
sources of uncertainty – numbers at age in
terminal year, effort devs).
• WCPFC advice.
• Define base-line catch/effort for each fishery.
• Recruitment – SRR, recent period.
• Projection period.
• Define probabilities.
• Define period for defining MSY.
Stochastic SB/SBMSY
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
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