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An exploration of alternative methods to deal with time-varying selectivity in
the stock assessment of YFT in the eastern Pacific Ocean
CAPAM – Selectivity WorkshopLa Jolla, USA, 11-14 March, 2013
Alexandre Aires-da-Silva and Mark Maunder
Outline
• Background on YFT assessment Stock Synthesis (SS3) model Selectivity issues: time-varying process Retrospective pattern in recent recruitments
• Explore SS3 approaches to deal with time-varying selectivity Ignore time-varying selectivity (base case model) Full time-varying selectivity (deviates) Time-varying for terminal years only
YFT fishery definitions
40
30
20
10
0
10
20
30
40
150 140 130 120 110 100 90 80 70
10
40
30
20
10
0
10
20
30
40
150 140 130 120 110 100 90 80 70
11
12
6
5
40
30
20
10
0
10
20
30
40
150 140 130 120 110 100 90 80 70
40
30
20
10
0
10
20
30
40
150 140 130 120 110 100 90 80 70
1, 13
2, 143, 15
4, 16 7
9
8
40
30
20
10
0
10
20
30
40
150 140 130 120 110 100 90 80 70
Baitboat Unassociated Longline
DolphinFloating Objects
• Quarterly time-step model• Fishery definitions: 16 fisheries• Data weighting: the CV of the southern LL fishery
was fixed (0.2), others estimated (NOA, DEL)• Growth modeling: Richards curve, L2 and variance
of length-at-age are fixed
• Modeling of catchability and selectivity: Catchability coefficients for 5 CPUE time series are estimated
(NOA-N, NOA-S, DEL-N, DEL-I, LL-S) Size-based selectivity curves for 11 of the 16 fisheries are
estimated (fit to size composition data) Logistic selectivity for LL-S and DEL-S, and dome-shape for
other fisheries
YFT Stock Synthesis model
YFT size selectivity
OBJ time-varying selectivity?
F1-OBJ_S
F2-OBJ_C
F3-OBJ_I
F4-OBJ_N
OBJ LF residual pattern
F1-OBJ_S F2-OBJ_C
F3-OBJ_I F4-OBJ_N
Retrospective pattern
Projections
CATCHES
SPAWNING BIOMASS
Purse seine
Longline
Numerical and convergence issues
• Unstable selectivites (OBJ) Sensitive to initial parameter values and phases Long run times (> 4 hours) Issues inverting hessian matrix (steepness run)
Objectives of study• Test approaches available in SS to deal time-
varying selectivity Improve selectivity process (time-varying) Minimize retrospective pattern Shortcoming: more parameters, longer run times
• Simplify model Less data, collapse fisheries (OBJ)
• Some considerations We assume that retrospective pattern is mainly driven by
model misfit to recent OBJ LF data caused by misspecified selectivity
We recognize that other sources of bias and misspecifcation may exist
F1-OBJ_S
F2-OBJ_C
F3-OBJ_I
F4-OBJ_N
A single “lumped” OBJ fishery
Model 0: Constant selectivity• Selectivity: Estimate “average” constant selectivity• Data: Fit to OBJ length-frequency data for all historic
period• Base case model configuration
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 25 50 75 100 125 150 175 200
Sele
ctivi
ty
Length (cm)
OBJ-F1 - SAC3
OBJ-F2 - SAC3
OBJ-F3 - SAC3
OBJ-F4 - SAC3
OBJ - lumped
Model 0: Constant selectivity
Model 1 - Full time-varying selectivity
• Selectivity: Quarterly time-varying selectivity• Estimate quarterly deviates on base selex parameters
of double normal OBJ selectivity curve• Data: Fit to OBJ LF data for all historic period• SD of quarterly deviates need to be defined:
First run: freely estimate devs with high flexibility (SD=1) Second run: Use SD of estimated devs from first run in penalized
likelihood approach
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 25 50 75 100 125 150 175 200
Sele
ctivi
ty
Length (cm)
OBJ Fishery
Paramter M1-P2fixed M1-P2estP1 - peak 0.13 0.14P2 - top fixed at -15 1.08P3 - ascending 0.55 0.51P4 - descending 1.03 0.41
Model 1 - Full time-varying selectivity
Model 1 - Full time-varying selectivity
Model 1 - Full time-varying selectivity
Constant selectivity model 0 Time-variant model (M1-P2fix)
Model 1 - Full time-varying selectivity
0
50,000
100,000
150,000
200,000
250,000
300,000
350,000
400,000
2006 2007 2008 2009 2010 2011 2012 2013 2014 2015
Recr
uitm
ent (
x100
0 fis
h)
Year
Mod 0 - cons. Selex (BC)
Mod 1 - Full tvar selex
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016
Spaw
ning
bio
mas
s ra
tio
Year
Mod 0 - cons. Selex (BC)
Mod 1 - Full tvar selex
Model 1 - Full time-varying selectivity
Model 2 – “hybrid” approach• Recent period is the most influential on management
quantities (recent recruitments, Fs)• Time-varying selectivity process in recent period only• Estimate quarterly deviates on base selex parameters
of double normal OBJ selectivity curve• Fit to OBJ LF data for recent period only
3 terminal years (3-year average used for management quantities) 5 terminal periods (a longer period)
• As for early period, fix to “average” constant selectivity from terminal years (base parameters)
Tvar selex- 3 years Tvar selex - 5 years
Model 2 – “hybrid” approach
Model 2 – “hybrid” approachTvar selex- 3 years Tvar selex - 5 years
0
50,000
100,000
150,000
200,000
250,000
300,000
350,000
2006 2007 2008 2009 2010 2011 2012 2013 2014 2015
Recr
uitm
ent (
x100
0 fis
h)
Year
Mod 0 - cons. Selex (BC)
Mod 1 - Full tvar selex
Mod 2 - Hybrid 3 yrs
Mod 2 - Hybrid 5 yrs
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016
Spaw
ning
bio
mas
s rati
o
Year
Mod 0 - cons. Selex (BC)
Mod 1 - Full tvar selex
Mod 2 - Hybrid 3 yrs
Mod 2 - Hybrid 5 yrs
Model 2 – “hybrid” approach
Conclusions• Allowing for OBJ time-varying selectivity helped to minimize
retrospective pattern in recent YFT recruitment estimates• Balance between the amount of selectivity process (# of
params.) needed in the model and the OBJ LF data to include in model fit (whole series or few recent years only?)
• Allowing for time-varying selectivity (quarterly deviates) in terminal years of the assessment only while fitting to LF data
for this period seems a reasonable compromise• An “average” constant selectivity curve is applied to the early
period while not fitting to the LF data for that period• A simulation study is needed to more rigorously investigate
selectivity issues and associated bias in the YFT assessment
QUESTIONS?
0
50 000
100 000
150 000
200 000
250 000
300 000
350 000
400 000
450 000
500 000
1975 1980 1985 1990 1995 2000 2005 2010
Cat
ch (
t)
Year
LL
LP
DEL
NOA
OBJ
Total catches
Fix selectivity
• Assume “average” stationary OBJ selectivity• “Drop” (not fit) all OBJ LF data• Fix to base selectivity parameters estimated in full
time-varying runs (models 1)
Models
Fix selectivityM2-P2fixed M2-P2est
Models
Fix selectivityM2-P2fixed M2-P2est
Models
Recruitment – all models
0
100,000
200,000
300,000
400,000
500,000
600,000
700,000
1975 1980 1985 1990 1995 2000 2005 2010 2015
Recr
utim
ent (
x 10
00 fi
sh)
Year
SAC3
M1-P2fix
M2-P2fix
M3-P2fix_3YRS
M3-Pfix_5YRS
M4-Pfix_Tblocks_5YRS
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
1970 1980 1990 2000 2010 2020
SBR
Year
SAC3
M1-P2fix
M2-P2fix
M3-P2fix_3YRS
M3-Pfix_5YRS
M4-Pfix_Tblocks_5YRS
SBR – all models
Model type 1
a) MODELS 0 and 1
Model 0SAC3 M1-P2fixed M1-P2est
Fit to OBJ LF Yes Yes, all period Yes, all period Yes, all periodBase sel params Estimated Estimated Estimated EstimatedDevs No No Yes, all qrts Yes, all qrts
MANAG QUANTmsy 262,642 262,852 255,597 260,027 Bmsy 356,682 348,836 353,123 348,560 Smsy 3,334 3,208 3,304 3,203 Bmsy/Bzero 0.31 0.31 0.31 0.30Smsy/Szero 0.26 0.25 0.25 0.25Crecent/msy 0.79 0.78 0.81 0.79Brecent/Bmsy 1.00 1.04 0.87 0.91Srecent/Smsy 1.00 1.07 0.90 0.91Fmultiplier 1.15 1.20 1.07 1.05
MODEL 1 CONFIGURATION
Model type 3
c) MODELS 3
M3-P2fixed-3yrs M3-P2fixed-5yrsFit to OBJ LF Yes, last 3 yrs Yes, last 5 yrsBase sel params Estimated EstimatedDevs Yes, last 3 yrs Yes, last 5 yrs
MANAG QUANTmsy 261,728 257,126 Bmsy 350,789 351,377 Smsy 3,278 3,273 Bmsy/Bzero 0.32 0.31Smsy/Szero 0.26 0.25Crecent/msy 0.79 0.8Brecent/Bmsy 0.99 0.84Srecent/Smsy 0.99 0.86Fmultiplier 1.14 1.03
MODEL 3 CONFIGURATION