an exploration of alternative methods to deal with time-varying selectivity in the stock assessment...

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