A retrospective investigation of selectivity for Pacific halibut

CAPAM Selectivity workshop14 March, 2013

Ian Stewart & Steve Martell

Overview1) History2) Contributing factors3) 2012 Assessment investigation4) Path forward

Years Model Issues

Pre-1977 Yield, yield-per-recruit, simple stock-production models No growth or recruitment variability

1978-1981 Cohort analysis, coastwide, natural mortality (M)=0.2 Unstable estimates

1982-1983 Catch-AGE-ANalysis (CAGEAN; age-based availability), coastwide, M=0.2

Migratory dynamics not accounted for

1984-1988 CAGEAN, area-specific, migratory and coastwide, M=0.2 Trends differ by area

1989-1994 CAGEAN, area-specific, M=0.2, age-based selectivity Retrospective pattern

1995-1997 Statistical Catch-Age (SCA), area-specific, length-based selectivity, M=0.2

M estimate imprecise

1998-1999 SCA, area-specific, length-based selectivity, M=0.15 Poor fit to data

2000-2002 New SCA, area-specific, constant age-based selectivity, M=0.15

Retrospective pattern

2003-2006 SCA, area-specific, constant length-based selectivity, M=0.15

Migratory dynamics created bias

2006-2011 SCA, coastwide, constant length-based selectivity, M=0.15

Retrospective pattern

Assessment model evolution

Retrospective I: Age-based selectivity

Interim: Length-based selectivity

Figure from: Clark and Hare, 2002

3A

Retrospective II: Age-based selectivity

Figure from: Clark and Hare, 2002

3A

Interim II: Length-based selectivity

3A E

xplo

itabl

e bi

omas

s (M

lb)

Figure from: Clark and Hare, 2004

Retrospective III: Length-based selectivity

Overview1) History2) Contributing factors3) 2012 Assessment investigation4) Path forward

Factors contributing to selectivity:- Highly dimorphic growth- Size-at-age: temporal trends and differences by area- Fishery minimum size limit- Hook-size effects – few small fish observed

Regulatory areas

Growth curves by area

Age (years)

Leng

th (c

m)

Dimorphic and spatial variability

05

10

15

1920 1960 2000

Age 6 05

10

15

1920 1960 2000

Age 7 05

10

15

20

25

30

1920 1960 2000

Age 8 010

20

30

40

1920 1960 2000

Age 9 010

20

30

40

50

1920 1960 2000

Age 10

010

30

50

70

1920 1960 2000

Age 11 020

40

60

80

1920 1960 2000

Age 12 020

40

60

80

100

1920 1960 2000

Age 13 020

40

60

80

100

1920 1960 2000

Age 14 020

40

60

80

100

1920 1960 2000

Age 15

020

40

60

80

120

1920 1960 2000

Age 16 050

100

150

1920 1960 2000

Age 17 050

100

150

1920 1960 2000

Age 18 050

100

150

1920 1960 2000

Age 19 050

100

150

1920 1960 2000

Age 20

Weig

ht

(net

lbs)

Year (1926 to 2011)

Historical weight-at-age

(Ageing methods, sampling locations, selectivity itself, etc. may bias these trends)

Trends in size-at-age

Minimum size limit

Trends in size-at-age

1997

2012

(Age-11 male halibut)

Minimum size limit

Directly observed gear selectivity (vulnerability)

Based on Didson acoustic camera observations (S. Kaimmer; In prep)

Figures from: Clark and Hare, 2003 & 2004

Selectivity by area may differ

~40%

Fishery

SurveyFishery

Abundance by area has changed

Length-based selectivity: area (vulnerability) vs. coast-wide (vulnerability + availability)

Changes in proportional abundance

+

Differences in: - Biology (age, length, length-at-age) - Vulnerability

Length-based selectivity: area (vulnerability) vs. coast-wide (vulnerability + availability)

Coast-wide “average” selectivity changes over time

Spatial approaches: Separate stocks < 2006

J.D. Herder 2008

Fishery

J.D. Herder 2008

Survey

J.D. Herder 2008

Survey

J.D. Herder 2008

Fishery

J.D. Herder 2008

FisheryJ.D. Herder 2008

Survey

J.D. Herder 2008

Survey

J.D. Herder 2008

Fishery

Spatial approaches: coastwide dynamics 2006+

J.D. Herder 2008

Fishery

J.D. Herder 2008

Survey

Population

Overview1) History2) Contributing factors3) 2012 Assessment investigation4) Path forward

Non-parametric length-based selectivity

Inputs:Minimum size binBin at which selectivity = 1.0Maximum size binType switchSDsize

SDtime (added this year)

Specifications:Operates on 10cm binsSex-specificType: Asymptotic, ‘Ramp’, or domed above size bin = 1.0Smoother for second difference b/w adjacent sizes within yearSmoother for second difference b/w adjacent years within size binYears for which to estimate separate curvesScaled by sex-specific catchability (so values above 1.0 are ok, since that bin is fixed)Catchability (q) can also vary among years

Crux: There is no underlying growth model, nor distribution of lengths for a given age.

The approach uses ‘true’ observed survey length-at-age to translate size- to age-based selectivity.

This is done via interpolating the values at age from the values at each bin.

Non-parametric length-based selectivity

Retrospective within the 2011 assessment(Sequentially removing data)

Retrospective: SymptomsAg

e-8

Recr

uits

(mill

ions

)

0

50

100

150

200

250

300

350

400

450

1995 1997 1999 2001 2003 2005 2007 2009 2011 2013

Spaw

ning

bio

mas

s (m

illio

ns n

et lb

s)

Increasing penalty on large recruitment estimates

Increasing penalty on large recruitment estimatesSS

Qs

Increasing initial recruitment penalty

Males

Females

Total

Secondary exploration: Investigate increasing the relative survey weight Explore process error in selectivity (time-varying)

Increased survey index weighting

Three tests: similar results

Selectivity – implementations

Time-varying selectivity

Selectivity SDtime: Base-case: 0.025 (50% of smoothing over length) 0.050.001

Selectivity SDtime:

Retrospective: Solution

Retrospective: Solution (Data only through 2011)

Retrospective: Contributing factors

1) Transition from area-specific to coastwide model in 2006(and retaining the assumption of constant availability)

2) Changes in the coastwide population distribution3) Too much emphasis on the age data

(and not the survey trend)4) Short time-series

Looking forward:

Comparison of spatial modeling approaches: - Coast-wide: time-varying selectivity

- Implicitly spatial: fleets-as-time-periodsfleets-as-areas

- Explicitly spatial: Multi-area assessment

Once selectivity is treated as time-varying, either length- or age-based formulations can capture the process.

Questions?