A retrospective investigation
of selectivity for Pacific halibut
CAPAM Selectivity workshop
14 March, 2013
Ian Stewart & Steve Martell
Overview
1) History
2) Contributing factors
3) 2012 Assessment investigation
4) Path forward
Assessment model evolution
Years
Pre-1977
Model
Issues
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),
Migratory dynamics not
accounted for
coastwide, M=0.2
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
M estimate imprecise
selectivity, M=0.2
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,
Retrospective pattern
M=0.15
2003-2006 SCA, area-specific, constant length-based selectivity,
M=0.15
2006-2011 SCA, coastwide, constant length-based selectivity,
M=0.15
Migratory dynamics
created bias
Retrospective pattern
Retrospective I: Age-based selectivity
3A
Interim: Length-based selectivity
Figure from: Clark and Hare, 2002
3A
Retrospective II: Age-based selectivity
Figure from: Clark and Hare, 2002
3A Exploitable biomass (M lb)
Interim II: Length-based selectivity
Figure from: Clark and Hare, 2004
Retrospective III: Length-based selectivity
Overview
1) History
2) Contributing factors
3) 2012 Assessment investigation
4) 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
Length (cm)
Dimorphic and spatial variability
Growth curves by area
Age (years)
1960
1960
20
10
2000
Age 10
1960
2000
80 100
1920
60
40
20
20
2000
1920
1960
0
Age 14
2000
Age 15
1920
1960
2000
150
150
150
1920
1960
2000
100
100
1920
1960
50
50
Age 19
2000
1920
1960
0
Age 18
0
Age 17
0
0
2000
1960
50
50
1920
1920
100
100
120
20 40 60 80
Age 16
Age 13
0
0
2000
1960
60
80 100
40
1920
1920
0
0
2000
20
20
0
2000
150
1960
Age 12
30
30
20
10
1960
60
60
40
50
30
0 10
1920
Age 9
80 100
2000
40
40
50
10 15 20 25 30
1960
80
1920
Age 8
40
2000
70
1960
Age 11
1920
0
Weight (net lbs)
1920
Age 7
0
Age 6
0
0
5
5
5
10
10
15
15
Historical weight-at-age
2000
Age 20
1920
1960
2000
Year (1926 to 2011)
(Ageing methods, sampling locations, selectivity itself, etc. may bias these trends)
Trends in size-at-age
Minimum size limit
Trends in size-at-age
Minimum size limit
1997
2012
(Age-11 male halibut)
Directly observed gear selectivity
(vulnerability)
Based on Didson acoustic camera observations (S. Kaimmer; In prep)
Selectivity by area may differ
Fishery
~40%
Fishery
Survey
Figures from: Clark and Hare, 2003 & 2004
Abundance by area has changed
Length-based selectivity:
area (vulnerability) vs. coast-wide (vulnerability + availability)
Differences in:
- Biology (age, length, length-at-age)
- Vulnerability
Changes in proportional abundance
+
Length-based selectivity:
area (vulnerability) vs. coast-wide (vulnerability + availability)
Coast-wide “average” selectivity
changes over time
Spatial approaches: Separate stocks < 2006
Fishery
J.D. Herder 2008
Survey
Fishery
J.D. Herder 2008
Survey
Fishery
Survey
J.D. Herder 2008
Fishery
J.D. Herder 2008
Survey
Spatial approaches: coastwide dynamics 2006+
Fishery
Survey
J.D. Herder 2008
Overview
1) History
2) Contributing factors
3) 2012 Assessment investigation
4) Path forward
Non-parametric length-based selectivity
Inputs:
Minimum size bin
Bin at which selectivity = 1.0
Maximum size bin
Type switch
SDsize
SDtime (added this year)
Specifications:
Operates on 10cm bins
Sex-specific
Type: Asymptotic, ‘Ramp’, or domed above size bin = 1.0
Smoother for second difference b/w adjacent sizes within year
Smoother for second difference b/w adjacent years within size bin
Years for which to estimate separate curves
Scaled by sex-specific catchability (so values above 1.0 are ok, since that bin is fixed)
Catchability (q) can also vary among years
Non-parametric length-based selectivity
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.
Retrospective within the 2011 assessment
(Sequentially removing data)
Age-8 Recruits (millions)
Retrospective: Symptoms
Increasing penalty on large recruitment estimates
450
Spawning biomass (millions net lbs)
400
350
300
250
200
150
100
50
0
1995
1997
1999
2001
2003
2005
2007
2009
2011
2013
Increasing penalty on large recruitment estimates
Males
Total
SSQs
Females
Increasing initial recruitment penalty 
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:
0.001
Base-case: 0.025
(50% of smoothing over length)
0.05
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 distribution
3) 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-periods
fleets-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?