Gulf of Maine cod SCAA/ASPM vs ADAPT-VPA Doug Butterworth and Rebecca Rademeyer _____________________________________________________________ _____ Marine Resource Assessment and Management Group, University
Feb 05, 2016
Gulf of Maine cod
SCAA/ASPM vs ADAPT-
VPA
Doug Butterworth and Rebecca Rademeyer__________________________________________________________________Marine Resource Assessment and Management Group, University of Cape Town
METHODSADAPT-VPA- Backward calculation
- Oldest-age F assumption
- Catches-at-age exact
SCAA/ASPM- Based on separability: Fy,a = SaFy
- Forward estimation, typically likelihood based
- Errors in proportions-at-age
SCAA - Statistical treatment of age data errors
May include S/R relationship
ASPM - Age-structured dynamics
Must include S/R relationship
Age data not necessary
ASPM methodology updates
- M fixed (0.2) (not estimated)
- Ricker-like not Beverton-Holt S/R relationship
spB
speBR- MSY calculated internally
- All Sa’s estimated (no functional form imposed)
- Model to 11+, though fit to 7+ data
- Fully Bayesian PI computations
VPA methodology
- RC-VPA: as Mayo and Col (2006) – asymp. flat
selectivity
Fit either to ages 1-6 or 1-7+
MSY calculated externally
- Alt-VPA (=1): removes inconsistency in plus-
group eqns- Alt-VPA (=est): estimates where 1,,
ˆ mymy FF
Data used
Mayo and Col (2006)
BUT
Scaled to get a
ayayy CwC ,,ayC ,
2003 ResultsGulf of Maine cod
ResultsRC-ASPM (M=0.2, Ricker)
0
50000
100000
150000
200000
250000
1893 1913 1933 1953 1973 1993
spaw
ning
bio
mas
s (t
)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1893 1913 1933 1953 1973 1993Bsp
/Ksp
Shading shows 95% PIs
Abundance index fitsRC-ASPM (M=0.2, Ricker)
a) Fit to NEFSC-Spr
0
2
4
6
8
10
12
14
16
18
20
1967 1972 1977 1982 1987 1992 1997 2002
Stan
dard
ised
mea
n w
eigh
t (kg
/tow
) b) Fit to NEFSC-Aut
0
5
10
15
20
25
30
1963 1973 1983 1993 2003
Sta
ndar
dise
d m
ean
wei
ght (
kg/to
w)
c) Fit to MASpr
0
5
10
15
20
25
30
1977 1982 1987 1992 1997 2002
Str
atif
ied
mea
n w
eigh
t (kg
/tow
) d) Fit to MAAut
0
1
2
3
4
5
6
7
8
1977 1982 1987 1992 1997 2002
Str
atif
ied
mea
n w
eigh
t (kg
/tow
) e) Fit to LPUE
0.00
0.05
0.10
0.15
0.20
0.25
0.30
1981 1983 1985 1987 1989 1991 1993
Cat
ch r
ate
Average age-proportion fitsRC-ASPM (M=0.2, Ricker)
a) NEFSC-Spr
0.00
0.05
0.10
0.15
0.20
0.25
1 2 3 4 5 6 7+
Pro
port
ion
b) Fit to WHAut
0
5
10
15
20
25
30
1963 1973 1983 1993 2003
Stan
dard
ised
mea
n w
eigh
t (kg
/tow
)
c) Fit to MASpr
0
5
10
15
20
25
30
1977 1982 1987 1992 1997 2002
Str
atif
ied
mea
n w
eigh
t (kg
/tow
)
d) Fit to MAAut
0
1
2
3
4
5
6
7
8
1977 1982 1987 1992 1997 2002
Stra
tifi
ed m
ean
wei
ght (
kg/t
ow)
e) Fit to CM_CPE
0
0.05
0.1
0.15
0.2
0.25
0.3
1981 1983 1985 1987 1989 1991 1993
Str
atif
ied
mea
n w
eigh
t (kg
/tow
)
b) NEFSC-Aut
0.00
0.05
0.10
0.15
0.20
0.25
1 2 3 4 5 6 7+
Pro
port
ion
c) MASpr
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
1 2 3 4+
Pro
port
ion
d) MAAut
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
1 2 3+
Pro
port
ion
e) Commercial
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
2- 3 4 5 6 7+
Pro
port
ion
Selectivity estimatesRC-ASPM (M=0.2, Ricker)
Commercial, pre-1992Commercial, post-1991
0.0
0.2
0.4
0.6
0.8
1.0
1 2 3 4 5 6 7 8 9 10 11Age
Sele
ctiv
ity
Selectivity estimatesRC-ASPM (M=0.2, Ricker)
0.0
0.2
0.4
0.6
0.8
1.0
1 2 3 4 5 6 7 8 9 10 11Age
Sel
ecti
vity
Commercial, pre-1992Commercial, post-1991NEFSC-SpringNEFSC-Autumn
0
5
10
15
20
25
30
0 25000 50000 75000 100000 125000 150000 175000
Spawning biomass (t)
N1
(x10
6 )
0
5
10
15
20
25
30
0 25000 50000 75000 100000 125000 150000 175000
Spawning biomass (t)
N1
(x10
6 )
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
Sto
ck-r
ecru
itm
ent r
esid
uals
0
5
10
15
20
25
30
0 25000 50000 75000 100000 125000 150000 175000
0
10
20
30
40
50
60
70
80
0 10000 20000 30000 40000 50000 60000
Spawning biomass (t)
N1
(x10
6 )
0
5
10
15
20
25
30
0 25000 50000 75000 100000 125000 150000 175000
Spawning biomass (t)
N1
(x10
6 )
0
5
10
15
20
25
30
35
40
0 25000 50000 75000 100000 125000 150000 175000
Spawning biomass (t)
N1
(x10
6 )
0
5
10
15
20
25
30
35
40
0 25000 50000 75000 100000 125000 150000 175000
Spawning biomass (t)
N1
(x10
6 )
spMSYB
ASPMStock-recruit relationships
-lnL = -46.3
Ricker
ASPMStock-recruit relationships
-lnL = -46.3
0
5
10
15
20
25
30
0 25000 50000 75000 100000 125000 150000 175000
Spawning biomass (t)
N1
(x10
6 )
0
5
10
15
20
25
30
0 25000 50000 75000 100000 125000 150000 175000
Spawning biomass (t)
N1
(x10
6 )
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
Sto
ck-r
ecru
itm
ent r
esid
uals
0
5
10
15
20
25
30
0 25000 50000 75000 100000 125000 150000 175000
Spawning biomass (t)N
1 (x
106 )
spMSYB
0
10
20
30
40
50
60
70
80
0 10000 20000 30000 40000 50000 60000
Spawning biomass (t)
N1
(x10
6 )
0
5
10
15
20
25
30
0 25000 50000 75000 100000 125000 150000 175000
Spawning biomass (t)
N1
(x10
6 )
0
5
10
15
20
25
30
35
40
0 25000 50000 75000 100000 125000 150000 175000
Spawning biomass (t)
N1
(x10
6 )
0
5
10
15
20
25
30
35
40
0 25000 50000 75000 100000 125000 150000 175000
Spawning biomass (t)
N1
(x10
6 )
spMSYB
Ricker
Beverton-Holt
-lnL = -39.9
If estimate parameter ( =1 for Ricker): 1.05 [0.54; 1.15]
ASPMSelectivity dome
-lnL = -46.3
1980 1985 1990 1995 2000 2005
1980 1985 1990 1995 2000 2005
Age
7+
3
2-
4
5
6
S7/S6 =0.52 [0.41; 0.64]
-lnL = -11.4
1980 1985 1990 1995 2000 2005
Age
7+
3
2-
4
5
6
Asymp. flat selectivity
ASPMPast catch selectivity
1992-2004: Estimated
1981-1991: Estimated
Pre-1982: Set equal to 1982-1991
Second order effect(Important assumption is unchanging survey selectivity)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
0 1 2 3 4 5 6 7 8 9 10 11+
Per
-rec
ruit
con
trib
utio
nto
coh
ort b
iom
ass
ASPM Results
ASPM Results
ASPM Results
ADAPT-VPA comparisons
VPA as Mayo and Col (2006)
0
10000
20000
30000
40000
50000
60000
70000
80000
90000
1982 1987 1992 1997 2002
Bsp
(t)
ADAPT-VPA comparisons
VPA as Mayo and Col (2006)RC-VPA
0
10000
20000
30000
40000
50000
60000
70000
80000
90000
1982 1987 1992 1997 2002
Bsp
(t)
0
10000
20000
30000
40000
50000
60000
70000
80000
90000
1982 1987 1992 1997 2002
ADAPT-VPA comparisons
VPA as Mayo and Col (2006)RC-VPAAlt-VPA, =1
0
10000
20000
30000
40000
50000
60000
70000
80000
90000
1982 1987 1992 1997 2002
Bsp
(t)
0
10000
20000
30000
40000
50000
60000
70000
80000
90000
1982 1987 1992 1997 2002
ADAPT-VPA comparisons
VPA as Mayo and Col (2006)RC-VPAAlt-VPA, =1Alt-VPA, =est
0
10000
20000
30000
40000
50000
60000
70000
80000
90000
1982 1987 1992 1997 2002
Bsp
(t)
0
10000
20000
30000
40000
50000
60000
70000
80000
90000
1982 1987 1992 1997 2002
ADAPT-VPA comparisons
VPA as Mayo and Col (2006)RC-VPAAlt-VPA, =1Alt-VPA, =estASPM – Data from 1982
0
10000
20000
30000
40000
50000
60000
70000
80000
90000
1982 1987 1992 1997 2002
Bsp
(t)
0
10000
20000
30000
40000
50000
60000
70000
80000
90000
1982 1987 1992 1997 2002
ADAPT-VPA comparisons
VPA as Mayo and Col (2006)RC-VPAAlt-VPA, =1Alt-VPA, =estASPM – Data from 1982RC – ASPM
0
10000
20000
30000
40000
50000
60000
70000
80000
90000
1982 1987 1992 1997 2002
Bsp
(t)
0
10000
20000
30000
40000
50000
60000
70000
80000
90000
1982 1987 1992 1997 2002
ADAPT-VPA comparisons
VPA as Mayo and Col (2006)RC-VPAAlt-VPA, =1Alt-VPA, =estASPM – Data from 1982RC – ASPM
b)
0
10000
20000
30000
40000
50000
60000
70000
80000
1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004
Bsp
(t)
ASPM, M=0.2, Ricker
RC-VPA
Alt-VPA, alpha=1
Alt-VPA, alpha=est
0
10000
20000
30000
40000
50000
60000
70000
80000
90000
1982 1987 1992 1997 2002
0
20000
40000
60000
80000
100000
120000
140000
160000
180000
1890 1910 1930 1950 1970 1990
Bsp
(t)
ADAPT-VPASelectivities
RC-VPA
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1 2 3 4 5 6 7 8 9 10 11Age
Sel
ectiv
ity
ADAPT-VPASelectivities
RC-VPAAlt-VPA, =1
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1 2 3 4 5 6 7 8 9 10 11Age
Sel
ecti
vity
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1 2 3 4 5 6 7 8 9 10 11
ADAPT-VPASelectivities
RC-VPAAlt-VPA, =1Alt-VPA, =est
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1 2 3 4 5 6 7 8 9 10 11Age
Sel
ecti
vity
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1 2 3 4 5 6 7 8 9 10 11
ADAPT-VPASelectivities
RC-VPAAlt-VPA, =1Alt-VPA, =estASPM – Data from 1982
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1 2 3 4 5 6 7 8 9 10 11Age
Sel
ecti
vity
ADAPT-VPASelectivities
RC-VPAAlt-VPA, =1Alt-VPA, =estASPM – Data from 1982RC – ASPM
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1 2 3 4 5 6 7 8 9 10 11Age
Sel
ecti
vity
0.0
0.2
0.4
0.6
0.8
1.0
1 2 3 4 5 6 7 8 9 10 11
0.0
0.2
0.4
0.6
0.8
1.0
1 2 3 4 5 6 7 8 9 10 11
ADAPT-VPA Results
ADAPT-VPA Results
ADAPT-VPA Results
Conclusions
General
- Careful treatment of plus-group
- Fully flexible Sa parametrization
- Take care with use of Beverton-Holt S/R relationship
Conclusions
Gulf of Maine cod- 2003 difference as ADAPT-VPA imposed asymp. flat selectivity- Asymp. flat selectivity statistically inconsistent with data Independent evidence of mechanisms to give dome
shape ?
- close to and spB2004
spMSYB MSYFF 2004
Robust to sensitivities
- SCAA to be preferredEnables use of pre-1982 data Greater range of Bsp Better precision of estimates M-S Act focus on MSY
Thank you for your attention