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