IOTC–2013–WPTT15–31 Rev_1 Stock assessment of bigeye tuna

IOTC–2013–WPTT15–31 Rev_1

Page 1 of 14

Stock assessment of bigeye tuna (Thunnus obesus)

in the Indian Oceanby Age-Structured Production Model (ASPM)

Tom Nishida

National Research Institute of Far Seas Fisheries,

Fisheries Research Agency, Shimizu, Shizuoka, Japan

Kiyoshi Itoh and Kazuharu Iwasaki

Environmental Simulation Laboratory (ESL),

Kawagoe, Saitama, Japan

October, 2013

Abstract

We applied an Age-Structured Production Model (ASPM) to assess the status of the

bigeye tuna stock (Thunnus obesus) in the Indian Ocean using 61 years of data

(1952-2012). The assessment results suggested that MSY=120,500 tons (catch in

2012=99,899 tons) and the SSB ratio (2012) is near the MSY level (1.10), while F ratio

(2012) is much lower than the MSY level (0.42). The results suggested that the bigeye

stock is in the healthy condition and the projection based on the current catch level

(99,899 tons) suggest that the current level can increase the stock from 2013 and after.

_____________________________________________________

Submitted to the IOTC WPTT15 (October 23-28, 2013), San Sebastian, Spain

david

Typewritten text

Received: 19 and 27 October 2013


Page 2 of 14

1. Introduction

In this paper, we attempted to assess the bigeye tuna (Thunnus obesus) (BET) stock in the Indian

Ocean using the ADMB implemented Age-Structured Production Model (ASPM) software. We

assume that BET in the Indian Ocean is a single stock. The (previouly used) Fortran-implemeted

ASPM software (Restrepo, 1997) has been recoded using AD Model Builder (Otter Research) and

used here. The ADMB implemented ASPM software is detailed in the users’ manual in another

document submitted to this meeting (IOTC-2011-WPTT13-46).

An initial run was conducted before the meeting and the final run will be conducted during the

meeting using the agreed parameters. In addition we plan to conduct a risk assessement based on

the final ASPM results to investigate the probablities for SSB of falling below the estimated MSY

level and F exceeding this level in next 10 years (2012-2022) during the meeting.

As the SS3 assessment is avaiable, we try to use same input inofrmation as much as possible, so

that results between SS3 and ASPM can be comparable to some etxrtent.

2. Input data

To implement ASPM, we used BET annual nominal catch, standardized (STD) CPUE, CAA

(catch-at-age) data by gear and also biological information for the period 1952 to 2012 (61 years).

Below are descriptions of the data used in the ASPM runs.

2.1 Nominal catch and type of fleets

IOTC Secretariat provided nominal catch by gear type, longline (frozen and fresh), purse seines (log

school and free school), BB (pole and line), line and others (Fig. 1). As LL (frozen and fresh) are

similar gear, we use one LL. In addition, line is very small catch, it is included to others. Thus we use

five fleets (LL, LOG, FREE, BB and OTH).

2.2 Standardized (STD) CPUE

As the base case, we used the Japanese STD_CPUE (Matsumoto et. al, 2013) (1960-2012). From

the previous assessment (Nishida et al, 2011), it was learned that STD_CPUE in the tropical region

had the better relation to the catch. This is due to major catch are from the tropical area. Thus we

used STD_CPUE in tropical area.


Page 3 of 14

Catch by gear [weight]

0

50000

100000

150000

200000

1950

1953

1956

1959

1962

1965

1968

1971

1974

1977

1980

1983

1986

1989

1992

1995

1998

2001

2004

2007

2010

Catch by gear (tons)

OTH

LINE

BB

FREE

LOG

FL

LL

0%

20%

40%

60%

80%

100%

1950

1953

1956

1959

1962

1965

1968

1971

1974

1977

1980

1983

1986

1989

1992

1995

1998

2001

2004

2007

2010

Comp of catch (weight) by gear

OTH

LINE

BB

FREE

LOG

FL

LL

Catch by gear [number]

0

2

4

6

8

10

12

1950

1953

1956

1959

1962

1965

1968

1971

1974

1977

1980

1983

1986

1989

1992

1995

1998

2001

2004

2007

2010

Catch by gear (million fish)

OTH

Line

BB

FREE

LOG

FL

LL

0%

20%

40%

60%

80%

100%

1950

1953

1956

1959

1962

1965

1968

1971

1974

1977

1980

1983

1986

1989

1992

1995

1998

2001

2004

2007

2010

Comp of catch (no) by gear

OTH

Line

BB

FREE

LOG

FL

LL

Fig. 1 trend of catch by gear (above: weight and below: number) (1950-2012)

0

2

4

6

8

10

12

14

STD_CPUE (Japan) (tropical area)

Fig. 2 Trend of STD_CPUE (Japan) (1960-2012)


Page 4 of 14

2.3 Catch-At-Age (CAA)

The IOTC Secretariat provided the CAA matrix data by gear. Fig. 3 shows annual trends of CAA by

gear.

0.0E+00

5.0E+05

1.0E+06

1.5E+06

2.0E+06

2.5E+06

3.0E+06

1950

1954

1958

1962

1966

1970

1974

1978

1982

1986

1990

1994

1998

2002

2006

2010

CAA (LL) (number)

age9

age8

age7

age6

age5

age4

age3

age2

age1

age0

0.0E+00

2.0E+06

4.0E+06

6.0E+06

8.0E+06

1.0E+07

1950

1953

1956

1959

1962

1965

1968

1971

1974

1977

1980

1983

1986

1989

1992

1995

1998

2001

2004

2007

2010

CAA (PS:LOG) (number) age9

age8

age7

age6

age5

age4

age3

age2

age1

age0

0.0E+00

2.0E+05

4.0E+05

6.0E+05

8.0E+05

1.0E+06

1950

1953

1956

1959

1962

1965

1968

1971

1974

1977

1980

1983

1986

1989

1992

1995

1998

2001

2004

2007

2010

CAA (PS:FREE)(number)age9

age8

age7

age6

age5

age4

age3

age2

age1

age0

0.0E+00

5.0E+05

1.0E+06

1.5E+06

2.0E+06

1950

1953

1956

1959

1962

1965

1968

1971

1974

1977

1980

1983

1986

1989

1992

1995

1998

2001

2004

2007

2010

CAA (BB) (number) age9

age8

age7

age6

age5

age4

age3

age2

age1

age0

0.0E+00

5.0E+05

1.0E+06

1.5E+06

1950

1953

1956

1959

1962

1965

1968

1971

1974

1977

1980

1983

1986

1989

1992

1995

1998

2001

2004

2007

2010

CAA (OTHERS) (number)

age9

age8

age7

age6

age5

age4

age3

age2

age1

age0

Fig. 3 CAA by gear (LL, PS: LOG, PS:FREE, BB and OTHER)

The horizontal red line represents the 1 million fish level.

LL and PS (LOG) are the similar catch level, while PS (FREE), BB and OTHER, the similar level.

As for the age compositions, LL catch older fish (age 3 or older), while other 4 gears (LOG, FREE,

BB and OTHEDR) catch younger fish (age 2 or younger)


Page 5 of 14

2.4 Biological information

In the ASPM analyses, three types of age-specific biological inputs are needed, i.e., natural

mortality-at-age (M), weights-at-age (beginning and mid-year) and proportion maturity-at-age.

(1) Natural mortality vector (M)

We applied annual M vectors used in Fig. 12 of the SS3 paper (Langley et al, 2013) (Box 1).

Box 1 M vectors # Natural mortality by age #age 0 1 2 3 4 5 6 7 8 9 0.8 0.8 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4

(2) Beginning- and mid-year weights-at-age

Using the growth curve derived by Eveson and Polacheck (2009, IOTC-2008-WPTT-09) (Box 2) and

the LW relationships (Box 3), we computed weight-at-age by 0.5 year (Box 4). These are also used

in SS3 (Langley et al 2013).

Box 2 Indian Ocean BET growth equation (Laslett et al, 2008)

0

20

40

60

80

100

120

140

160

180

0 1 2 3 4 5 6 7 8 9 10 11 12

Age

Length

(cm)


Page 6 of 14

Box 3 LW relation

For fork length < 80 cm: W = (2.74 x 10-5

)l2.908

Poreeyanond (1994) (Indian Ocean)

For 80cm <=fork length: W = (3.661x10-5

)l2.90182

Nakamura and Uchiyama (1966) (Pacific Ocean)

Box 4 BET Weights-at-age (tons) in the Indina Ocaen

# Beginning of the year weights by age (tons) # age 0 1 2 3 4 5 6 7 8 9 0.00065 0.00149 0.00296 0.00891 0.02353 0.04013 0.05452 0.06565 0.07373 0.07938 # # Middle of the year weights by age (tons) # age 0 1 2 3 4 5 6 7 8 9 0.00106 0.00206 0.00473 0.01552 0.03195 0.04771 0.06050 0.07004 0.07682 0.08150

(3) Maturity-at-age

We assume that the proportion-at-maturity is 0% for age 0-2, 50% for age 3 and 100% for age 4-9+

(Box 5).

Box 5 Maturity and fecundity of YFT in the Indian Ocean

# Proportion maturity by age # age 0 1 2 3 4 5 6 7 8 9 0 0 0 0.5 1 1 1 1 1 1

3. ASPM

3.1 Base case (initial) run

We attempted to conduct the initial (base case) ASPM runs using same input

parameters in SS3 as much as possible, so that both results are comparable. Table 1

compare specs of the base case runs between SS3 (Langley et al, 2013) and ASPM

(this paper).

Using base case steepness (h=0.7, 0.8 and 0.9), we could not get the parameters

(Table 2). Then we explored h=0.65 and h=0.6. With h=0.6 we could get conversion

and we further explore Sigma-R for 0.2, 0.3 and 0.4 in addition to the base case

Sigma-R=0.6. As a results, Sigma-R=0.3 produced the best good-of-fitness of the data

to ASPM. Then we selected this scenario (h=0.6, Sigma-R=0.3) as the result of the

initial ASPM run. Table 2 and Figs. 4-6 show results.


Page 7 of 14

Table 1 Comparison of specs of the base case between SS3 (Langley et al, 2013) and ASPM (this paper)

SS3 ASPM

Stock

structure

Single stock hypothesis

Spatial

structure

3 areas 1 area

(aggregated)

Temporal

structure

quarterly annual

Age

structure

Age 0-9+

(quarterly basis)

Age 0-9+

(annual basis)

Fleet 7 fleets: LL, LL(fresh), BB, PS(free),

PS(log),Line and OTH by area

5 fleets :

LL, BB, PS(free), PS(log) and OTH

Catch 1952-2011 1952-2012

CAS 1952-2011

CAA 1952-2012

STD_CPUE Japan 1960-2011 by Q

per. comm. with Satoh et al (2012)

Japan 1960-2012 by year

Matsumoto et al (2013)

CV

STD_CPUE

0.1

Tagging

data

applied

Steepness 0.7, 0.8 and 0.9

R-sigma 0.6

Selectivity Estimated

by models

Estimated

by ad hoc (model-free)

Natural

mortality

0.8/yr (age 0-2)+0.4/yr(age 3-9+)

Quarterly basis

0.8/yr (age 0-2)+0.4/yr(age 3-9+)

Annual basis

LW

relation

For fork length < 80 cm: W = (2.74 x 10-5)l

2.908 Poreeyanond (1994) (Indian Ocean)

For 80cm <=fork length: W = (3.661x10-5 )l

2.90182 Nakamura and Uchiyama (1966) (Pacific Ocean)

Growth

Equation

Eveson and Polacheck (2009, IOTC-2008-WPTT-09)


Page 8 of 14

Table 2 Results of the base case runs

Steep-

ness

seeding

values

SSB (1952)

Million tons

(in natural log)

Sigma

R

Results

Likelihood_components

_and_weights

Kobe plot

Base case runs

0.90 10 (13.82) 0.6 Hessian does not appear to be positive definite

15 (16.52) Not converged

0.80

10 (13.82) Not converged

15 (16.52) Hessian does not appear to be positive definite

0.70 10 (13.82) Hessian does not appear to be positive definite


Extra runs as no parameters were obtained in the base case runs

0.65 10 (13.82) 0.6 Hessian does not appear to be positive definite


0.60 10 (13.82)

0.6 Total -107.861

Indices -96.238

CAA -14.019

SR_fits 2.217

Negpen 0.006

R-square 0.855

0.4 Total -105.098

Indices -96.173

CAA -12.805

SR_fits 3.732

Negpen 0.006

R-square 0.852

0.3

Best

Goodne

ss of

fitness

Total -102.338

Indices -96.08

CAA -11.744

SR_fits 5.376

Negpen 0.006

R-square 0.848

0.2 Hessian does not appear to be positive definite

15 (16.52) 0.6 Hessian does not appear to be positive definite


Page 9 of 14

1 5

2 6

3 7

4 8

0

50000

100000

150000

200000

250000

300000

350000

1952 1962 1972 1982 1992 2002 2012

SS

B (

1,0

00t)

SSB

SSB

SSBmsy

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

1952 1962 1972 1982 1992 2002 2012

SS

B/S

SB

msy

SSB/SSBmsy

0

5000

10000

15000

20000

25000

30000

35000

0 50000 100000 150000 200000 250000 300000

Recru

itm

en

t (m

il.

fish

)

SSB(1,000t)

S/R Relation

0.00.51.01.52.02.53.03.54.04.55.05.56.06.57.07.58.08.59.09.5

10.010.511.011.512.012.513.0

1952 1962 1972 1982 1992 2002 2012

CP

UE

CPUE

Observed

Predicted

0

2000

4000

6000

8000

10000

12000

14000

1952 1962 1972 1982 1992 2002 2012

Catc

h (

1,0

00t)

Catch

Catch

MSY

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1952 1962 1972 1982 1992 2002 2012

F/F

msy

F/Fmsy

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

0.50

1940 1950 1960 1970 1980 1990 2000 2010 2020Recru

itm

en

t (x

10^6)

S/R (residuals)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 2 4 6 8 10

Sele

cti

vit

y

Selectivity

Fleet1 Fleet2

Fleet3 Fleet4

Fleet5

0

1

0 1 2 3 4

F/F

msy

SSB/SSBmsy

Kobe Plot

Fig. 4

Results of the base

case ASPM run (I)


Page 10 of 14

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 2 4 6 8 10

Sele

cti

vit

y

Age

LL

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0 1 2 3 4 5 6 7 8 9

Pro

po

rtio

n

Age

LLavObs

avPred

0

2

4

6

8

10

1940 1950 1960 1970 1980 1990 2000 2010 2020

Ag

e

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 2 4 6 8 10

Sele

cti

vit

y

Age

PS(LOG)

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0 1 2 3 4 5 6 7 8 9

Pro

po

rtio

n

Age

PS(LOG)avObs

avPred

0

2

4

6

1940 1950 1960 1970 1980 1990 2000 2010 2020

Ag

e0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 2 4 6 8 10

Sele

cti

vit

y

Age

PS)FREE)

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0 1 2 3 4 5 6 7 8 9

Pro

po

rtio

n

Age

PS)FREE)avObs

avPred

-2

0

2

4

6

8

10

1940 1950 1960 1970 1980 1990 2000 2010 2020A

ge

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 2 4 6 8 10

Sele

cti

vit

y

Age

BB

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0 1 2 3 4 5 6 7 8 9

Pro

po

rtio

n

Age

BBavObs

avPred

-2

0

2

4

6

8

10

1940 1950 1960 1970 1980 1990 2000 2010 2020

Ag

e

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 2 4 6 8 10

Sele

cti

vit

y

Age

OTHER

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0 1 2 3 4 5 6 7 8 9

Pro

po

rtio

n

Age

OTHERavObs

avPred

-2

0

2

4

6

8

10

1940 1950 1960 1970 1980 1990 2000 2010 2020

Ag

e

Fig. 5 Results of the base case ASPM run (II)


Page 11 of 14

Fig. 6 Kobe plot (stock trajectory) for the initial ASPM run

Table 3 Indian Ocean bigeye stock status summary based on the ASPM analyses

Management quantity ASPM

Most recent catch estimate (t) (2012) 115,793

Mean catch over last 5 years (t) (2008–2012) 107,603

MSY (80% CI)

120,530 (90,722–150,288)

Data period (catch) 1952-2012

CPUE series Japan (tropical area)

CPUE period 1960-2012

Fcurrent/FMSY (80% CI)

0.42 (0.27–0.74)

Bcurrent/BMSY (80% CI) n.a.

SB2012/SBMSY (80% CI)

1.10 (0.88–1.32)

B2012/B1952 (80% CI) n.a.

SB2012/SB1952 (80% CI) 0.38 (n.a.)

SB2012/SBcurrent, F=0 n.a.


Page 12 of 14

Deterministic projection based on the 2012 catch for 5 fleets.

1 5

2 6

3Graph

0

500

1000

1500

2000

2500

1950 1960 1970 1980 1990 2000 2010 2020

SS

B (

1,0

00t)

SSB

median

90% PI

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1950 1960 1970 1980 1990 2000 2010 2020

F/F

msy

F/Fmsy

median

90% PI

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

1950 1960 1970 1980 1990 2000 2010 2020

SS

B/S

SB

msy

SSB/SSBmsy

median

90% PI

0.0

0.1

0.1

0.2

0.2

0.3

0.3

0.4

0.4

1950 1960 1970 1980 1990 2000 2010 2020

F

F

median

90% PI

0

500000

1000000

1500000

2000000

2500000

0 200 400 600 800 1000

K (

ton

s)

K

Year of Boundary

2012 Apply


Page 13 of 14

Acknowledgements

We sincerely thank to Miguel Herrera, Data manager (IOTC) for providing the nominal catch and

Catch-At-Age (CAA) data of bigeye tuna in the Indian Ocean.

References

Anonymous (2001) Report of the IOTC ad hoc working party on methods, Sète, France 23-27, April,

2001: 20pp.

Beverton, R. J. H., and S. Holt. 1957. On the dynamics of exploited fish populations. Reprinted in

1993 by Chapman and Hall, London. 553 pp.

Deriso, R. B., T. J. Quinn, and P. R. Neal.1985. Catch-age analysis with auxiliary information. Can. J.

Fish. Aquat.Sci.42:815-824.

Goodyear, C. P. 1993. Spawning stock biomass per recruit in fisheries management: foundation

and current use.p.67-81 in S. J. Smith, J. J. Hunt, and D. Rivard (eds.) Risk evaluation

and biological reference points for fisheries management. Can. Spec. Publ. Fish. Aquat.

Sci. 120

Hilborn, R.1990. Estimating the parameters of full age structured models from catch and abundance

data. Bull. Int. N. Pacific Fish Comm.50: 207-213.

ICCAT. 1997. Report for biennial period 1996-97. Part I (1996), Vol.2. Int. Int. Comm. Cons. Atl.

Tunas. 204pp.

IOTC. 2002-2008. Working documents in WPTT (Working party on Tropical Tuna) available in the

IOTC web site at http://www.iotc.org/

Matsumoto, T., H. Okamoto and T. Kitakado, 2013. Japanese longline CPUE for yellowfin tuna in

the Indian Ocean up to 2012 standardized by generalized linear model.

IOTC-2013-WPTT15-37, 1-43.

Prager, M. H. 1994. A suite of extensions to a no equilibrium surplus-production model. Fish. Bull.

92:374-389.

Punt, A. E. 1994. Assessments of the stocks of Cape hakes, Merluccius spp. Off South Africa. S. Afr.

J. Mar. Sci. 14 : 159-186.

Restrepo, V. 1997. A stochastic implementation of an Age-structured Production model (ICCAT/

SCRS/97/59), 23pp. with Appendix

Schaefer, M. B 1957. A study of dynamics of the fishery for yellowfin tuna in the eastern tropical

Pacific Ocean. IATTC Bull. Vol. 2: 247-285.


Page 14 of 14

APPENDIX

Documents

IOTC–2013–WPTT15–31 Rev_1 Stock assessment of bigeye tuna