Developing a statistical-multispecies framework for a predator-prey system in the eastern Bering Sea:

Jesús Jurado-MolinaUniversity of Washington

Jim Ianelli, Patricia LivingstonAlaska Fisheries Science Center

Ecological considerations in fisheries management

Competition Predation Environmental Regime

Shifts Habitat alteration

Scientific Framework to provide ecosystem-based advice in the Bering Sea Main goals for protecting ecosystem

attributes:1. Maintain predator/prey relationships 2. Maintain energy flow and balance 3. Maintain diversity Tools:1. Multispecies models (biological interactions)2. Multispecies models (technological

interactions)3. Full ecosystem models (ECOPATH,

ECOSIM…)

Multispecies models (biological interactions)

Deterministic models:1. Multispecies virtual population

analysis (MSVPA)2. Multispecies forecasting model

(MSFOR) Statistical models:1. Multispecies statistical model

(MSM)

Multispecies VPA

Data

Population Dynamics Equations

Predation Equations

Point

Estimates

Data

MSVPA-MSFOR models

Statistical catch-at-age models

Data

Priors

Population Dynamics Equations

Objective Function

Posterior Distribution

Likelihood

Profile

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Multispecies statistical model

Data

Prior

information

Population Dynamics

O bjective function

Predation equations

Posterior D istribution

Likelihood

Profile

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Data

MSM: assumptions Separable fishing mortality

assumption (Fa,t = saFfull,t) M= M1+ M2 Constant annual predator ration Stomach content measured

without error

Advantages of MSM: Multispecies approach Measuring indirect effects of fishing We can use the tools used in single-species

stock assessments Likelihood profile Bayesian analysis (posterior distributions) Decision analysis Model selection (Akaike’s information

criterion,likelihood ratio ) Able to make comparisons with the single-species

stock assessment models in the same statistical framework

MSM (previous version) Included only two species (walleye

pollock and Pacific cod) Set up in Excel Fitted only to catch at age data,

total catch, bottom trawl survey and EIT survey

Updated to 2002 data

MSM (new version) Three species, walleye pollock, Pacific

cod and arrowtooth flounder Set up in AD model builder Fitted to total catch data, bottom trawl

survey, pollock age composition, Pacific cod and arrowtooth length composition (from fishery), survey age and size composition, EIT survey (pollock)

Updated to 2006 data

MSM system for the Bering Sea

Walleye pollock

Pacific codFishery

Arrowtooth flounder

Walleye pollock N3+

0

5000000

10000000

15000000

20000000

25000000

30000000

35000000

1975 1980 1985 1990 1995 2000 2005

Year

N3+

(10

00's

)

MSVPA MSM AFSC

0

5000000

10000000

15000000

20000000

25000000

30000000

35000000

40000000

1975 1980 1985 1990 1995 2000 2005 2010

Year

N3+

(10

00's

)

Pacific cod N3+

0

200000

400000

600000

800000

1000000

1200000

1400000

1975 1980 1985 1990 1995 2000 2005 2010

Year

N3+

(10

00's

)

MSVPA MSM AFSC

Bottom trawl survey fitWalleye pollock

0.00E+00

1.00E+06

2.00E+06

3.00E+06

4.00E+06

5.00E+06

6.00E+06

7.00E+06

8.00E+06

1980 1985 1990 1995 2000 2005

Year

Bio

ma

ss

(t0

Obs Est

Pacific cod

0

200000

400000

600000

800000

1000000

1200000

1400000

1600000

1980 1985 1990 1995 2000 2005

Year

Bio

ma

ss

(t)

Obs Est

Total catch fitPacific cod

0

200000

400000

600000

800000

1000000

1200000

1400000

1600000

1980 1985 1990 1995 2000 2005

Year

Bio

ma

ss

(t)

Obs Est

Walleye pollock

0.00E+00

5.00E+05

1.00E+06

1.50E+06

2.00E+06

2.50E+06

3.00E+06

1975 1980 1985 1990 1995 2000 2005

Year

Cat

ch (

t)

Obs Est

Arrowtooth flounder

0

5000

10000

15000

20000

25000

1975 1980 1985 1990 1995 2000 2005

Year

Catc

h (

t)

Obs Est

Average predation mortality at age

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 2 4 6 8 10 12 14

Age

Avg

. Pre

dat

ion

mo

rtal

ity

msvpa adm

Walleye pollock

Pacific cod

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 1 2 3 4 5

Age

Avg

. Pre

dat

ion

mo

rtal

ity

MSVPA MSM

Pollock predation mortality

0

0.5

1

1.5

2

2.5

3

1975 1980 1985 1990 1995 2000 2005 2010

Year

Pre

dat

ion

mo

rtal

ity

(yea

r-1)

MSVPA MSM

Comparison of age-1 pollock predation mortality

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

1975 1980 1985 1990 1995 2000 2005 2010

Year

Pre

dat

ion

mo

rtal

ity

(yea

r-1)

MSVPA MSM

Comparison of age-2 pollock predation mortality

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

1975 1980 1985 1990 1995 2000 2005 2010

Year

Pre

dat

ion

mo

rtal

ity

(yea

r-1)

MSVPA MSM

Comparison of age-3 pollock predation mortality

0

0.02

0.04

0.06

0.08

0.1

0.12

1975 1980 1985 1990 1995 2000 2005 2010

Year

Pre

dat

ion

mo

rtal

ity

(yea

r-1)

MSVPA MSM

Comparison of age-4 pollock predation mortality

Walleye pollock predation mortality in 1979 (from MCMC with 3 million iterations)

MSVPA

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

Predation mortality

Po

ste

rio

r d

istr

ibu

tio

n

Age-1

MSVPA

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0 0.05 0.1 0.15 0.2 0.25

Predation mortality

Po

ste

rio

r d

istr

ibu

tio

n

Age-2

Age-3

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0 0.005 0.01 0.015 0.02 0.025 0.03

Predation mortality

Po

ste

rio

r d

istr

ibu

tio

n

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Predation mortality

Po

ste

rio

r d

istr

ibu

tio

n

Age-1 Age-2 Age-3

Walleye predation mortality in 1979

Predation mortality comparison

Slope = 0.9±0.02

r2 = 0.92

Predation mortality

0.00E+00

5.00E-01

1.00E+00

1.50E+00

2.00E+00

2.50E+00

3.00E+00

0 0.5 1 1.5 2 2.5 3

MSVPA

MS

M

Comparison of causes of death (numbers) - Pollock

0.0E+00

2.0E+07

4.0E+07

6.0E+07

8.0E+07

1.0E+08

1.2E+08

1979

1981

1983

1985

1987

1989

1991

1993

1995

1997

1999

2001

2003

Year

Nu

mb

ers

(10

00

's)

Catch M1 M2

0

0.2

0.4

0.6

0.8

1

1.2

1979

1981

1983

1985

1987

1989

1991

1993

1995

1997

1999

2001

2003

Year

% o

f d

eath

s (n

um

be

rs)

Catch M1 M2

Comparison of causes of death (biomass) - Pollock

0.0E+002.0E+064.0E+06

6.0E+068.0E+061.0E+071.2E+07

1.4E+071.6E+071.8E+07

1979

1981

1983

1985

1987

1989

1991

1993

1995

1997

1999

2001

2003

Year

Bio

mas

s (

t)

Catch M1 M2

0

0.2

0.4

0.6

0.8

1

1.2

1979

1981

1983

1985

1987

1989

1991

1993

1995

1997

1999

2001

2003

Year

% o

f d

eath

s (b

iom

ass)

Catch M1 M2

Comparison of causes of death (spawning biomass) - Pollock

0.00E+00

5.00E+05

1.00E+06

1.50E+06

2.00E+06

2.50E+06

3.00E+06

3.50E+06

4.00E+06

4.50E+06

1979

1981

1983

1985

1987

1989

1991

1993

1995

1997

1999

2001

2003

Year

Sp

awn

ing

bio

mas

s (t

)

Catch M2 M1

0

0.2

0.4

0.6

0.8

1

1.2

1979

1981

1983

1985

1987

1989

1991

1993

1995

1997

1999

2001

2003

Year

% o

f d

eath

s (

SS

B)

Catch M2 M1

Walleye pollock Recruitment

0.0E+00

2.0E+07

4.0E+07

6.0E+07

8.0E+07

1.0E+08

1.2E+08

1975 1980 1985 1990 1995 2000 2005 2010

MSVPA MSM SSP

Year

Rec

rutm

ent

(100

0's)

Future tasks Addition of the complete set of

stomach content data Module for model projections Module for technological

interactions

Developing a statistical-multispecies framework for a predator-prey system in the eastern Bering Sea:

Jesús Jurado-MolinaUniversity of Washington

jjurado@u.washington.eduJesus.Jurado-Molina@noaa.gov