Multispecies Catch at Age Model (MSCAGEAN): incorporating predation interactions and statistical assumptions for a predator‑prey system in the eastern Bering Sea

Jesus Jurado-MolinaUniversity of Washington

Patricia A. LivingstonAlaska Fisheries Science

Center

Fisheries models

Age Structured Models

Statistical Assumptions

Statistical Catch at Age Models

Assumption:

Population Isolated

Constant Natural Mortality

Fisheries models

Virtual

Population Analysis

Predation Equations

M=M1+M2

Multispecies Virtual

Population Analysis (MSVPA)

No statistical assumptions on error structure included

Multispecies Catch at age Analysis?

Predation interactions

Age structured model

Statistical assumptions

on error structure

Multispecies Catch at age Analysis

Objectives: To add the predation equations to

a CAGEAN model (MSCAGEAN): Comparison of the MSCAGEAN

results to the ones estimated with the multispecies VPA, the Multispecies Forecasting Model (MSFOR) and the single species CAGEAN.

Input and outputs of MSVPA-MSFOR

Statistical models

Error assumption

Prior information

Data

Model equations

0

0.03

0.06

0.09

0.3

0.9

1.5

2.1

2.7

3.3

3.9

4.5

5.1

5.7

6.3

6.9

7.5

8.1

8.7

9.3

9.9

10.5

11.1

11.7

B3+ ratio

0

0.25

0.5

0.75

1

0 2 4 6 8 10 12 14

B3+ ratio

Predation equations

i a ai

aiaibpaibp BS

NRSM

,

,,,,,,2

p bbpbpbpaiai NWSBS ,,,,,,

S - suitability coefficient of prey p for predator i

BS - suitable prey biomass

R - annual ration of the predator i

W - weight at age of prey p

M2 - predation mortality

Multispecies CAGEAN

Error assumptio

n

Prior informatio

n

Data

Model equations

Predation equations

0

0.03

0.06

0.09

0.3

0.9

1.5

2.1

2.7

3.3

3.9

4.5

5.1

5.7

6.3

6.9

7.5

8.1

8.7

9.3

9.9

10.5

11.1

11.7

B3+ ratio

0

0.25

0.5

0.75

1

0 2 4 6 8 10 12 14

B3+ ratio

Equations:

2222 2/)/ln(2/)/ln( obspredobspred IICCL

)21(,1,1

,,, yayaya FMMyaya eNN

ayFullya SFF ,,

)(,

,,,

,,

,,,1 yayaya M2M1Fya

yayaya

yaya eN

M2M1F

FC

Advantages: Multispecies approach We can use the tools used in single

species stock assessments Likelihood profile Bayesian statistics (probability

distributions) Model selection (Akaike’s information

criterion,likelihood ratio )

Assumptions Stomach content measured without

error Suitabilities constant (estimated as the

average of the annual suitabilities) Recruitment for the simulation is log-

normal distributed Recruitment of age-0 individuals for the

simulation takes place in the third quarter

Walleye pollock and Pacific cod interactions

Walleye pollock

Pacific cod

Fishery

Methods Initial run of the MSVPA updated to

1998. Run of Multispecies forecasting (F40%). Spawning Biomass in 2015 as indicator

of performance. Multispecies Catch at Age Analysis

updated to 1998 Single species CAGEAN updated to 1998

MSVPA and MSCAGEAN results: Age-0 walleye pollock Natural mortality (1990)

MSCAGEANMSVPA

1.55

M2 = 1.70 ± 57

Age-0 walleye pollock natural mortaliy in 1990

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.35

327

0.50

327

0.65

327

0.80

327

0.95

327

1.10

327

1.25

327

1.40

327

1.55

327

1.70

327

1.85

327

2.00

327

2.15

327

2.30

327

2.45

327

2.60

327

2.75

327

2.90

327

3.05

327

3.20

327

M

MSVPA and MSCAGEAN results: suitability coefficients

MSCAGEANMSVPA

0.303

0.683 ± 0.140

Age-0 - age-1 walleye pollock suitability

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.0125

0.0625

0.1125

0.1625

0.2125

0.2625

0.3125

0.3625

0.4125

0.4625

0.5125

0.5625

0.6125

0.6625

0.7125

0.7625

0.8125

0.8625

0.9125

0.9625

MSVPA AND MSCAGEAN results: Spawning biomass in 2015

MSCAGEANMSFOR

SSB = 5.52E6 ± 2.36E6

SSB = 1.33E7 ± 5.25E6

Waleye pollock spawning biomass in 2015

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

5625

00

3937

500

7312

500

1068

7500

1406

2500

1743

7500

2081

2500

2418

7500

2756

2500

3093

7500

3431

2500

3768

7500

4106

2500

4443

7500

SSB(2015)/SSB(1998)

Walleye pollock spaw aning biomass in 2015

00.010.020.030.040.050.060.070.080.09

SUM=SUM+1 SUM=SUM+L

MSCAGEAN and CAGEAN results: Spawning biomass in 2015

CAGEAN

MSCAGEAN

SSB = 1.19E07 ± 5.06E06

Waleye pollock spawning biomass in 2015

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

5625

00

3937

500

7312

500

1068

7500

1406

2500

1743

7500

2081

2500

2418

7500

2756

2500

3093

7500

3431

2500

3768

7500

4106

2500

4443

7500

SSB(2015)/SSB(1998)

SSB = 1.33E07 ± 5.25E06

Walleye pollock spaw ning biomass in 2015

0

2000000

4000000

6000000

8000000

10000000

12000000

14000000

16000000

Future tasks To implement the predation

equations in the stock assessments methods used in the AFSC assessments