Estimation of age-specific migration in an age-structured population dynamics model of

Eastern Bering Sea walleye pollock (Theragra chalcogramma)

Sara E. Miller and Terrance J. Quinn II

Juneau Center, School of Fisheries and

Ocean SciencesUniversity of Alaska

Fairbanks

James N. Ianelli Resource Ecology and

Fisheries Management Division, Alaska

Fisheries Science Center, NMFS

OutlineBackgroundSpatial Movement Model and

Migration EstimationMethodsResultsFuture WorkConclusions

BackgroundWhy develop a migration model?

Spatial structure of the fishery can affect potential yields and impact fishing mortality

Add to the biological understanding of walleye pollock

Reduce uncertainty in the yearly EBS pollock stock assessments

•However, no estimates of movement rates However, no estimates of movement rates from a mark-recapture experiment; Can from a mark-recapture experiment; Can migration be estimated from current migration be estimated from current assessment data?assessment data?

Distribution

Alaska Distribution

Source: Mecklenburg et al. 2002

Bering Sea

Gulf of Alaska

Eastern Bering Sea

Background

Groundfish catch in the commercial fisheries in the Bering Sea/Aleutian Islands region off Alaska by species from 1989 to 2003 by round weight. Walleye pollock accounted for 76% (1.49 million t) of the total groundfish catch in 2003 in the BSAI fishery (Source: Hiatt et al. 2004).

Total Groundfish Catch by Species (BSAI)

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Background Current stock

assessment model (standard model)

-age-structured population

dynamics model -standard catch

equation -Ages-1+ -no seasonal movement -spatially aggregated -estimates values for

entire population in EBS

Fishery Seasons:

“A season,” mainly for roe, opens on January 20th and lasts until mid-March or April

“B season,” mainly for surimi and fillets, opens mid to late June and extends until October or early November

Both depending on catch rates

Background

Background

Current Stock Assessment Model (Standard Model) DATA:

-bottom trawl survey-acoustic survey-fishery catch-at-age

•Spatial distribution from surveys has poor Spatial distribution from surveys has poor correspondence to the commercial catch (different correspondence to the commercial catch (different times of the year)times of the year)

Methods Current Stock Assessment Model (Standard Model)

Ianelli et al. 2004

Spatial Age-Specific Movement Model (ASM Model) Simplified Ages-3 to 10+, 1977-2005 Extended the standard model

Stratified survey data into 2 areas (NW and SE EBS)Fishery data (2 areas, 2 seasons)

Population parameters area-specific Added movement between the two areas Implemented in ADModel Builder

Spatial Non-Movement Model Special case of spatial movement model, but NO movement included

ASM Model 13 data sources: (1) (2) Bottom trawl survey NW and SE

(1982-2004) (3) (4) EIT NW and SE (1994, 1996, 1997, 1999,

2000, 2002) (5) (6) NW_A fishery numbers & yield (1977-2004) (7) (8) NW_B fishery numbers & yield (1977-2004) (9) (10) SE_A fishery numbers & yield (1977-2004) (11) (12) SE_B fishery numbers & yield (1977-

2004) (13) Total catch yield (1977-2005)

Methods

ASM Model 13 data sources: (1) (2) Bottom trawl survey NW and SE

(1982-2004) (3) (4) EIT NW and SE (1994, 1996, 1997,

1999, 2000, 2002) (5) (6) NW_A fishery numbers & yield (1977-2004) (7) (8) NW_B fishery numbers & yield (1977-2004) (9) (10) SE_A fishery numbers & yield (1977-2004) (11) (12) SE_B fishery numbers & yield (1977-

2004) (13) Total catch yield (1977-2005)

Methods

ASM Model 13 data sources: (1) (2) Bottom trawl survey NW and SE (1982-

2004) (3) (4) EIT NW and SE (1994, 1996, 1997, 1999,

2000, 2002) (5) (6) NW_A fishery numbers & yield (1977-2004) (7) (8) NW_B fishery numbers & yield (1977-2004) (9) (10) SE_A fishery numbers & yield (1977-2004) (11) (12) SE_B fishery numbers & yield (1977-

2004) (13) Total catch yield (1977-2005)

Methods

Initial Abundance

Jan-May fishery removals (A_season)

Movement to summer distribution &

1/2 of natural mortality

Fisherycatch-

age data

Fishery catch-age and survey data

One Year

(Ages-3 to 10+)

June-Oct. fishery removals (B_season)

Movement to winterdistribution &

1/2 of natural mortality

A

A

B

B

A

Methods

Initial Abundance

Jan-May fishery removals (A_season)

Movement to summer distribution &

1/2 of natural mortality

Fisherycatch-

age data

Fishery catch-age and survey data

One Year

(Ages-3 to 10+)

June-Oct. fishery removals (B_season)

Movement to winterdistribution &

1/2 of natural mortality

A

A

B

B

A

Methods

Abundance and fishing mortality during the A season (A to )…

.

A

Age-specific fishing mortality with a logistic equation for fishery selectivity. Assumed: no natural mortality during fishing.

Methods

Ex. of logistic equation

Methods

Initial Abundance

Jan-May fishery removals (A_season)

Movement to summer distribution &

1/2 of natural mortality

Fisherycatch-

age data

Fishery catch-age and survey data

One Year

(Ages-3 to 10+)

June-Oct. fishery removals (B_season)

Movement to winterdistribution &

1/2 of natural mortality

A

A

B

B

A

Methods Natural mortality and movement

from end of A season ( ) to start of B season (feeding)…

A

# in NW (B)=# that stay in NW x natural survival + # that move from SE→NW x natural survival

Methods

Initial Abundance

Jan-May fishery removals (A_season)

Movement to summer distribution &

1/2 of natural mortality

Fisherycatch-

age data

Fishery catch-age and survey data

One Year

(Ages-3 to 10+)

June-Oct. fishery removals (B_season)

Movement to winterdistribution &

1/2 of natural mortality

A

A

B

B

A

Methods

Initial Abundance

Jan-May fishery removals (A_season)

Movement to summer distribution &

1/2 of natural mortality

Fisherycatch-

age data

Fishery catch-age and survey data

One Year

(Ages-3 to 10+)

June-Oct. fishery removals (B_season)

Movement to winterdistribution &

1/2 of natural mortality

A

A

B

B

A

MethodsModeling Movement:

NW: Movement (age-3) estimated

Movement (age a+1)= γ Movement (age a)

0.8 0.9

SE: Movement (all ages) constant

4 estimated movement parameters ( )

A

B

NW_A, NW_B, SE_A, SE_B

The probability of moving (NW→SE)=

1-probability of staying in the NW.

[Based on reasonable guess]

Methods

Objective function:

Negative log likelihood -addition of fourteen

components [13 data sources and penalty function (constrained parameters)] that assumed a lognormal distribution

ResultsSpatial non-movement model:

Non-sensical results

Estimates of year-class abundance (NW and SE), and total beginning year biomass (ages-3+) much higher than ASM model and the 2005 stock assessment estimates (standard model).

If movement not included in spatially-explicit model, can’t estimate realistic population parameters.

Results

ASM Model

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NW_B

SE_A

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ResultsOverall ASM model fitted data

well (√):1.Bottom trawl survey age-composition data

(NW, SE) √

1.Yearly bottom trawl survey data (NW, SE) √

2.Acoustic survey age-composition data (NW, SE) √

3.Yearly acoustic survey data (NW, SE) √

4.Catch data in numbers and biomass (NW, SE) √

5.Fishery age-composition data

(NW_A, NW_B, SE_A, SE_B) √

Data Conflicts:

Tradeoffs with individual data sources (i.e. certain years)

Frequent in stock assessment

1982 1989 1996 2003

1983 1990 1997 2004

1984 1991 1998 EIT 1994

1985 1992 1999 EIT 1996

1986 1993 2000 EIT 1997

1987 1994 2001 EIT 1999

1988 1995 2002 EIT 2000

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ResultsYear-Class Abundance

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1974 2002

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ASM

stock assess.2005

Estimates of recruitment from the standard stock assessment were usually somewhat lower than the ASM model though of the same order of magnitude.

Total Beginning Year Biomass (Ages 3-10+)

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24,000

1977 2005

Bio

mas

s to

ns (

x1,0

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ASM

stockassess.2005

Estimates of beginning year biomass from the standard stock assessment were lower than the ASM model (similar pattern).

Results

EBS Abundance

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1977 2005

x 1,

000,

000

Currently….

One yearly total allowable catch (TAC) for the whole EBS divided by the 3 fishing sectors and 2 fishery seasons (A and B) by fixed percentages

Advantage of ASM model:

More in-depth information for fishery management and allocation of quota both spatially (NW and SE separately) and temporally (within the year)

ASM

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SE_B

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ResultsReasonable estimates of many population and movement parameters obtained from existing data disaggregated by area and season.

Yet, this configuration of ASM model overly simplistic case of migration estimation with only 4 estimated migration parameters.

More realistic migration estimation would vary by year and age.

Future Work1. Combined age- and year-specific movements

(cold versus warm year movements)

2. More areas (oceanographic domains, Steller sea lions)

3. Test the robustness of the ASM model by a simulation experiment with known population and migration parameters (e.g., Fu and Quinn 2000; Hilborn and Mangel 1997).

4. Management strategy evaluation-How should harvest be allocated by area and season in the presence of movement?

Cold Year(more overlap)

Warm Year (less overlap)

Age-1 pollock

Adult pollock

cold pool

Adults are distributed more NW, offshore during cold years (Wyllie-Echeverria and Wooster 1998; Kotwicki et al. 2005).

Source:

Wyllie-Echeverria and Wooster 1998

Conclusions

*Key finding – more in-depth information on

finer spatial and temporal scales are likely from spatially-explicit studies of EBS walleye pollock. Having additional information

from tagging studies (movement studies) would help stabilize the

model.*

AcknowledgmentsReviewers: Dr. Brenda Norcross, Dr. Gordon

Haas, Pete Hulson, Cindy Tribuzio

Funding: North Pacific Research Board, Alaska Fisheries Science Center Population Dynamics Fellowship

Data: Dan Nichol (AFSC) bottom trawl survey data, Taina Honkalehto (AFSC) EIT survey data, Jim Ianelli (AFSC) fishery data

Pictures: Jenny Stahl (ADFG)

Any Questions?

Ray Troll