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					Estimation of age-specific migration in an
    age-structured population dynamics
    model of Eastern Bering Sea walleye
     pollock (Theragra chalcogramma)

      Sara E. Miller and
                                         James N. Ianelli
    Terrance J. Quinn II
        Juneau Center,           Resource Ecology and Fisheries
   School of Fisheries and        Management Division, Alaska
       Ocean Sciences                Fisheries Science Center,
University of Alaska Fairbanks                NMFS
                Outline
 Background

        Movement Model and
 Spatial
 Migration Estimation
     Methods

     Results

     FutureWork
     Conclusions
                    Background
 Why   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 from a
   mark-recapture experiment; Can migration be
   estimated from current assessment data?
                       Distribution

  Alaska Distribution

    Bering Sea


            Eastern Bering Sea

                                  Gulf of Alaska



Source: Mecklenburg et al. 2002
                                      Background
                                     Total Groundfish Catch by
                                           Species (BSAI)
                       2,000                                              atka
 X 1,000 metric tons




                                                                          mackerel
   (round weight)



                                                                          flatfish
                       1,500
                                                                          Pacific cod
                       1,000
                                                                          other
                        500                                               walleye
                                                                          pollock
                          0
                         89

                                91

                                       93

                                             95

                                                   97

                                                         99

                                                               01

                                                                     03
                        19

                               19

                                     19

                                            19

                                                  19

                                                        19

                                                              20

                                                                    20
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).
                        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
                         Background
   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

 CurrentStock Assessment Model
 (Standard Model)
 DATA:
    -bottom trawl survey
    -acoustic survey
    -fishery catch-at-age


  • Spatial distribution from surveys has poor correspondence to
    the commercial catch (different 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
                  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
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
           A                                                  A
                                                                              Fishery
 Movement to winter                                 Jan-May fishery           catch-
    distribution &                                removals (A_season)        age data
1/2 of natural mortality
                                   One Year
                                (Ages-3 to 10+)               A
                  B
                                                  Movement to summer
         June-Oct. fishery                            distribution &
       removals (B_season)              B         1/2 of natural mortality




         Fishery catch-age
          and survey data
                      Methods
                             Initial Abundance
           A                                                  A
                                                                              Fishery
 Movement to winter                                  Jan-May fishery          catch-
     distribution &                                removals (A_season)       age data
1/2 of natural mortality
                                   One Year
                                (Ages-3 to 10+)               A
                  B
                                                  Movement to summer
         June-Oct. fishery                             distribution &
       removals (B_season)              B         1/2 of natural mortality




         Fishery catch-age
          and survey data
                    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.




                                Ex. of logistic equation
                        Methods
                             Initial Abundance
           A                                                  A
                                                                              Fishery
 Movement to winter                                 Jan-May fishery           catch-
    distribution &                                removals (A_season)        age data
1/2 of natural mortality
                                   One Year
                                (Ages-3 to 10+)               A
                  B
                                                  Movement to summer
         June-Oct. fishery                            distribution &
       removals (B_season)              B         1/2 of natural mortality




         Fishery catch-age
          and survey data
                 Methods
Natural mortality and movement from end of A
season ( A ) to start of B season (feeding)…
                               # in NW (B)=
                               # that stay in NW
                               x natural survival
                                       +
                                # that move from
                               SE→NW x
                               natural survival
                       Methods
                             Initial Abundance
           A                                                  A
                                                                              Fishery
 Movement to winter                                  Jan-May fishery          catch-
     distribution &                                removals (A_season)       age data
1/2 of natural mortality
                                   One Year
                                (Ages-3 to 10+)               A
                  B
                                                  Movement to summer
         June-Oct. fishery                             distribution &
       removals (B_season)              B         1/2 of natural mortality




         Fishery catch-age
          and survey data
                      Methods
                             Initial Abundance
           A                                                  A
                                                                              Fishery
 Movement to winter                                 Jan-May fishery           catch-
    distribution &                                removals (A_season)        age data
1/2 of natural mortality
                                   One Year
                                (Ages-3 to 10+)               A
                  B
                                                  Movement to summer
         June-Oct. fishery                            distribution &
       removals (B_season)              B         1/2 of natural mortality




         Fishery catch-age
          and survey data
                 Methods
Modeling Movement:

 The probability estimated
 NW: Movement (age-3) of moving
 (NW→SE)= a+1)= γ Movement (age a)
     Movement (age
                          0.8 A [Based on
 1-probability of staying in the
                          0.9 B   reasonable guess]


 NW.
 SE: Movement (all ages) constant

        4 estimated movement parameters
           ( NW_A, NW_B, SE_A, SE_B)
               Methods

Objective function:

Negative log likelihood
  -addition of fourteen components [13 data
  sources and penalty function (constrained
  parameters)] that assumed a lognormal
  distribution
                  Results
Spatial 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
                  1.00
                                                             NW_A
Proportion that




                                                             NW_B
     Stay




                                                             SE_A
                  0.50
                                                             SE_B



                  0.00
                         3   4   5    6    7    8   9   10

                                          Age           NW_A
                   Results
Overall ASM model fitted data well (√):
1. Bottom trawl survey age-composition data
 Data Conflicts:
 (NW, SE) √
1. Yearly bottom trawl survey data (NW, SE) √
  Tradeoffs with individual dataSE) √
2. Acoustic survey age-composition data (NW,
                               years)
  sources (i.e. certain(NW, SE) √
3. Yearly acoustic survey data
 Frequent in stock assessment
4. Catch data in numbers and biomass (NW, SE) √
5. Fishery age-composition data
 (NW_A, NW_B, SE_A, SE_B) √
                                                         Survey-age composition (NW)
                                              1982                1989          1996             2003


       (x1,000,000)
       Abundance
                  2500                                   2500            1200          1500




                      0
                          3   4   5   6   7   8   9 10

                                      Ages
                                                           0               0             0

3000
                                              1983       2500
                                                                  1990   1200
                                                                                1997   1000
                                                                                                 2004



  0                                                        0               0             0

2500
4000
                                              1984       1000
                                                                  1991   1200
                                                                                1998   2000
                                                                                              EIT 1994
2000

  0




  0                                                        0               0             0

3000
                                              1985       2500
                                                                  1992   2000
                                                                                1999   3000
                                                                                              EIT 1996



  0                                                        0               0             0

2000
                                              1986       1500
                                                                  1993   1200
                                                                                2000   2000
                                                                                              EIT 1997



  0                                                        0               0             0

4000
                                              1987       1500
                                                                  1994   1200
                                                                                2001   4000
                                                                                              EIT 1999



  0                                                        0               0             0

3000
                                              1988       2000
                                                                  1995   1200
                                                                                2002   2500
                                                                                              EIT 2000



  0                                                        0               0             0
                                                     Results
                                              Total Beginning Year Biomass
                                                     Year-Class Abundance        ASM
                                                       (Ages 3-10+)
                    24,000                                         ASM
  Biomass tons (x1,000,000)



                                                                                 stock
                   30,000                                                        assess.
                                                                   stock assess. 2005
                              X 1,000,000




                                                                   2005




                                             0
                                            0 1977                               2005
                                            1974                                   2002

             beginning year biomass from stock assessment
Estimates of recruitment from the standardthe standard stock
assessment somewhat than than the ASM (similar pattern).
were usually were lower lowerthe ASM modelmodel though of the
same order of magnitude.
                       Results

Advantage of ASM
Currently….
model:                        40,000
                              40,000                             ASM




                                 x 1,000,000
One yearly total       NW_A                                      EBS Abundance
                                                                NW_B
More in-depth




                                                  x 1,000,000
allowable catch
information for                          0

(TAC) for the                             1977                           2005

fishery management                                                                      SE_AASM
whole EBS divided                                                      40,000                              SE_B




                                                                          x 1,000,000
and allocation of                                    -
by the 3 fishing
quota both spatially                                  1977                                     2005
sectors and 2                                                                0




                                                                                                  (x1,00
                                                                                                  Catch
                                               0.001                        2000
                                                                              500
                                                                               1200
                                                                          12002000                1750 5000
                                                                                                  900
                                                                                                   1800
                                                                                                   400
                                                                                                    3000

(NW and SE
                                                 0.001                     2000
                                                                           9001200
                                                                               1100
                                                                               1000               502800
                                                                                                    2600
                                                                                                      2005NW_B
                                                                                900               1500
                                                                                                   1500
                                                                                                    2400  0
                                                                           1500 800
                                                                           600 1977
                                                                            1000
                                                                                700
                                                                                600
                                                                                800
                                                                           3001000
                                                                                500
                                                                             0 400
                                                                                300
                                                                              1000
                                                                                        NW_A        2200
                                                                                                  1250
                                                                                                   1200
                                                                                                    2000
                                                                                                  600
                                                                                                    1800
                                                                                                  1000
                                                                                                    1600
                                                                                                    900
                                                                                                    1400    3 4 5 6 7 8 9 10

fishery seasons (A
                                                                                  200
                                                                                  100              750
                                                                                                    1200
                                                                                                    1000
                                                                                                    600
                                                                                                  300
                                                                                 400
                                                                               500 0               500
                                                                                                     800
                                                                                                     600
                                                                                                    300
                                                                                                   250
                                                                                                     400
                                               0.000
                                                 0.000                           00 0
                                                                                 0                   200
                                                                                                      00
                                                                                                    0000          Age

separately) and
and B) by fixed
temporally (within
percentages
the year)
                 Results
 Reasonable 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 Work
  1.   Combined age- and year-specific movements (cold
       versus warm year movements)
Adults are distributed more cold offshore during cold
                                  NW,
  2. More areas (oceanographic domains, Steller sea lions)
                                 pool
years (Wyllie-Echeverria and Wooster 1998; Kotwicki et al. 2005).

  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).

        Management strategy evaluation
  4. Year
  Cold                  Age-1 pollock
           -How shouldAdult pollock be Warm Year by area and
                                       allocated
                         harvest (less overlap)
                                                        Source:
(more overlap)                                          Wyllie-Echeverria and

           season in the presence of movement?          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.*
              Acknowledgments
Reviewers: 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

				
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posted:9/30/2011
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