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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 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)
0
500
1,000
1,500
2,000
X 1
,00
0 m
etri
c to
ns
(ro
un
d w
eig
ht)
atkamackerel
flatfish
Pacific cod
other
walleyepollock
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
0.00
0.50
1.00
3 4 5 6 7 8 9 10
Age
Pro
port
ion t
hat
Sta
y
NW_A
NW_B
SE_A
SE_B
NW_A
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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Ages
Ab
un
da
nc
e
(x1
,00
0,0
00
) Survey-age composition (NW)
ResultsYear-Class Abundance
0
30,000
1974 2002
X 1
,000
,000
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+)
0
24,000
1977 2005
Bio
mas
s to
ns (
x1,0
00,0
00)
ASM
stockassess.2005
Estimates of beginning year biomass from the standard stock assessment were lower than the ASM model (similar pattern).
Results
EBS Abundance
-
40,000
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
0
40,000
1977 2005
x 1,
000,
000
ASM
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1977 2005
x 1,
000,
000
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0100200300400500600700800900100011001200
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0250500750
1000125015001750
020040060080010001200140016001800200022002400260028003000
0300600900
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Age
Cat
ch
(x1,
00
SE_A SE_B
NW_A
SE_B
NW_B
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