Modeling fisheries and Modeling fisheries and stocks spatially for stocks spatially for Pacific Northwest Pacific Northwest Chinook salmonChinook salmon

Rishi Sharma, CRITFCRishi Sharma, CRITFC

Henry Yuen, USFWSHenry Yuen, USFWS

Mark Maunder, IATTCMark Maunder, IATTC

Structure of TalkStructure of Talk

Background Background Life History and relationship to modelLife History and relationship to model Estimating catch in Fisheries by stock.Estimating catch in Fisheries by stock. Statistical Catch at Age Analysis (SCAA).Statistical Catch at Age Analysis (SCAA). Adapting to a multi-stock framework.Adapting to a multi-stock framework. Precision in Exploitation rates.Precision in Exploitation rates. Wrap Up.Wrap Up.

BackgroundBackground

•Jurisdiction.

•Fisheries.

•Value ($20-50 M/yr X-vessel price).

•Cost tagging and assessment ($15 M/yr).

Chinook Life CycleChinook Life Cycle

Eggs, Fry & Juveniles

NaturalSpawning

Escapement (Age 2, 3,4, 5,6)

Ocean (Age 2,3,4,5, 6)

Age 2 Ocean Recruits

Maturation (% 2, 3, 4, 5)

No

Yes

Nat Mortality

Freshwater

Ocean

Tag Data used in Tag Data used in assessmentassessment

Escapem

ent

# of fish

Life History (TIME)

Cohort AnalysisCohort Analysis

Pop

ulat

ion

Tot

al

Fishery

3

Fishery

4Fish

ery 1

Fishery

2

Natural Mortality

Catch

PopulationER =

Population

ERROR

Age 2 recruits

Estimate Age 2 recruits

Spawners

Ages 2,3,4,5

MaturationEstimated from tag data

Catch (ocean)

Ages 2,3,4,5

Catch

(fresh

water)

Ages 2,3,4,5

Natural Mortality

States of Nature (have a time dynamic)

CURRENT VPA MODEL MECHANISM

Projected

By Cohort analysis estimates from a Base Set of Years

CWT Based

Size limit adjustments

Projected

By Cohort analysis estimates from a BaseSet of Years

CWT Based

Size limit adjustments

Spawners

(Projected to equal Forecast & Observed Spawners over multiple ages, i.e. over the cohort)

Freshwater

Ocean

Age 2 recruits

Estimate Age 2 recruits

Spawners

Environmental Forcing functions

Ages 2,3,4,5

MaturationMaturation

estimated

Catch (ocean)

Ages 2,3,4,5

Catch

(fresh

water)

Ages 2,3,4,5

Natural Mortality

States of Nature (have a time dynamic)

SCAA MODEL MECHANISM

Catch (ocean)

Projected

Fn (abun, Vuln and Catchability, ocean)

Effort Known

Catch (f_water)

Projected

Fn (abun, Vuln and Catchability, Terminal)

Effort Known

Spawners

(Projected)

Fn

(TR-Term_Catch)

Trade-OffsTrade-Offs

Lesser assumptions.Lesser assumptions. Estimation framework.Estimation framework. Numerically intensive & Challenging.Numerically intensive & Challenging.

Essential ApproachEssential Approachta,timeage,timeage,1 time1,age MaturationDeathsNumberNumber

timeage,timeage,timeage, ityNat.MortalFishingDeaths

ttimeagetime Efforterabilityvutycatchabili *ln*rtalityFishing_Mo ,timeage,

n

f f

ftafta

f

fta

CCCL

12

2

,,,,

2,,2

)ˆ()exp

2

1)|(

n

f f

ftaftaffta

CCCL

12

2

,,,,,, 2

ˆlnlnln)|(ln

Maximum Likelihood Maximum Likelihood Estimation Estimation

Testing the ApproachTesting the Approach

Simulation TestingSimulation Testing

Used a Ricker stock recruit with process error. Used a Ricker stock recruit with process error. Simulated different catchability, vulnerability and Simulated different catchability, vulnerability and maturation schedules by different fisheries and maturation schedules by different fisheries and time periods.time periods.

Estimated the recruitment deviates, and thereby Estimated the recruitment deviates, and thereby age 2 recruitment.age 2 recruitment.

Estimated vulnerability, catchability and maturation Estimated vulnerability, catchability and maturation by time periods specified.by time periods specified.

Ran 10,000 times (each run takes approximately Ran 10,000 times (each run takes approximately 10 seconds-27 hours).10 seconds-27 hours).

Spawner to age 2 recruit curve

alpha

beta

Process Error

ε~N(0,σ2) F=qaEsaa

Ocean Catcha

Escapementa

OBS Error

SIMULATION MODEL

compare

Escapementa

Ocean Catcha

OBSERVATIONS WITH SIMULATED NOISE

Maturationaa

MODEL ESTIMATION

Terminal Catchaa

Age 2 Recruits

F=qaEsaa

Ocean Catcha

Terminal Catchaa

Escapementa

Terminal Catchaa

Escapementa

Maturationaa

Parameter Uncertainty25 year time series

Summary of simulationsSummary of simulations

Model has a high accuracy on estimating Model has a high accuracy on estimating Recruitment & Exploitation Rates.Recruitment & Exploitation Rates.

Model is biased (underestimating) on true Model is biased (underestimating) on true parameters on Catchability and Maturation.parameters on Catchability and Maturation.

The model does not appear to capture terminal The model does not appear to capture terminal vulnerability, though ocean vulnerability is vulnerability, though ocean vulnerability is marginally better. marginally better.

Adding measurement error to the data, creates Adding measurement error to the data, creates problems in estimation (lower error, CV<0.1, problems in estimation (lower error, CV<0.1, implies greater identifiability versus larger error, implies greater identifiability versus larger error, CV>0.1)CV>0.1)

4 Stock Model4 Stock Model

Spatial variation in stocks modeledSpatial variation in stocks modeled Spatial variation in fisheries modeledSpatial variation in fisheries modeled 2 Pool Model structure.2 Pool Model structure.

1. S.E. Alaska

2. WCVI

3. Terminal WCVI

4. Terminal Fraser

5. Terminal Queets

6. Terminal Columbia

1

32 4

5

6

Fisheries

URB

Lower FraserWCVI

Queets

4

1

4

12

,

2

,,,,

2

)ˆln()ln()ln()|((

i f if

ifif

ifif

CCCLLn

4 stock- 4 fishery model4 stock- 4 fishery model Parameters estimated:Parameters estimated:

– Recruitment deviate over time (25 years X 4 stocks)Recruitment deviate over time (25 years X 4 stocks)– Selectivity (3-ages and 4 fishery over 3 time periods for Selectivity (3-ages and 4 fishery over 3 time periods for

4 stocks =144)4 stocks =144)– Maturation (3 ages and 3 time periods=9*4=36)Maturation (3 ages and 3 time periods=9*4=36)– Initial Cohort abundance (3*4=12)Initial Cohort abundance (3*4=12)– Catchability by 3 time periods for 4 fisheries and 4 Catchability by 3 time periods for 4 fisheries and 4

stocks=48stocks=48

Total =350 parametersTotal =350 parameters

Tricks to Make Model ConvergeTricks to Make Model Converge

Maturation: Logistic by stock and time period Maturation: Logistic by stock and time period (Prior)(Prior)

Vulnerability: Logistic by stock, time period & Vulnerability: Logistic by stock, time period & fishery (Penalty).fishery (Penalty).

Recruitment: Stock recruit functions by Area Recruitment: Stock recruit functions by Area with time specific deviates (Prior).with time specific deviates (Prior).

Overall Model Fits by StockOverall Model Fits by StockSEAK (URB)

0

50,000

100,000

150,000

200,000

250,000

300,000

350,000

1979 1984 1989 1994 1999 2004Year

Cat

ch

WCVI (URB)

0

20000

40000

60000

80000

100000

120000

1979 1984 1989 1994 1999 2004Year

Cat

ch

TERMINAL CATCH (URB)

0

50,000

100,000

150,000

200,000

250,000

300,000

350,000

400,000

450,000

1979 1984 1989 1994 1999 2004

Year

Cat

ch

ESCAPEMENT (URB)

0

100,000

200,000

300,000

400,000

500,000

600,000

1979 1984 1989 1994 1999 2004

Year

ES

CA

PE

ME

NT

0

50000

100000

150000

200000

250000

300000

1979 1984 1989 1994 1999 2004

Year

Escapement (WCVI)

0

50,000

100,000

150,000

200,000

250,000

300,000

350,000

400,000

450,000

500,000

1979 1984 1989 1994 1999 2004

Year

Es

ca

pe

me

nt

TERMINAL CATCH (WCVI)

0

50,000

100,000

150,000

200,000

250,000

300,000

350,000

400,000

450,000

1979 1984 1989 1994 1999 2004

Year

Ca

tch

WCVI (WCVI STOCK)

0

50000

100000

150000

200000

250000

300000

350000

400000

1979 1984 1989 1994 1999 2004

Year

Ca

tch

SEAK (WCVI)

0

50,000

100,000

150,000

200,000

250,000

300,000

350,000

400,000

450,000

500,000

1979 1984 1989 1994 1999 2004

Year

Ca

tch

0

200

400

600

800

1,000

1,200

1,400

1984 1989 1994 1999 20040

20000

40000

1984 1989 1994 1999 2004

Year

SEAK (FRL)

0

200

400

600

800

1,000

1,200

1,400

1984 1989 1994 1999 2004

Year

Cat

ch

WCVI (FRL)

0

20000

40000

1984 1989 1994 1999 2004

Year

Cat

ch

Terminal

0

5,000

10,000

15,000

20,000

25,000

30,000

35,000

1984 1989 1994 1999 2004

Year

Cat

ch

Escapement

0

20,000

40,000

60,000

80,000

100,000

120,000

140,000

160,000

180,000

1984 1989 1994 1999 2004

Year

Esc

apem

ent

SEAK (QUEETS)

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

9,000

1979 1984 1989 1994 1999 2004Year

Cat

ch

WCVI (Queets)

0500

100015002000250030003500

1979 1984 1989 1994 1999 2004

Year

Cat

ch

Observed vs predicted Fit (TERM Catch)

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

16,000

1979 1984 1989 1994 1999 2004

Year

Cat

ch

Observed vs predicted Fit (ESC)

0

5,000

10,000

15,000

20,000

25,000

1979 1984 1989 1994 1999 2004

Year

Esc

apem

ent

RecruitmentRecruitmentURB & WCVI Recruitment

0

500,000

1,000,000

1,500,000

2,000,000

2,500,000

3,000,000

3,500,000

1975 1980 1985 1990 1995 2000 2005 2010

Age 2 Ocean Year

Nu

mb

ers

Queets & Fraser

0

50,000

100,000

150,000

200,000

250,000

300,000

350,000

400,000

1979 1984 1989 1994 1999 2004

Age 2 Ocean Year

Rec

ruit

men

t

SEAK vuln -URB

0.00

0.20

0.40

0.60

0.80

1.00

1.20

2 3 4 5age

1977-841985-951996-2002

SEAK (WCVI)

0.00

0.20

0.40

0.60

0.80

1.00

1.20

2 3 4 5age

1977-841985-951996-2002

SEAK (Queets)

0.00

0.20

0.40

0.60

0.80

1.00

2 3 4 5age

SEAK (FRL)

0.00

0.20

0.40

0.60

0.80

1.00

1.20

2 3 4 5age

Selectivity By Age in SEAKSelectivity By Age in SEAK

Exploitation in SEAK (1-exp(-F)) of the Vulnerable Population

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

1980 1985 1990 1995 2000 2005

Year

Rat

e

HR (URB)

HR(WCVI)

HR(QTS)

SEAK ExploitationSEAK Exploitation

WCVI SelectivityWCVI SelectivityWCVI (URB)

0

0.2

0.4

0.6

0.8

1

1.2

2 3 4 5Age

Vu

lner

abil

ity

1977-84

85-95

96-02

WCVI (FRL)

0

0.2

0.4

0.6

0.8

1

1.2

2 3 4 5Age

Vu

lner

abil

ity

1977-84

96-02

WCVI (WCVI)

0

0.2

0.4

0.6

0.8

1

1.2

2 3 4 5Age

Vu

lner

abil

ity

1977-84

85-95

96-02

WCVI (Queets)

0

0.2

0.4

0.6

0.8

1

1.2

2 3 4 5Age

Vu

lner

abil

ity

1977-84

85-95

96-02

WCVI ExploitationWCVI Exploitation

0.000

0.020

0.040

0.060

0.080

0.100

0.120

0.140

0.160

0.180

1980 1985 1990 1995 2000 2005

Year

Rat

e

HR (URB)

HR(QTS)

HR(FRL)

0.000

0.100

0.200

0.300

0.400

0.500

0.600

0.700

0.800

0.900

1980 1985 1990 1995 2000 2005

Year

Rat

e

HR (URB)

HR(WCVI)

HR(QTS)

HR(FRL)

Terminal SelectivityTerminal SelectivityTERMINAL (URB)

0

0.2

0.4

0.6

0.8

1

1.2

0 1 2 3 4 5Age

Vu

lner

abil

ity

1977-84

85-95

96-02

TERMINAL (FRL)

0

0.2

0.4

0.6

0.8

1

1.2

0 1 2 3 4 5Age

Vu

lner

abil

ity

1977-84

96-02

TERMINAL (WCVI)

0

0.2

0.4

0.6

0.8

1

1.2

0 1 2 3 4 5Age

Vu

lner

abil

ity

1977-84

85-95

96-02

TERMINAL (Queets)

0

0.2

0.4

0.6

0.8

1

1.2

0 1 2 3 4 5Age

Vu

lner

abil

ity

1977-84

85-95

96-02

Terminal ExploitationTerminal ExploitationTERMINAL EXPLOITATION

0.000

0.100

0.200

0.300

0.400

0.500

0.600

0.700

0.800

0.900

1.000

1980 1985 1990 1995 2000 2005

Year

Rat

e

HR (URB)

HR(WCVI)

TERMINAL EXPLOITATION

0.000

0.100

0.200

0.300

0.400

0.500

0.600

0.700

0.800

1980 1985 1990 1995 2000 2005

Year

Rat

e

HR(QTS)

HR(FRL)

Incorporating GeneticsIncorporating Genetics

Using catch composition estimates.Using catch composition estimates. Added to the Objective function using a Added to the Objective function using a

Multinomial Likelihood.Multinomial Likelihood. Explicitly taking the values from Genetic Explicitly taking the values from Genetic

Analysis.Analysis. Estimating proportions with assignment error Estimating proportions with assignment error

within the model structure.within the model structure.

4

1

4

1,,,, )ln(),|((

i fifififif pCpCLLn

SummarySummary

Spatially stocks and fisheries could be modeled in Spatially stocks and fisheries could be modeled in a single pool context using different selectivity a single pool context using different selectivity curves over stocks, fisheries and time.curves over stocks, fisheries and time.

Model complexity trade-off.Model complexity trade-off. Statistical catch at age models are more robust Statistical catch at age models are more robust

(empirical data and likelihood functions). (empirical data and likelihood functions). Can quantify the Uncertainty in our estimates, and Can quantify the Uncertainty in our estimates, and

use in predictive models.use in predictive models. Could add environmental forcing into the model.Could add environmental forcing into the model. Have the ability to incorporate genetic information.Have the ability to incorporate genetic information.

Next StepsNext Steps

Add genetics.Add genetics. Stratify by gear.Stratify by gear. Use age-length based estimates for selectivity by Use age-length based estimates for selectivity by

gear and area.gear and area. Add environmental covariates.Add environmental covariates. Quantify the scale at which fisheries and stocks Quantify the scale at which fisheries and stocks

could be aggregated for model.could be aggregated for model. Develop a migration module that connects Develop a migration module that connects

fisheries and stocks.fisheries and stocks.

AcknowledgementsAcknowledgements Mike Matylewich (CRITFC) for supporting Mike Matylewich (CRITFC) for supporting

this project.this project. Henry Yuen (USFWS) & Mark Maunder Henry Yuen (USFWS) & Mark Maunder

(IATTC) for help with the ADMB coding, (IATTC) for help with the ADMB coding, Robert Kope (NMFS) for initial review of Robert Kope (NMFS) for initial review of the approach.the approach.

John Carlile (ADFG), & members of the John Carlile (ADFG), & members of the Chinook Technical Committee (CTC-AWG).Chinook Technical Committee (CTC-AWG).

NOAA for funding this research.NOAA for funding this research.