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Biological Models Used to

Evaluate Medium-Term Impacts

9-January-2004

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Stock Assessment

Objectives of an assessment:

Stock status

Uncertainties

Projections

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Assessment Input Data

Basic Biology: lifespan

growth

movements

Fishery Information: maturity rate

historical development (areas, gears)

past and current regulations (size limits, gear restrictions). catch (landings, discards, age/size distribution)

effort (catch rates)

Surveys distribution

relative abundance and biomass over time

age/size structure

life history (growth, maturity)

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Types of Assessments

A nonlinearprogression from data-poor to data-rich situations.

Index Methods (n = 7):

Descriptive assessment of catch and survey data.

Biomass Dynamics Methods (n = 1): Combined analysis of catch and survey data with a simplebiomass-based population model.

Age-Structured Methods (n = 11, 8 of 11 include discards): Virtual Population Analysis: Back-calculate stock numbers at

age using age distribution of the catch, calibrated with surveyindices to minimize measurement error.

Statistical Catch-at-Age Analysis: Forward-projection ofstock numbers at age using age distribution of the catch,calibrated with survey indices or other auxiliary informationin a likelihood-based framework.

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Age-Based

Methods Age distribution of

the catch.

From census of total

catch biomass and port

samples.

SNE yellowtail

example:

1987 yearclass

dominated the catch in

the late 80s early 90s.

Southern New England Yellowtail Catch

-2003

-1998

-1993

-1988

-1983

-1978

-1973

0 1 2 3 4 5 6 7 8

Age

Year

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VPA

Reconstruction of allyearclasses gives a

total population

estimate.

Input Data:

catch at age

estimate of natural

mortality

initial guess aboutabundance of

survivors at the

oldest age.

Southern New England Yellowtail Abundance

-2003

-1998

-1993

-1988

-1983

-1978

-1973

0 1 2 3 4 5 6 7 8

Age

Year

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VPA Calibration

Initial guesses are replacedwith estimates:

oldest age of historical

yearclasses estimated by

assuming that age-7 fish havethe same vulnerability to the

fishery as ages 4-6:

yearclasses that are alive now

require more information. need an independent index of

relative abundance over time.

Southern New England Yellowtail Abundance

-2003

-1998

-1993

-1988

-1983

-1978

-1973

0 1 2 3 4 5 6 7 8

Age

Year

( )tZttt

teF

ZCN

=

1

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VPA Calibration

Abundance oflivingyearclasses in2002 areestimated using a

predictiverelationshipbetween

historical VPAabundance andsurvey indices.

0

5

10

15

20

25

0 10 20 30 40 50 60 70

Age-3 Abundance from VPA (millions)

Age-3SpringSurvey

Index(#/tow)

observed

predicted

2002

1990

(1987 yearclass)

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VPA Estimates

Informative

Assessment:

Example: SNEyellowtail

Estimates of stock size

and F,

But also age

distribution,recruitment, mature

biomass, etc.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

1973

1975

1977

1979

1981

1983

1985

1987

1989

1991

1993

1995

1997

1999

2001

FishingMortality(4-6)

F40%

0

5

10

15

20

25

1972

1974

1976

1978

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

SSB Year; Recruitment Yearclass

Spawning

Biomass('000smt)

0

20

40

60

80

100

120

140

Age-1Abundance(millions)

recruitment

SSB

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Groundfish Stock Status - 1996

Biomass 1996 / B-MSY

0.0 0.3 0.5 0.8 1.0

F1996/F-MS

Y

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.05.5

6.0

GM Cod

GB Cod

GM HadGB Had

CC YT

GB YT

SNE YT

Witch

Plaice

GM WinGB Win

SNE Win

W Hake

Pol

RedfishPout

N Wind

S Wind

overfishingnot overfished

no overfishing

overfished

no overfishing

not overfished

overfishingoverfished

F-MSY

1/2 B-MSY

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Groundfish Stock Status - 2002

Biomass 2002 / B-MSY

0.0 0.3 0.5 0.8 1.0 1.6 1.8 2.0

F2002/F-MS

Y

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

GM Cod

GB Cod

GM Had

GB Had

CC YT

GB YT

SNE YT

Witch

Plaice

GB Win

SNE Win

W Hake

Pol

Redfish

PoutN Wind

S Wind

overfishingnot overfished

no overfishingoverfishedno overfishingnot overfished

overfishing

overfished

F-MSY

1/2 B-MSY

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VPA Uncertainty

Similar to productionmodel: surveymeasurement errors arereshuffled many timesto estimate precision.

(bootstrapping). The estimate of 2001

SSB is 1850mt, with a

80% confidence limitof 1500 to 2500mt.

SNE Yellowtail

0

10

20

30

40

50

60

70

1200

1300

1400

1500

1600

1700

1800

1900

2000

2100

2200

2300

2400

2500

2600

2700

2800

2900

3000

3100

3200

3300

2001 SSB (mt)

Freq

uency

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Projections

"It is far better to

foresee evenwithout certainty

than not toforesee at all"

Poincare, The

Foundations ofScience

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Short-Term Projection

Fluke (SAW35):

Landings in 2003would need to be

10,580 mt (23.3

million lbs) tomeet the target F

rate of Fmax =

0.26 with 50%probability.

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Long-Term Projection

GeorgesBank Cod

the stock isexpected tohaveapproximately a 50%chance ofrebuilding to

SSBMSYby2026 iffished at anF of 0.18.

Year

2002 2006 2010 2014 2018 2022 2026

Spawn

ing

Biomass

(000sm

t)

0

50

100

150

200

250

300

75th percentile

Median Spawning Biomass

25th percentile

BMSY

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Age-Structured Model

Population Numbers, Survival, Spawning Biomass

Catch, Landings, and Discards

Population Harvest

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Population Numbers at Age

( )

( )( )

( )

( )

N t

N tN t

N t

N t

R

R

R

A

=

+

+

1

2

M

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Survival by Age Class

N t N t e

for a R to A

a aM t F ta( ) ( ) ( ) ( )=

= +

11 11

1 1

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Survival of Plus Group

N t N t e

N t e

A A

M t F t

A

M t F t

A

A

( ) ( )

( )

( ) ( )

( ) ( )

=

+

1

1

1 1

1

1 11

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Spawning Biomass

[ ]

SSB t W FM N t eS a a aZ t M t F t

a R

A

PROJ a

( ) ( ),( ) ( ) ( )= +

=

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Catch Numbers at Age

[ ]C tF t

M t F t e N taa

a

M t F t

a

a

( )

( )

( ) ( ) ( )

( ) ( )=+

1

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Landings

[ ]L t C t DF t Waa

A

a L a( ) ( ) ( ) ,= =1 1

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Discards

D t C t DF t Wa a D aa

A

( ) ( ) ( ) ,= =1

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Population Harvest

Input fully-recruited

fishing mortality F(t)

Input partial recruitment

vector PR(t) and ZPROJ(t)

Input discard fraction atage vector DF(t) if

applicable

Input landings quota Q(t)

Input partial recruitment

vector PR(t) and ZPROJ(t)

Input discard fraction at

age vector DF(t) ifapplicable

Solve for F(t)

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Fishing Mortality at Age

F t F t PR ta a( ) ( ) ( )=

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Catch Numbers at Age as a Function

of Fishing Mortality

[ ]C F

PR t F

M t PR t Fe N t

a

a

a

M t PR t F

a

a( )( )

( ) ( )( )( ) ( )=

+ 1

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Landings as a Function of F

[ ]L F C F DF t Waa

A

a L a( ) ( ) ( ) ,= =1 1

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Solve for Fishing Mortality to Harvest

Landings Quota

Q L F =( ) 0

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Age-Structured Model

Stock-Recruitment Relationship

Initial Population Abundance

Abundance and Fishing Mortality Thresholds

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Stock-Recruitment Relationship

Deterministic component

Stochastic component

( ) ( )N t f SSB t R tR ( ) ( ) , ,=

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Recruitment Models Dependent on spawning biomass (n = 10)

Independent of spawning biomass (n = 5)

Uncorrelated stochastic component (n = 10)

Correlated stochastic component (n = 5)

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Beverton-Holt Curve Lognormal Error

( )

n t a ssb t R

b ssb t R

e

where w N

R

w

w

( ) ( )

( )

~ ,

= +

0 2

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Empirical Cumulative

Distribution Function

( )

N t T R R US

TR

where S U T

R S S S( ) ( )

( )

=

+

= +

+1

1

1

1 1

1

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Georges Bank yellowtail flounder recruitment CDF

Recruitment (000,000s age-1 fish)

0 20 40 60 80 100

Frequency

R