A A multi-species population multi-species population

assessment model for the Gulf assessment model for the Gulf of Alaskaof Alaska

Kray F. Van Kirk, SFOS, UAF, Juneau Terrance J. Quinn II, SFOS, UAF, Juneau Jeremy S. Collie, GSO, URI, Narragansett

ftkv@uaf.edu

Jointly funded by AK and RI Sea Jointly funded by AK and RI Sea GrantGrant

Also collaboration with North Sea Also collaboration with North Sea colleagues: Lewy, Vinther (Denmark)colleagues: Lewy, Vinther (Denmark)

Project started February, 2004Project started February, 2004 Species groupsSpecies groups

Gulf of AlaskaGulf of Alaska Georges BankGeorges Bank North SeaNorth Sea

Sea GrantSea Grant

JustificationJustification

Crisis in Fisheries ManagementCrisis in Fisheries Management Single species analysis does not Single species analysis does not

answer questions of multi-species answer questions of multi-species interactionsinteractions

Ecosystem approaches desiredEcosystem approaches desired Natural mortality is not constant!Natural mortality is not constant! Harvest strategies cannot evolve Harvest strategies cannot evolve

until models dountil models do

Previous MSVPA ModelsPrevious MSVPA Models Predation mortality estimated from Predation mortality estimated from

gut studiesgut studies Single predation coefficientSingle predation coefficient Works backwards from oldest agesWorks backwards from oldest ages Catch-at-age is measured without Catch-at-age is measured without

errorerror Applied to North, Baltic and Bering Applied to North, Baltic and Bering

Seas, Georges Bank, and a few Seas, Georges Bank, and a few tropical areastropical areas

Model OverviewModel Overview Catch-age Catch-age

measured with measured with errorerror

Forward time Forward time progression from progression from age 1 recruitmentage 1 recruitment

Cohort abundance Cohort abundance subject to fishing,subject to fishing,flexible predation,flexible predation,and residual and residual naturalnaturalmortalitymortality

taiZtaitai eNN ,,

,,1,1,

)(,1,1

,tiSBtiti eSBN

Age-structured AnalysisAge-structured Analysis

Age

3 4 5 6 7 8 ... Total

1989

1990

1991

1992

1993

1994

Year 1995

1996

1997

1998

1999

2000

Recruitment

Natural MortalityFishing MortalityGrowthMovement

Progression of aYear-class or Cohort

Spawner-RecruitRelationship

Modeling Predation MortalityModeling Predation MortalityAnnual Ingestion of Predator Age (grams)Annual Ingestion of Predator Age (grams)

= consumption of modeled prey of interest= consumption of modeled prey of interest

+ consumption of non-modeled ‘other food’.+ consumption of non-modeled ‘other food’.

Where annual ingestion rate is given by:Where annual ingestion rate is given by:

bj

bjbj GE

GII

,

,, 5.0*1

11.0

inf,

,,

j

bjbj W

wGE

Growth Increment

Growth Efficiency Hall et al. in press

Components of Modeled Prey (1)Components of Modeled Prey (1)

Predator Predator j j of size of size bb preference for prey of preference for prey of size size aa.. (from Ursin 1971, where size-preference is (from Ursin 1971, where size-preference is

a function of predator-prey weight-at-age a function of predator-prey weight-at-age ratio)ratio)

Predator Predator jj preference for prey of species preference for prey of species ii.. (from AFSC data, as a ratio of prey (from AFSC data, as a ratio of prey ii

consumed relative to total prey consumed; consumed relative to total prey consumed; changes over time)changes over time)

g~

Components of Modeled Prey (2)Components of Modeled Prey (2)

Suitability of prey Suitability of prey i,ai,a to predator to predator j,b j,b ::

size/age preference * prey size/age preference * prey preferencepreference

Availability of prey Availability of prey i,a i,a to predator to predator j,b j,b ::

prey suitability * prey abundanceprey suitability * prey abundance

Total Annual ConsumptionTotal Annual ConsumptionConsumption of prey Consumption of prey i,ai,a by predator by predator j,bj,b

tbj

tbjaitbjbj NI

,,

,,,,,,,

Prey Availability

Predator Abundance

PredatorIngestion

Total Available Food(Modeled Prey And Other Food)

Total Available FoodTotal Available Food

T.A.F. = Modeled prey + all other prey

How to quantify ‘other prey’? - Very little data

Use factor to multiply modeled prey (10x, 50x…) to obtain estimated biomass of Other Prey

Set multiplier as parameter to be estimated

Modeled prey, species i

tothbjothtaitaibjaitbj BwN ,,,,,,,,,,,,

All other prey

Total ‘P’ for prey Total ‘P’ for prey i,ai,a by predator by predator jj

Predation Mortality ‘P’Predation Mortality ‘P’

j b tbj

tbjaitbjbj

taitaitai NI

wNP

,,

,,,,,,,

,,,,,,

1

j tbj

tbjai

btbjbj NI

,,

,,,,,,, Sum of ALL predation

on species i age a by ALL ages of predator j

Total predation on species i,a (grams)

Total biomass of species i,a (grams)

Cohort AbundanceCohort Abundance

)....(,,1,1,

21 nPPPFRtaitai eNN

Residual Natural Mortality

Fishing Mortality

Predation Mortality

nPPPRM ...21

Traditional Natural Mortality ‘M’

Initial Model Set-upInitial Model Set-up

Pacific Cod (Pacific Cod (Gadus Gadus macrocephalus)macrocephalus)

Arrowtooth Flounder Arrowtooth Flounder (Atheresthes stomias)(Atheresthes stomias)

Walleye Pollock Walleye Pollock (Theragra chalcogramma)(Theragra chalcogramma)

Initialization ParametersInitialization Parameters

Abundance at age for year 1(SAFE)Abundance at age for year 1(SAFE) Fixed overall F (Mean 1981 – 2001)Fixed overall F (Mean 1981 – 2001) Fixed R (0.1)Fixed R (0.1) Spawner-Recruit alpha and betaSpawner-Recruit alpha and beta Prey Preference (Mean 1981 – 2001)Prey Preference (Mean 1981 – 2001)

Changes in Prey PreferenceChanges in Prey PreferenceProportion of Walleye Pollock in

Pacific Cod diet by Decade

0.185

0.146

0.0620.000

0.050

0.100

0.150

0.200

0.250

1980 1990 2000

Proportion of Walleye Pollock inArrowtooth Flounder diet

0.3970.391

0.285

0.000

0.100

0.200

0.300

0.400

0.500

1980 1990 2000

Proportion of Walleye Pollock inWalleye Pollock diet by Decade

0.1540.169

0.070

0.000

0.050

0.100

0.150

0.200

0.250

1980 1990 2000

LN Biomass estimates from triennial surveys

12

12.5

13

13.5

14

14.5

15

1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002

Year

Population Trends (SAFE)Population Trends (SAFE)

Arrowtooth Flounder

Walleye Pollock

Pacific Cod

Initial Results Initial Results

Fishing pressure on pollock too great

Insufficient food available to pollock

LN Biomass

0

3

6

9

12

15

18

1980 1985 1990 1995 2000 2005

Arrowtooth Flounder

Pacific Cod Walleye Pollock

LN Biomass

14

14.5

15

1980 1985 1990 1995 2000

Increase ‘Other Food’ factor Increase ‘Other Food’ factor from 10x to 50xfrom 10x to 50x

Walleye Pollock

Arrowtooth Flounder Pacific Cod

BASE CASE SCENARIO

Predation Mortality from Base CasePredation Mortality from Base Case

Predation on ATF 1981 - 2001

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

1980 1985 1990 1995 2000

Predation on Pollock 1981 - 2001

0

0.05

0.1

0.15

0.2

1980 1985 1990 1995 2000

Predation on Cod 1981 - 2001

0

0.0002

0.0004

0.0006

0.0008

0.001

1980 1985 1990 1995 2000

Pollock

Pollock

Cod

Cod

ATF

ATF

ATF

LN biomass

0

24

68

10

1214

16

1980 1985 1990 1995 2000

Full Recruitment ‘F’ for pollock at 1Full Recruitment ‘F’ for pollock at 1

Predation on ATF 1981 - 2001

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

1980 1985 1990 1995 2000

Pollock

Cod ATF

ATF

Cod

Predation on ATF 1981 - 2001

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

1980 1985 1990 1995 2000 2005

Cod

Predation on ATF 1981 – 2001 Base Case Predation on ATF 1981 – 2001 F = 1

Full Recruitment ‘F’ for pollock at 1Full Recruitment ‘F’ for pollock at 1

LN Biomass

02468

10121416

1980 1985 1990 1995 2000

Predation on ATF 1981 - 2001

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

1980 1985 1990 1995 2000 2005

LN biomass

0

24

68

10

1214

16

1980 1985 1990 1995 2000

Predation on ATF 1981 - 2001

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

1980 1985 1990 1995 2000

Other Food factor = 50x Other Food factor = 100x

Predation on Pollock 1981 - 2001

0

0.05

0.1

0.15

0.2

1980 1985 1990 1995 2000

Predation on Pollock 1981 - 2001

0

0.05

0.1

0.15

0.2

1980 1985 1990 1995 2000

Full Recruitment ‘F’ for pollock at 0Full Recruitment ‘F’ for pollock at 0LN Biomass

14

15

16

17

18

19

1980 1985 1990 1995 2000

Pollock

Cod

ATF

Pollock

ATF

ATFCod

Cod

Predation on Pollock 1981-2001: Base Case Predation on Pollock 1981-2001: F = 0

Pollock

Full Recruitment ‘F’ for pollock at 0Full Recruitment ‘F’ for pollock at 0

Predation on ATF 1981 - 2001

0

0.002

0.004

0.006

0.008

0.01

0.012

1980 1985 1990 1995 2000

Predation on ATF 1981-2001: F = 0Predation on ATF 1981 - 2001

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

1980 1985 1990 1995 2000

Predation on ATF 1981 – 2001 Base Case

LN Biomass

14

15

16

17

18

19

1980 1985 1990 1995 2000

Pollock

Cod

Cod

Cod

ATF

ATF ATF

Model SensitivitiesModel Sensitivities

Prey AbundancePrey Abundance Predator AbundancePredator Abundance Prey preference and ‘Other Prey preference and ‘Other

Food’ factorFood’ factor Fishing PressureFishing Pressure

Next StepsNext Steps Parameter EstimationParameter Estimation

Rho (species preference)Rho (species preference) Elements of size-preference functionElements of size-preference function ‘‘Other food’ multiplierOther food’ multiplier

Objective FunctionsObjective Functions Fishery catch at ageFishery catch at age Survey catch at ageSurvey catch at age Stomach contents (predation rates)Stomach contents (predation rates)

Addition of Pacific halibut and Steller Addition of Pacific halibut and Steller Sea LionSea Lion

Areas for ExplorationAreas for Exploration Predation between age classes Predation between age classes

and connection with fishing and connection with fishing pressurepressure

Complexity of multi-species Complexity of multi-species model vs. robustness of single model vs. robustness of single species modelsspecies models

Estimation of recruitment Estimation of recruitment parameters once other parameters once other parameters are setparameters are set