Estimating long term yield of cod from BifrostSigurd Tjelmeland

Estimating long-term yield

• Must be done by long term simulation

• Since cod and capelin interact recruitment relations (recruits as function of spawning stock) for both cod and capelin are needed

Basics of Bifrost - Steps

• Calculate stochastic inputs– Capelin– Consumption per cod

• Estimate perameters

• Estimate recruitment relations

• Simulate

Basics of Bifrost(documented on www.imr.assessment)• Capelin-cod simulator

• Herring affects capelin recruitment– Forward simulations: Bifrost and SeaStar are coupled

• Input data– Stochastic September estimates of capelin– Catch data for capelin

• Monthly by age• Divided by maturing component

– Stochastic consumption per cod by quarter of• Capelin

• Cod

• Other food

– Cod assessment from Arctic Fisheries WG– Stochastic herring assessment from SeaStar

Basics of Bifrost(documented on www.imr.assessment)• Modelling

– Large number of recruitment relations per historic replicate, AIC– Overlap model depending on cod and capelin stock size– Cannibalism modelled after size distributions– Weight and maturation estimated internally, malformation of eggs implemented– Proportion immature capelin being preyed, proportion mature cod preying

• Estimation– Overall likelihood

• Capelin: Age 4 during 1970s, lognormal• Consumption by quarter of capelin,cod and other food, lognormal• Inner loop

– Capelin age 1– Cod age 0– Capelin residual M

• Other parameters

Recruitment in Bifrost• A large number of apriori possible formulations of the spawning stock – recruitment relation exist

– Part of the model uncertainty

– Estimates a large number on each historic replicate

– Draws one using Akaike’s weights for each run• Best balance between fit and number of parameters

• Capelin independent variables– Herring

– 0-group herring

– Temperature

– 0-group cod

– Inflection point

– Different levels of lowest herring abundance

• Cod independent variables– Temperature

– Mean weight

– Mean Age

• Possible estimation of exponents

• Lognormal, gamma, weibull

• Covariates possibly in halfvalue

• Different months for temperature in Kola section

Recruitment in Bifrost

0.5 1 1.5 2Spawning stock

200

400

600

800

Recruitment

89

89

90

90

96

96

97

97

98

9895

95

99

99

91

91

8484

00

00

9494

02

02

01

0192929393

200 400 600 800Model

200

400

600

800

1000

Rec

89

90

8177

83

79

80

96

74

75

73

82

97

76

98

95

78

99

91

84

00

94

0201

9293

0.2 0.4 0.6 0.8 1Spawning stock

0.5

1

1.5

2

2.5

3

3.5

Recruitment

95

95

94

94

83

83

75

75 90

90

8989

00

007373

88

88

91

91

92

92

81

817474

87

87

98

989999

97

97

96

96

8282

93

93

86868585

01

01

80

80

84

84

76

767979

78

78

77

77

1 2 3 4Model

0.5

1

1.5

2

2.5

3

3.5

Rec

9594

83

75

908900 73

88

91 92

81 7487

9899

9796

82

93

868501

8084

767978 77

Capelin Cod

Consumption by cod age 10Million tonnes per quarter

1980 1985 1990 1995 2000

0.0025

0.005

0.0075

0.01

0.0125

0.015

0.0175

Consumption of otherFoodBlue : SimulationRed : EmpiricalGreen : 0.1 Per cod

1980 1985 1990 1995 2000

0.001

0.002

0.003

0.004

0.005

0.006

0.007

Consumption of codBlue : SimulationRed : EmpiricalGreen : 0.1 Per cod

1980 1985 1990 1995 2000

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

Consumption of capelinBlue : SimulationRed : EmpiricalGreen : 0.1 Per cod

Consumption by cod age 4Million tonnes per quarter

1980 1985 1990 1995 2000

0.1

0.2

0.3

0.4

0.5

Consumption of otherFoodBlue : SimulationRed : EmpiricalGreen : 0.25 Per cod

1980 1985 1990 1995 2000

0.01

0.02

0.03

0.04

Consumption of codBlue : SimulationRed : EmpiricalGreen : 0.25 Per cod

1980 1985 1990 1995 2000

0.1

0.2

0.3

0.4

Consumption of capelinBlue : SimulationRed : EmpiricalGreen : 0.25 Per cod

Consumption by cod age 8Million tonnes per quarter

1980 1985 1990 1995 2000

0.02

0.04

0.06

0.08

Consumption of otherFoodBlue : SimulationRed : EmpiricalGreen : 0.125 Per cod

1980 1985 1990 1995 2000

0.0025

0.005

0.0075

0.01

0.0125

0.015

0.0175

Consumption of codBlue : SimulationRed : EmpiricalGreen : 0.125 Per cod

1980 1985 1990 1995 2000

0.005

0.01

0.015

0.02

0.025

Consumption of capelinBlue : SimulationRed : EmpiricalGreen : 0.125 Per codFit to data - Consumption

Fit to data - Capelin

1975 1980

20

40

60

80

Measured redand simulated bluefemale capelin , 4 years

1975 1980

20

40

60

80Measured redand simulated bluemale capelin , 4 years

1975 1980

50

100

150

200

250

Measured redand simulated bluefemale capelin , 3 years

1975 1980

50

100

150

200

250

Measured redand simulated bluemale capelin , 3 years

Results

0.2 0.4 0.6 0.8 1.

Catchmilliontonnes

0.2

0.3

0.4

0.5

Target spawning stockmilliontonnes

Longtermyield of capelinRelative F for cod 1.

0.01 0.5 1.0.5

1.

1.5

0.01 0.5 1.0.5

1.

1.5

0.3

0.55

0.8

0.

0.37

0.75

0.75 1. 1.25 1.5

Relative Fcod

0.5

0.6

0.7

Catchmilliontonnes Longterm yield of cod for capelin target SSB 0.5 million tonnes

Warning – periods of different productivity!

0.25 0.5 0.75 1 1.25 1.5 1.75

0.25

0.5

0.75

1

1.25

Equilibrium yield curves , WG assessmentRed : before1973Blue : 1973 and later

0.5 1 1.5 2

0.2

0.4

0.6

0.8

1

1.2

1.4