Modelling the effects of hypoxia on fish Kenneth Rose Dept. of Oceanography and Coastal Sciences...

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Modelling the effects of hypoxia on fish Kenneth Rose Dept. of Oceanography and Coastal Sciences Louisiana State University plus Many Co-authors

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Transcript of Modelling the effects of hypoxia on fish Kenneth Rose Dept. of Oceanography and Coastal Sciences...

Page 1: Modelling the effects of hypoxia on fish Kenneth Rose Dept. of Oceanography and Coastal Sciences Louisiana State University plus Many Co-authors.

Modelling the effects of hypoxia on fish

Kenneth RoseDept. of Oceanography and Coastal Sciences

Louisiana State University

plusMany Co-authors

Page 2: Modelling the effects of hypoxia on fish Kenneth Rose Dept. of Oceanography and Coastal Sciences Louisiana State University plus Many Co-authors.

• Aaron Adamack and Shaye Sable - Louisiana State University

• Cheryl A. Murphy – LSU, now University of Toronto

• Peter Thomas and Saydur Rahman – University of Texas Marine Science Institute

• Marius Brouwer and Nancy Brown-Peterson - University of Southern Mississippi

• Ann O. Cheek - University of Texas Health Science Center

• Carl Cerco - U.S. ACOE

• Sandra Diamond, Texas Tech University

Page 3: Modelling the effects of hypoxia on fish Kenneth Rose Dept. of Oceanography and Coastal Sciences Louisiana State University plus Many Co-authors.

Acknowledgements

• EPA’s Science to Achieve Results (STAR) Program to University of Texas

• STAR Estuarine and Great Lakes (EaGLe) Program through funding to the Consortium for Estuarine Ecoindicator Research for the Gulf of Mexico (CEER-GOM), US EPA Agreement (R 82945801)

• NOAA Aquatic Research Consortium (ARC, Phase 2) to USM and Texas State University

Page 4: Modelling the effects of hypoxia on fish Kenneth Rose Dept. of Oceanography and Coastal Sciences Louisiana State University plus Many Co-authors.

Introduction

• Quantifying and forecasting effects of hypoxia is needed for effective management

• Today: four examples– Physiological– Croaker matrix projection– Marsh community– Bay anchovy coupled to water quality

Page 5: Modelling the effects of hypoxia on fish Kenneth Rose Dept. of Oceanography and Coastal Sciences Louisiana State University plus Many Co-authors.

Disclaimer

No real data were harmed

in the preparation of this

presentation

Page 6: Modelling the effects of hypoxia on fish Kenneth Rose Dept. of Oceanography and Coastal Sciences Louisiana State University plus Many Co-authors.

1. Physiological Model1. Physiological Model

ViableOocytes

Relate physiological biomarkers to number of viable oocytes using ordinarydifferential equations

pituitary

ovary

GonadotropinGonadotropin

EstradiolEstradiol

liver TestosteroneTestosterone

Estrogen receptorEstrogen receptor

VitellogeninVitellogenin

Gonadotropin = GtHTestosterone = TEstradiol = E2Estrogen Receptor = ERVitellogenin = VtgGonadal Somatic Index = GSI

Page 7: Modelling the effects of hypoxia on fish Kenneth Rose Dept. of Oceanography and Coastal Sciences Louisiana State University plus Many Co-authors.

Testosterone(x1)

Vitellogenin(x8)

Estradiol(x2)

Estrogen Receptor

(x7)Estradiol

Gonadotropin(driving)

Estrogen Receptor (x6)

pituitary

liver

k1 k-1

Synthesis E2 (T)

k1

k-1

k2

k2

ovary

Synthesis T (GtH)

blood

SBP

(x3)

SBP

(x3)

k1

k-1

k1

k-1

Page 8: Modelling the effects of hypoxia on fish Kenneth Rose Dept. of Oceanography and Coastal Sciences Louisiana State University plus Many Co-authors.

Vit

ello

gen

in (

mg

/mL

)

0

50

100

150

200

Est

rog

en r

ecep

tor

(pm

ol/g

)

0

2

4

6

1 2 3 4 5 6

To

tal T

esto

ster

on

e (p

g/m

L)

0

500

1000

1500

1 2 3 4 5 6

To

tal E

stra

dio

l (p

g/m

L)

0

500

1000

1500

1. Baseline Simulation 1. Baseline Simulation

Time (months) Time (months)

A M J J A S O A M J J A S O

A M J J A S O

SPOTTED SEATROUTSmith and Thomas,1991Gen. Comp. Endocrinol.81:234-245

Year 1

Year 2

161 mg/ml

cumulative

Page 9: Modelling the effects of hypoxia on fish Kenneth Rose Dept. of Oceanography and Coastal Sciences Louisiana State University plus Many Co-authors.

1. Hypoxia Simulation1. Hypoxia Simulation

1. Simulate gonadotropin suppression

• Multiply gonadotropin driving variable by 0.74

2. Simulate aromatase impairment

• Less Testosterone converted to estradiol • Small % of Estradiol sent to a “sink” every timestep • Total E2 is 41% of Control

Page 10: Modelling the effects of hypoxia on fish Kenneth Rose Dept. of Oceanography and Coastal Sciences Louisiana State University plus Many Co-authors.

1: Hypoxia Simulation 1: Hypoxia Simulation

1 2 3 4 5 60

500

1000

1500

2000

0

2

4

6

1 2 3 4 5 60

500

1000

1500

2000

1 2 3 4 5 61 2 3 4 5 60

50

100

150

200

To

tal T

esto

ster

on

e (p

g/m

L)

To

tal E

stra

dio

l (p

g/m

L)

Vit

ello

gen

in (

mg

/mL

)

Est

rog

en r

ecep

tor

(pm

ol/g

)

Time (months) Time (months)

No change

Lab~ 59% decrease

Lab~ 67 % decrease ER mRNA

Lab~ 62% decrease fecundity

61% 73%

59%

GtH

GtH + aromatase

Baseline

Page 11: Modelling the effects of hypoxia on fish Kenneth Rose Dept. of Oceanography and Coastal Sciences Louisiana State University plus Many Co-authors.

1.1. Field EvaluationField Evaluation(Pensacola Bay)(Pensacola Bay)

Percent reduction of Total E2 (of control Lab)

0 20 40 60 80 1000

20

40

60

80

100

0

20

40

60

80

100

Sim

ulat

ed c

umul

ativ

e V

tg

as %

bas

elin

e cu

mul

ativ

e V

tg

Simulated

3.0

4.9

Field

1.2 1.9 ppm1.3

1.4

4.6 ppm

GS

I at field as % G

SI control lab

Laboratory results

1.7 ppm

2.7 ppm

Page 12: Modelling the effects of hypoxia on fish Kenneth Rose Dept. of Oceanography and Coastal Sciences Louisiana State University plus Many Co-authors.

PA1 FA1 FA2 FA3 FA4 FA5 FA6 FA7 GA1 PA2 0 0 0 0 0 0 0 GA2 PA3 0 0 0 0 0 0 0 GA3 PA4 0 0 0 0 0 0 0 GA4 PA5 0 0 0 0 0 0 0 GA5 PA6 0 0 0 0 0 0 0 GA6 PA7 0 0 0 0 0 0 0 GA7 PA8

t+1

Egg

A1A2A3A4A5A6A7

t

2. Matrix Projection Model2. Matrix Projection Model

Egg

A1A2A3A4A5A6A7

Stage duration and mortality are used to calculate P and G

Classic formulation:

Page 13: Modelling the effects of hypoxia on fish Kenneth Rose Dept. of Oceanography and Coastal Sciences Louisiana State University plus Many Co-authors.

EggYolk-sac

Oceanlarva

Estuarylarva

Early juvenile

Late juvenile

Adult

Page 14: Modelling the effects of hypoxia on fish Kenneth Rose Dept. of Oceanography and Coastal Sciences Louisiana State University plus Many Co-authors.

Age 12 11 10 9 8 7 6 5 4 3 2 1

Egg

Yolk-sac Atlantic Bight

PG

P

North CarolinaNorth Carolina

Estuary LarvaEarly JuvenileLate

Juvenile

TransitionTransition

VirginiaVirginia

Ocean Larva

G

Ocean Larva

Ocean Larva

Ocean Larva

TransitionTransition

Estuary LarvaEarly JuvenileLate

Juvenile

Estuary LarvaEarly JuvenileLate

Juvenile

Estuary LarvaEarly JuvenileLate

Juvenile

DailyDaily

BiweeklyBiweekly MonthlyMonthly

July

July

Dec

Dec

AnnualAnnual

Mid-Atlantic Bight (MAB)

Page 15: Modelling the effects of hypoxia on fish Kenneth Rose Dept. of Oceanography and Coastal Sciences Louisiana State University plus Many Co-authors.

Age 8 7 6 5 4 3 2 1

Egg

Yolk-sacGulf of Mexico

Louisiana

Estuary Larva Early Juvenile Late Juvenile

TransitionTransition

Texas

Ocean Larva

Ocean Larva

TransitionTransition

Estuary Larva Early Juvenile Late Juvenile

DailyDaily

Biweekly MonthlySept

AnnualAnnual

Gulf of Mexico (GOM)Gulf of Mexico (GOM)

PG

P

G

Page 16: Modelling the effects of hypoxia on fish Kenneth Rose Dept. of Oceanography and Coastal Sciences Louisiana State University plus Many Co-authors.

2. Baseline Simulations2. Baseline Simulations

Age 1

Age 2

Age 3

Age 4

Age 5Age 6

Age 7

Age 8

Age 1

Age 2

Age 3

Age 4 Age 5Age 6

Age 7-12

Year of simulation

20 40 60 80 100

Tot

al a

dult

abun

danc

e (m

illio

ns)

0.0

1.0

2.0

3.0

Year of simulation

20 40 60 80 100

Tot

al a

dult

abun

danc

e (m

illio

ns)

0.0

1.0

2.0

3.0

GOMMAB

Reproductive output:

Page 17: Modelling the effects of hypoxia on fish Kenneth Rose Dept. of Oceanography and Coastal Sciences Louisiana State University plus Many Co-authors.

2. Baseline Simulations2. Baseline Simulations

0.0 0.2 0.4 0.6 0.80.0

0.2

0.4

0.6

0.8

0.0 0.1 0.2 0.3 0.4 0.50.00

0.01

0.02

0.0 0.1 0.2 0.3 0.4

Age

1 r

ecru

its (

mill

ions

)

0.0

0.5

1.0

1.5

2.0

Eggs (1 x 1012 )

0.0 0.2 0.4 0.60.00

0.05

0.10

0.15

Louisiana TexasVirginia North Carolina

Eggs (1 x 1012 )

GOMMAB

Density dependence: spawner-recruit relationships

Page 18: Modelling the effects of hypoxia on fish Kenneth Rose Dept. of Oceanography and Coastal Sciences Louisiana State University plus Many Co-authors.

Tot

al P

opul

atio

n (m

illio

ns)

2. Hypoxia Simulation - GOM2. Hypoxia Simulation - GOM

Reduced fecundityin lab exposure

Testosterone (ng/mL)1 2 3 4 5

Per

cent

0

10

20

30

40Control3.5 ppm DO

Baseline0.8

1.0

1.3

Year

Hypoxia

0 20 40 60 80 100

0.8

1.0

1.3

Page 19: Modelling the effects of hypoxia on fish Kenneth Rose Dept. of Oceanography and Coastal Sciences Louisiana State University plus Many Co-authors.

Blue Crab

Silversides

Shrimp

Killifish

Zooplankton(2 groups)

Benthos(3 groups)

IndividualProcessesGrowthMovementMortalitySpawning

3. Marsh CommunityConditionsDissolved O2

TemperatureTidal StagePrey DensityPredator DensityIndividual Size

Bay Anchovy

Sheepshead Minnow

Page 20: Modelling the effects of hypoxia on fish Kenneth Rose Dept. of Oceanography and Coastal Sciences Louisiana State University plus Many Co-authors.

3. Marsh Habitat4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 2 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 4 4 4 4 4 4 4 4 4 3 3 2 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 5 5 5 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 3 3 3 4 4 4 4 4 4 3 3 2 2 2 2 2 2 3 3 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 5 5 5 5 5 5 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 3 3 3 4 4 4 4 3 2 2 2 3 3 3 2 2 3 4 4 4 4 4 4 4 4 4 3 3 5 5 5 5 5 5 5 5 5 5 5 5 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 2 2 2 2 2 3 3 4 3 3 2 2 2 3 3 4 3 2 2 3 3 4 4 4 4 4 4 4 4 3 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 2 2 2 3 3 3 2 2 3 3 3 4 4 3 3 2 2 3 4 4 4 4 4 4 4 4 3 3 3 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 5 5 5 3 3 4 4 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 2 2 3 3 2 2 3 3 4 4 4 4 4 3 2 2 3 3 4 4 4 4 4 4 4 4 4 3 3 3 3 5 5 5 5 5 5 5 5 5 5 5 5 5 5 3 3 4 4 4 4 4 4 4 4 4 3 3 3 3 3 5 5 5 5 5 3 4 4 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 3 2 2 3 3 4 4 4 4 4 4 3 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 3 3 5 5 5 5 5 5 5 5 5 5 5 5 5 5 3 4 4 4 4 4 4 4 4 3 3 5 5 5 5 5 5 5 5 5 3 4 4 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 3 3 4 4 4 4 4 4 4 3 3 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 5 5 5 5 5 5 5 5 5 5 5 5 5 3 4 4 4 4 4 4 4 4 3 5 5 5 5 5 5 5 5 5 3 3 4 4 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 3 3 3 4 4 4 4 4 4 4 4 4 3 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 5 3 3 3 3 3 5 5 5 5 3 3 4 4 4 4 4 4 4 4 3 5 5 5 5 5 5 5 5 3 3 3 4 4 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 3 3 4 4 4 4 4 4 4 4 4 4 3 2 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 4 4 4 3 3 3 5 3 3 4 4 4 4 4 4 4 4 3 3 5 5 5 5 5 5 5 5 5 5 3 3 4 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 3 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 4 4 4 4 4 4 4 4 3 3 5 5 5 5 5 5 5 5 5 5 5 5 3 4 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 3 3 3 4 4 4 4 4 4 4 3 2 2 2 3 4 4 4 4 4 4 4 4 4 4 3 3 3 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 5 5 5 5 5 5 5 5 5 5 5 5 3 3 4 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 3 3 2 3 4 4 4 4 4 4 4 3 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 5 5 5 5 5 5 5 5 5 5 5 5 3 4 4 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 3 2 2 3 3 3 4 4 4 4 4 3 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 5 5 5 5 5 5 5 5 5 5 5 5 3 4 4 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 3 2 2 2 2 3 4 4 4 4 4 3 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 5 5 5 5 5 5 5 5 5 5 5 3 3 3 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 3 3 2 2 2 3 3 3 3 3 4 3 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 5 5 5 5 3 3 5 5 5 5 3 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 3 3 2 2 2 2 2 2 3 4 3 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 3 3 4 4 4 4 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 5 5 3 3 3 5 5 5 5 3 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 2 2 3 4 3 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 3 4 4 4 4 4 3 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 4 3 5 5 5 5 3 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 2 2 3 4 3 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 3 3 4 4 4 4 3 2 2 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 5 5 3 3 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 3 3 3 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 2 2 2 3 4 4 4 4 3 3 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 4 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 3 4 4 4 4 4 3 2 2 2 2 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 2 2 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 3 4 4 4 4 4 3 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 3 4 4 4 4 4 3 2 2 2 2 3 3 3 3 2 2 2 2 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 3 4 4 4 4 4 3 2 2 2 2 3 4 4 3 3 3 3 2 2 2 2 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 3 4 4 4 4 4 3 2 2 2 3 3 4 4 4 4 4 3 3 2 2 2 2 2 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 2 2 2 3 4 4 4 4 3 3 2 2 2 3 4 4 4 4 4 4 4 3 3 2 2 2 2 2 2 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 3 4 4 4 4 3 2 2 2 2 3 4 4 4 4 4 4 4 4 3 3 2 2 2 2 2 2 2 2 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 3 4 4 4 4 3 2 2 2 2 3 4 4 4 4 4 4 4 4 4 3 3 3 2 2 2 2 2 2 2 2 2 3 4 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 3 3 3 4 4 4 4 3 3 3 3 3 3 3 3 3 2 2 2 3 3 4 4 3 3 2 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 2 2 2 2 2 2 3 3 3 2 2 2 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 2 2 2 2 3 4 4 4 3 3 2 2 2 2 2 3 3 3 3 2 2 2 3 4 4 3 2 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 3 4 4 3 3 2 2 2 2 2 2 2 3 3 3 2 2 2 3 4 4 3 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 3 4 3 3 2 2 2 3 3 3 2 2 2 3 2 2 2 2 3 4 4 3 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 3 3 3 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 3 3 3 2 2 2 3 3 4 3 3 2 2 2 2 2 2 2 3 4 4 3 2 2 2 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 2 2 2 2 2 2 2 2 3 3 3 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 2 2 2 2 2 2 2 2 3 3 4 4 4 3 3 2 2 2 2 2 2 3 4 4 3 3 2 2 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 2 2 2 2 2 2 2 3 3 4 4 4 4 44 4 4 4 4 4 4 4 4 4 3 3 3 4 4 4 4 4 4 4 4 4 3 2 2 2 2 2 2 2 3 3 4 4 4 4 4 3 3 2 2 2 2 2 3 4 4 4 3 3 2 2 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 2 2 2 2 2 2 3 4 4 4 4 44 4 4 4 4 4 4 4 4 3 3 2 3 3 4 4 4 4 4 4 4 3 3 2 2 2 2 2 2 3 3 4 4 4 4 4 4 4 3 3 2 2 2 2 3 4 4 4 4 3 3 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 2 2 2 2 2 2 3 4 4 4 4 44 4 4 4 4 4 4 4 4 3 2 2 2 3 4 4 4 4 4 4 4 3 2 2 2 2 3 3 3 3 4 4 4 4 4 4 4 4 4 3 2 2 2 2 3 4 4 4 4 3 3 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 2 2 2 2 2 2 3 3 4 4 4 4 44 4 4 4 4 4 4 4 4 3 2 2 2 3 3 3 4 4 4 4 4 3 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 3 4 4 4 4 3 2 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 2 2 2 2 2 3 3 3 3 4 4 4 4 4 44 4 4 4 4 4 4 4 4 3 2 2 2 2 2 3 3 3 3 3 4 3 2 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 3 4 4 4 3 3 2 2 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 3 3 3 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 3 3 2 2 2 2 2 2 2 2 3 3 3 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 3 4 4 3 3 2 2 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 2 2 3 3 4 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 3 4 4 3 2 2 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 3 4 4 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 4 3 3 3 2 2 2 2 2 2 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 3 4 4 3 2 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 3 3 4 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 2 2 2 2 2 2 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 3 3 3 3 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 3 3 3 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 3 3 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 2 2 2 2 3 3 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 3 3 2 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 2 3 3 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 2 2 2 2 2 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 2 2 3 3 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 2 2 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 2 2 2 2 2 2 2 3 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 2 2 2 2 2 2 2 3 3 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 2 2 2 2 2 2 2 3 3 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 4 4 4 3 2 2 2 2 2 2 2 2 2 3 3 3 4 4 4 4 4 4 4 4 3 2 2 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 2 2 2 2 2 2 2 2 3 3 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 4 3 2 2 2 2 2 2 2 2 2 2 2 3 3 3 4 4 4 4 4 4 3 2 2 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 2 2 2 2 2 2 2 2 2 2 3 3 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 2 2 2 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2 3 4 4 4 4 4 4 3 2 2 2 2 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 2 2 2 2 2 2 2 2 2 2 2 3 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 4 4 3 3 2 2 2 2 2 3 3 2 2 2 2 3 3 3 2 2 2 2 2 2 3 4 4 4 4 4 4 3 3 2 2 2 2 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 2 2 2 2 2 3 3 3 2 2 2 2 2 3 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 3 3 4 3 3 2 2 2 2 2 3 4 4 4 4 4 4 4 3 3 2 2 2 2 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 3 3 3 4 3 3 3 2 2 2 3 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 3 3 2 2 2 2 2 2 3 3 3 2 2 2 2 2 3 3 4 4 4 3 3 2 2 2 2 3 3 3 4 4 4 4 4 4 3 3 2 2 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 3 4 4 4 4 4 3 2 2 2 3 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 3 3 2 2 2 2 2 2 3 3 4 3 3 3 3 3 3 3 4 4 4 4 4 3 2 2 2 2 2 2 3 4 4 4 4 4 4 3 3 2 2 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 2 2 2 3 4 4 4 4 4 3 2 2 2 3 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 3 3 2 2 2 2 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 2 2 3 4 4 4 4 4 4 3 2 2 2 2 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 3 3 4 4 4 4 3 2 2 2 3 3 3 3 4 4 4 4 4 4 44 4 4 4 4 3 3 2 2 2 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 2 2 3 4 4 4 4 4 3 3 2 2 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 3 3 3 4 4 4 4 3 2 2 2 2 2 2 3 3 4 4 4 4 4 44 4 4 4 3 3 2 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 2 2 3 4 4 4 4 4 3 2 2 2 2 2 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 2 2 2 3 3 4 4 4 4 4 3 3 2 2 2 2 2 2 3 4 4 4 4 4 44 4 4 4 3 2 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 2 2 3 4 4 4 4 4 3 3 2 2 2 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 3 3 4 4 4 4 4 4 4 3 3 3 3 3 2 2 3 3 4 4 4 4 44 4 3 3 3 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 2 2 3 3 3 4 4 4 3 3 2 2 2 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 2 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 3 4 4 4 4 44 4 3 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 2 2 2 2 2 2 3 4 4 4 3 2 2 2 2 2 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 2 2 2 2 2 2 3 3 3 4 4 4 4 4 4 4 4 4 3 3 2 2 3 4 4 4 4 44 4 3 2 2 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 2 2 2 2 2 3 4 4 3 3 2 2 2 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 2 2 2 2 2 2 2 2 2 2 2 3 4 4 4 4 4 4 4 4 3 3 3 2 2 3 4 4 4 4 44 3 3 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 2 3 4 4 3 2 2 2 2 2 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 2 2 2 2 2 2 2 3 3 3 4 4 4 4 4 4 4 4 3 2 2 2 2 3 4 4 4 4 44 3 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 2 3 4 4 3 2 2 2 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 2 2 2 2 2 2 3 3 4 4 4 4 4 4 4 4 4 3 3 2 2 3 3 3 4 4 4 4 44 3 2 2 2 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 2 3 4 4 3 3 2 2 2 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 2 2 2 2 2 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 3 2 2 3 3 4 4 4 4 4 4 44 3 2 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 2 3 4 4 4 3 2 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 2 2 2 2 2 2 3 3 3 4 4 4 4 4 4 4 4 4 3 3 2 2 3 4 4 4 4 4 4 4 44 3 2 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 2 3 4 4 3 3 2 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 3 4 4 4 4 4 4 4 44 3 3 3 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 2 3 4 4 3 2 2 2 2 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 2 2 2 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 3 2 2 3 3 4 4 4 4 4 4 4 44 4 4 3 2 2 2 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 2 3 4 4 3 2 2 2 2 2 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 2 2 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 3 4 4 4 4 4 4 4 4 44 4 4 3 2 2 2 2 2 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 2 3 4 4 3 3 2 2 2 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 3 3 2 2 2 2 2 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 3 4 4 4 4 4 4 4 4 44 4 4 3 2 2 2 2 2 2 2 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 2 3 4 4 4 3 3 2 2 2 2 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 2 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 3 3 4 4 4 4 4 4 4 44 4 4 3 2 2 2 2 2 2 2 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 2 3 4 4 4 4 3 2 2 2 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 3 3 2 2 2 2 2 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 2 2 3 3 4 4 4 4 4 4 44 4 4 3 3 2 2 2 2 2 2 2 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 2 2 2 2 2 3 4 4 4 4 3 3 2 2 2 2 2 2 3 3 4 4 4 4 4 4 4 4 3 3 2 2 2 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 3 4 4 4 4 4 4 44 4 4 4 3 2 2 2 2 2 2 2 2 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 2 2 3 3 4 4 4 3 3 2 2 2 2 2 2 2 3 4 4 4 4 4 4 4 4 3 2 2 2 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 2 2 2 3 4 4 4 4 4 4 44 4 4 4 3 3 2 2 2 2 2 2 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 2 2 2 2 2 2 2 3 3 4 4 3 2 2 2 2 2 2 2 2 3 3 4 4 4 4 4 4 3 3 2 2 2 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 2 2 2 3 4 4 4 4 4 4 44 4 4 4 4 3 2 2 2 2 2 2 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 2 2 2 2 2 2 3 4 3 3 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 2 2 2 2 2 2 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 3 3 2 2 2 2 3 3 3 3 4 4 4 4 4 4 44 4 4 4 4 3 3 3 3 2 2 2 2 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 4 3 3 2 2 1 1 1 1 1 1 1 2 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 3 3 2 2 3 3 3 3 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 3 2 2 2 2 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 2 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 3 3 2 2 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 2 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 3 3 3 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 4 4 4 3 3 3 3 4 4 3 2 2 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 44 4 4 4 4 3 3 2 2 2 2 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 4 4 3 2 2 3 3 4 3 2 2 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 44 4 4 4 4 3 2 2 2 2 2 2 2 3 3 4 4 4 4 4 4 4 4 4 3 3 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 4 3 2 2 2 3 3 3 2 2 2 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 44 4 4 4 4 3 2 2 2 2 2 2 2 2 3 3 4 4 4 4 4 4 4 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 3 3 4 4 4 4 4 4 4 4 4 4 44 4 4 4 4 3 2 2 2 2 2 2 2 2 2 3 3 4 4 4 4 4 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 4 4 4 4 4 4 4 4 4 44 4 4 4 4 3 3 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 3 3 3 2 2 2 2 2 2 3 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 2 2 3 3 4 3 3 2 2 2 2 2 3 3 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 3 3 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 4 4 3 3 3 3 4 4 4 3 3 3 2 2 2 2 3 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 3 3 3 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 3 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 3 3 3 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 4 3 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 4 3 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 4 3 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4 4 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 3 3 3 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4

200m

200m

Interior Marsh

Marsh Edge

Bay Channel

Tidal Creek

Marsh Pool

Time

T (

oC

)P

rey

(#/m

2 )S

tag

eD

O (

mg

/l)

Page 21: Modelling the effects of hypoxia on fish Kenneth Rose Dept. of Oceanography and Coastal Sciences Louisiana State University plus Many Co-authors.

• Growth:– bioenergetics– consumption based on prey and predator sizes; prey densities

• Movement: – neighborhood depends on tidal stage and individual motility– move to cell with highest fitness score in neighborhood

• Mortality: – predation; starvation; stranding; natural

• Spawning: – temperature and weight-dependent fecundity– fractional spawning with brood intervals

3. Individual Processes

Page 22: Modelling the effects of hypoxia on fish Kenneth Rose Dept. of Oceanography and Coastal Sciences Louisiana State University plus Many Co-authors.

Grass Shrimp

0

10

20

30

40

50

60

70

80

90Gulf Killifish

0

1

2

3

4

5

6

7

Inland Silverside

0

0.5

1

1.5

2

2.5

3

3.5

1 51 101 151 201 251 301 351

Blue Crab

0

1

2

3

1 51 101 151 201 251 301 351

Den

sity

(#/

met

er2 )

Days

3. Baseline Results: Densities

Interior Marsh

Marsh Edge

Bay Channel

Tidal Creek

Marsh Pool

Page 23: Modelling the effects of hypoxia on fish Kenneth Rose Dept. of Oceanography and Coastal Sciences Louisiana State University plus Many Co-authors.

3. Grass Shrimp Distribution

0 0.01-1 1-2 2-5 5-10 10-20 20-30 30-40

Tid

al S

tage

Page 24: Modelling the effects of hypoxia on fish Kenneth Rose Dept. of Oceanography and Coastal Sciences Louisiana State University plus Many Co-authors.

3. Cyclic Dissolved Oxygen Stress

Hours

0 15 30 45 60 75 90

Dis

solv

ed O

xyge

n (m

g/l)

0

1

2

3

4

5

6

7

Creek at High Tide - Baseline Creek at High Tide w/ DO Stress

* Grass shrimp:Larval z (hour-1) = 5.5E-4*(DO) + 0.0007

* Grass shrimp:Brood interval (days) = 350.4 + 255.1/ln(DO)

All species:Metabolism multiplier = 1.79*(DO)-0.362 when DO < 5 mg/l

* Grass shrimp functions fit to laboratory data provided by Brouwer & Brown-Peterson

Page 25: Modelling the effects of hypoxia on fish Kenneth Rose Dept. of Oceanography and Coastal Sciences Louisiana State University plus Many Co-authors.

3. DO StressGrass Shrimp

Tota

l A

bundance

0

50000

100000

150000

200000

250000

300000

350000

400000

450000

BaselineDO Stress

Days0 100 200 300

0

5000

10000

15000

20000

25000

30000

35000

Gulf Killifish

Blue Crab

Page 26: Modelling the effects of hypoxia on fish Kenneth Rose Dept. of Oceanography and Coastal Sciences Louisiana State University plus Many Co-authors.

3. DO Stress

Blue Crab

0 20 40 60 800

2

4

6

8

10

12

14

Grass Shrimp

0 10 20 30 40 50

Fre

qu

en

cy (

x1

05 )

0

6

12

18

180210240270

Gulf Killifish

0 20 40 60 80 1000

1

2

3

4

5

6

BaselineDO Stress

Length (mm)

Fre

quen

cy (

x105

)

Page 27: Modelling the effects of hypoxia on fish Kenneth Rose Dept. of Oceanography and Coastal Sciences Louisiana State University plus Many Co-authors.

3. Gene Chips• Episodes and fluctuations complicate exposure

• Data– Grass shrimp and sheepshead minnow– Lab: DO, growth and fecundity, up/down regulation– Field: gene responses

• Idea is to add damage-repair (Mancini; Breck) or vitality (Anderson) sub-model to individuals– Calibrate to lab– Apply to field exposures

Page 28: Modelling the effects of hypoxia on fish Kenneth Rose Dept. of Oceanography and Coastal Sciences Louisiana State University plus Many Co-authors.

4. Chesapeake Bay WQMDeveloped by the Army Corps

• 3D hydrodynamic model (CH3D), eutrophication model (CE-QUAL-ICM), and sediment diagenesis model

• Simulates 24 constituents– Forms of N, P, and Si– Spring and winter algae– Micro- and meso-zooplankton– DO and temperature

• Bay is divided into 4073 cells– 729 surface cells– Minimum 2 layers thick– Maximum 15 layers thick

Page 29: Modelling the effects of hypoxia on fish Kenneth Rose Dept. of Oceanography and Coastal Sciences Louisiana State University plus Many Co-authors.

4. Bay Anchovy Model• Spatially-explicit, individual-based

• Simulates growth, death, and movement

• Dynamically coupled to the WQM– Temperature and DO affect anchovy growth and mortality– Micro- and meso-zooplankton affect anchovy growth– Consumption by anchovy is mortality on zooplankton

• Movement depends on:– Horizontal: zooplankton density, temperature– Vertical: temperature, dissolved oxygen

• Fixed recruitment each year

Page 30: Modelling the effects of hypoxia on fish Kenneth Rose Dept. of Oceanography and Coastal Sciences Louisiana State University plus Many Co-authors.

4. DO Effects

Dissolved Oxygen (mg/liter)

0 2 4 6 8

Gro

wth

mu

ltip

lier

0.0

0.2

0.4

0.6

0.8

1.0

Dissolved oxygen (mg/liter)

0.0 0.2 0.4 0.6 0.8 1.0

Mo

rtal

ity

(%/d

ay)

-40

-30

-20

-10

0

DO effect on growth DO mortality

Page 31: Modelling the effects of hypoxia on fish Kenneth Rose Dept. of Oceanography and Coastal Sciences Louisiana State University plus Many Co-authors.

4. Results – Hypoxia (Normal Year, July, bottom layer)

50% Increase 50% ReduceBaseline

Nutrient Loading 0 mg/l

>3 mg/l

Page 32: Modelling the effects of hypoxia on fish Kenneth Rose Dept. of Oceanography and Coastal Sciences Louisiana State University plus Many Co-authors.

4. Results – Anchovy Spatial Distribution(Baseline year, late October)

Wet DryNormal

Water Year

35/m2

0/m2

Page 33: Modelling the effects of hypoxia on fish Kenneth Rose Dept. of Oceanography and Coastal Sciences Louisiana State University plus Many Co-authors.

4. Results – Anchovy Biomass

Julian Day

365 730 1095 1460 1825 2190 2555 2920 3285 3650

Bio

mas

s (m

etri

c to

ns)

0

10000

20000

30000

40000

50000ReducedBaselineIncreased

Page 34: Modelling the effects of hypoxia on fish Kenneth Rose Dept. of Oceanography and Coastal Sciences Louisiana State University plus Many Co-authors.

4. Results – Zooplankton(Station C5.2 – mid-bay, with anchovy)

Mic

rozo

op

lan

kto

n

(mg

/L)

0.000.020.040.060.080.10

Year

0 2 4 6 8 10

Mes

ozo

op

lan

kto

n(m

g/li

ter)

0.00

0.04

0.08

0.12

0.16

Baseline, no anchovyBaselineIncrease

Reduce

Page 35: Modelling the effects of hypoxia on fish Kenneth Rose Dept. of Oceanography and Coastal Sciences Louisiana State University plus Many Co-authors.

4. Results – YOY Anchovy Length(Late October)

Water Year

Dry Normal Wet

An

cho

vy l

eng

th (

mm

)

0

20

40

60

Reduced Baseline Increase

Page 36: Modelling the effects of hypoxia on fish Kenneth Rose Dept. of Oceanography and Coastal Sciences Louisiana State University plus Many Co-authors.

Overview of ModelsTaxa Level Time Space

Sciaenids Individual Single fish Daily 6 mo Point Point

Croaker Stage within age

Population 1,5,10,30 d

Annual

100 yr Point within 2 nursery boxes

GOM or MAB

Community Individual Population Hourly 1 yr 2-D grid

+ water stage

Marsh

Bay anchovy

Individual Psuedo-population (fixed rec)

15 min, 1 hr

10 yr 3-D grid Chesapeake Bay

Page 37: Modelling the effects of hypoxia on fish Kenneth Rose Dept. of Oceanography and Coastal Sciences Louisiana State University plus Many Co-authors.

Concluding Remarks

• Modeling techniques, measurements, and understanding are rapidly improving

• Advances:– Scaled models– Spatial data– Exposure– Multiple stressors

Page 38: Modelling the effects of hypoxia on fish Kenneth Rose Dept. of Oceanography and Coastal Sciences Louisiana State University plus Many Co-authors.

Concluding Remarks

• Optimism for

quantifying

indirect effects?

• Key will be

movement


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