atlantic salmon modeling an ecological risk

ATLANTIC SALMONModeling an Ecological Risk

Acevedo E.

Grant J.

• Introduction

• Models

• Remarks

• Acknowledgments

• Reference

• Introduction

• Models

• Remarks

• Acknowledgments

• Reference

0

200

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19781979

19801981

19821983

19841985

19861987

19881989

19901991

19921993

19941995

19961997

19981999

20002001

20022003

20042005

Year

Value (million USD )

Production (Hundred tons)

Introduction• Culture atlantic salmon is a million USD industry that

exceeds wild salmon catch by 70 % (Naylor et al. 2005).• From 1989-2000 1.4 million salmon escaped from the farms, because of: Hardware failures, fish-transfer and handling

mishaps and boat-operation problem (Kelso, 1999).

• Genetically engineered salmon have growth and reproductive advantages over the wild types (Muir and Howard, 2004).

Source FAO, 2007

• Introduction

• Models

• Remarks

• Acknowledgments

• Reference

Model assumptions

• Rate of escaped salmons is 1% of annual production (Kelso, 1999).

• Introduced species have double the growth rate of the wild type (Coghlan et al. 2007).

• Evaluating an independent gene.• No sexual selection associated with the

segregation of the genes.• Population are large and the interactions are

continuous.

F

I

H W

β

Farm

F

I

H W

β

Introduced

A A

A AA AA

A AA AA

A A

A AA AA

a Aa Aa

A a

A AA Aa

a Aa aa

F

I

H W

Wild

a a

a aa aa

a aa aa

a a

A Aa Aa

a aa aa

A a

A AA Aa

a Aa aa

β

F

I

H W

A a

A AA Aa

a Aa aa

Hybrid

A a

a Aa aa

a Aa aa

A a

A AA Aa

A AA Aa

a a

A Aa Aa

A Aa Aa

β

Model #1

22

22 4

1

2

112 IHIHFK

IIrI

2

22 2

1

2

1

2

112 HHWIWIHK

HHrH

.

22

22 4

1

2

11 WHHWK

WWrW

FK

FFrF

11 1

Pros•Terms have good biological meaning

Cons• No nontrivial fixed points• Difficult to analyse numerically or analytically

Model # 2

22

4

1

2

11 HWHW

K

IHWrW

Pros• Includes competition

terms• Nontrivial fixed points

Cons• Negative hybrid

population values

HWIWIHK

IHWrH

2

1

2

112

FIHIHK

IHWrI

22

4

1

2

112

FK

FFrF

11 1

Model #3

2

22

)(41

21

IHW

HWHWRWW

2

2

)(21

21

21

2IHW

HHWIWIHRHH

F

IHW

IHIHRII

2

22

41

21

2

22 1 K

HIWrR

FK

FFrF

11 1

Pros• No negative hybrid

population values• Interesting dynamics

between wild and the introduce

Cons• No hybrid population

appear• Spontaneous generation

Model # 4

FK

FFrF

11 1

WK

HWHWrW

22

41

21

1

FIK

HIIHrI

22

41

21

12

HK

HHWIWIHrH

2

21

21

21

12

Pros• Interesting

relationship between competition terms and genetic proportions

Cons• Wild population

always collapses• Negative values for

hybrid population

Model # 5

WIHWIHW

HWHWW

22

41

21

HIHWIHW

HHIIWHWH

2

21

21

21

2

FIIHWIHW

IHIHI

22

41

21

2

FK

FFrF

11 1

Model 5 (Finally) Works!Pros

•Solved most of the problems

•Integrate birth and death in terms of the genetic proportions

•Gave realistic results

•Nice mathematical form

Cons

•Unbounded values for some parameter choices

•Only depends on time (not spatial)

Fixed Points and Stability

Fixed points (β=0.01,µ=0.01,γ=49)

(w,h,i) = (0,0,9800)

Stability

Point is stable since all the eigenvalues are negative

• Introduction

• Models

• Remarks

• Acknowledgments

• Reference

Remarks

• Proving these hypothesis in the wild environment could cause irreversible harm

• Mathematical modelling is a helpful tool to solve this problem

• Model five is a good start but it needs improvement and validation

• Introduction

• Models

• Remarks

• Acknowledgments

• Reference

Acknowledgments

Dr. Thomas Hillen, Dr. Petro Babak , Dr. Jim Keener and Dr. Tomas de Camino Beck for their advice and NIMO and his NUCLEUS for his motivation

Thanks!

• Introduction

• Models

• Remarks

• Acknowledgments

• Reference

References

Coghlan, S., M. Connerton, N. Ringler, D. Stewart, J. Mead. 2007. Survival and growth responses of juvenil salmonines stocked in the eastern lake Ontario tributaries. Transactions of the American Fisheries Society 136: 56-71.

[FAO] Food and Agriculture Organization of the United Nation. 2007. FishStat-Fishery information, data and statistics unit [online] <http://www.fao.org/fi/default.asp>. Consulted: May 9, 2007.

Kelso, D. 1999. Genetically engineered salmon, ecological risk, and environmental policy. Bulletin of Marine Science 74(3): 509-528.

Naylor, R., K. Hindar, I. Fleming, R. Goldburg, S. Williams, J. Volpe, F. Whoriskey, J. Eagle, D. Kelso and M. Mangel. 2005. Fugitive Salmon: Assessing the risk of escaped fish from net-pen aquaculture. BioScience 55(5): 427-437.

Muir, W. and R. Howard. 2004. Characterization of environmental risk of genetically engineered organisms and their potential to control exotic invasive species. Aquatic Science 66:414-420.