atlantic salmon modeling an ecological risk
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ATLANTIC SALMON Modeling an Ecological Risk. Acevedo E. Grant J. Introduction Models Remarks Acknowledgments Reference. Introduction Models Remarks Acknowledgments Reference. Introduction. - PowerPoint PPT PresentationTRANSCRIPT
ATLANTIC SALMONModeling an Ecological Risk
Acevedo E.
Grant J.
• Introduction
• Models
• Remarks
• Acknowledgments
• Reference
• Introduction
• Models
• Remarks
• Acknowledgments
• Reference
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19901991
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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.