ATLANTIC SALMON Modeling an Ecological Risk

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ATLANTIC SALMONModeling an Ecological Risk

• Acevedo E.
• Grant J.

2

• Introduction
• Models
• Remarks
• Acknowledgments
• Reference

3

• Introduction
• Models
• Remarks
• Acknowledgments
• Reference

4
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
5

• Introduction
• Models
• Remarks
• Acknowledgments
• Reference

6
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.

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F
ß
I
H
W
Farm
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A A
A AA AA
A AA AA
A A
A AA AA
a Aa Aa
F
ß
A a
A AA Aa
a Aa aa
I
H
W
Introduced
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a a
a aa aa
a aa aa
a a
A Aa Aa
a aa aa
F
ß
A a
A AA Aa
a Aa aa
I
H
W
Wild
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A a
A AA Aa
a Aa aa
A a
A AA Aa
A AA Aa
F
ß
A a
a Aa aa
a Aa aa
a a
A Aa Aa
A Aa Aa
I
H
W
Hybrid
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Model 1

• Pros
• Terms have good biological meaning
• Cons
• No nontrivial fixed points
• Difficult to analyse numerically or analytically

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Model 2

• Pros
• Includes competition terms
• Nontrivial fixed points
• Cons
• Negative hybrid population values

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Model 3

• Pros
• No negative hybrid population values
• Interesting dynamics between wild and the
  introduce
• Cons
• No hybrid population appear
• Spontaneous generation

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Model 4

• Pros
• Interesting relationship between competition
  terms and genetic proportions
• Cons
• Wild population always collapses
• Negative values for hybrid population

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Model 5
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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)

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Fixed Points and Stability

• Fixed points
• (ß0.01,µ0.01,?49)
• (w,h,i) (0,0,9800)
• Stability
• Point is stable since all the eigenvalues are
  negative

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• Introduction
• Models
• Remarks
• Acknowledgments
• Reference

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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

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• Introduction
• Models
• Remarks
• Acknowledgments
• Reference

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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!
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• Introduction
• Models
• Remarks
• Acknowledgments
• Reference

23
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
  lthttp//www.fao.org/fi/default.aspgt. 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 66414-420.