ATLANTIC SALMON Modeling an Ecological Risk Acevedo E. Grant J.

Introduction Models Remarks Acknowledgments Reference

Introduction Models Remarks Acknowledgments Reference

Introduction Culture atlantic salmon is a million USD industry that exceeds wild salmon catch by 70 % (Naylor et al. 2005). From 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 AA AAA A AA A aAa Aa AAAAa a aa

F I H W Wild aa aaa a aa AAa aaa Aa AAAAa a aa β

F I H W Aa AAAAa a aa Hybrid Aa aAaaa aAaaa Aa AAAAa AAAAa aa A A β

Model #1 Pros Terms have good biological meaning Cons No nontrivial fixed points Difficult to analyse numerically or analytically

Model # 2 Pros Includes competition terms Nontrivial fixed points Cons Negative hybrid population values

Model #3 Pros No negative hybrid population values Interesting dynamics between wild and the introduce Cons No hybrid population appear Spontaneous generation

Model # 4 Pros Interesting relationship between competition terms and genetic proportions Cons Wild population always collapses Negative values for hybrid population

Model # 5

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 Survival and growth responses of juvenil salmonines stocked in the eastern lake Ontario tributaries. Transactions of the American Fisheries Society 136: [FAO] Food and Agriculture Organization of the United Nation FishStat- Fishery information, data and statistics unit [online]. Consulted: May 9, Kelso, D Genetically engineered salmon, ecological risk, and environmental policy. Bulletin of Marine Science 74(3): Naylor, R., K. Hindar, I. Fleming, R. Goldburg, S. Williams, J. Volpe, F. Whoriskey, J. Eagle, D. Kelso and M. Mangel Fugitive Salmon: Assessing the risk of escaped fish from net-pen aquaculture. BioScience 55(5): Muir, W. and R. Howard Characterization of environmental risk of genetically engineered organisms and their potential to control exotic invasive species. Aquatic Science 66: