1. The Effects of a Parasitic Copepod (Achtheres) on Smith Mountain Lake Presented by: Douglas Thomasey Tom Shahady and Joe Ashwell

2. Background Information Striped Bass (Morone saxatilis) Striped Bass (Morone saxatilis) ** Travel in schools ** Travel in schools Localize in cooler, oxygenated areas Localize in cooler, oxygenated areas ** Reproduction is prevented in Smith Mountain Lake ** Reproduction is prevented in Smith Mountain Lake Have made Smith Mountain Lake nationally known Have made Smith Mountain Lake nationally known Parasitic Copepod (Achtheres) Parasite becomes attached to the host ** Dies with the host ** Larva is free-swimming First outbreak occurred in 1981 in the Tellico Reservoir “Gill Maggot”

3. Mathematical Modeling Lokta-Volterra Lokta-Volterra Describes a Predator vs. Prey relationship Describes a Predator vs. Prey relationship x represents the Prey x represents the Prey y represents the Predator y represents the Predator a, b, c, d, are known as parameters a, b, c, d, are known as parameters xy is the likelihood of an encounter xy is the likelihood of an encounter Vito Volterra and A.J. Lotka created the system Vito Volterra and A.J. Lotka created the system

4. Oscillation Source: Edelstein-Keshet L, Mathematical Models in Biology (Random House: New York, 1988), 218.

5. Smith Mountain Lake Model Considerations forming model Considerations forming model No reproduction No reproduction Stocking rates (21 fish per acre) Stocking rates (21 fish per acre) Almost ½ million fish per year Almost ½ million fish per year

6. Probability Fraction Is a built-in probability that an encounter with another fish would result in the transmitting of the parasite Is a built-in probability that an encounter with another fish would result in the transmitting of the parasite The chance of actually contracting the parasite is dependent on the ratio of infected fish to the entire population The chance of actually contracting the parasite is dependent on the ratio of infected fish to the entire population

7. Sensitivity Sensitivity of parameters Sensitivity of parameters Drastic changing the values of our parameters will not influence the outcome Drastic changing the values of our parameters will not influence the outcome These values do not have to be correct to gain correct assumption about our model These values do not have to be correct to gain correct assumption about our model Keeping parameters d,v, constant, while changing the values of b, gives us an idea its sensitivity d =.1 d =.1 v =.25 v =.25 b = 1 b =.5 b=.1

8. Results What can be done to solve this problem? What can be done to solve this problem? Stocking rates Stocking rates Introduce a new fish with a lower interaction Introduce a new fish with a lower interaction Stocking Rates: 21 fish per acre 7 fish per acre no stock

9. Stock a different type of fish? Interaction rates: Interaction rates: 90% 10% 90% 10% The effects of stocking a type of fish with a low interaction rate Schooling fish vs. territorial fish

10. Using Phase Plane Diagrams Visual of solutions to a system of equations Visual of solutions to a system of equations In order to find solutions, and give an idea to the stability of any given system In order to find solutions, and give an idea to the stability of any given system Saddle, sink, and source Saddle, sink, and source Smith Mountain Lake Diagram