C:\Documents and Settings\Doug Thomasey\My Documents\DT's Academic\Math 451 - Senior Project\Visual Basic\Game of Life 4\Game of Life 4.exe

The Effects of a The Effects of a Parasitic Copepod Parasitic Copepod

((AchtheresAchtheres) on Smith ) on Smith Mountain LakeMountain Lake

Presented by: Douglas Presented by: Douglas ThomaseyThomasey

Tom Shahady and Joe Ashwell

Background InformationBackground Information Striped Bass Striped Bass

((Morone saxatilisMorone saxatilis)) Travel in schoolsTravel in schools Localize in cooler, Localize in cooler,

oxygenated areasoxygenated areas Reproduction is Reproduction is

prevented in Smith prevented in Smith Mountain LakeMountain Lake

Have made Smith Have made Smith Mountain Lake Mountain Lake nationally knownnationally known

Parasitic Copepod Parasitic Copepod ((AchtheresAchtheres)) Parasite becomes Parasite becomes

attached to the hostattached to the host Dies with the hostDies with the host Larva is free-Larva is free-

swimmingswimming First outbreak First outbreak

occurred in 1981 in occurred in 1981 in the Tellico Reservoirthe Tellico Reservoir

““Gill Maggot”Gill Maggot”

Mathematical ModelingMathematical Modeling Lokta-VolterraLokta-Volterra

Describes a Describes a Predator vs. Prey Predator vs. Prey relationshiprelationship

x x represents the represents the PreyPrey

y y represents the represents the PredatorPredator

aa,, b b,, c c,, d d,, are known are known as parametersas parameters

xy xy is the likelihood is the likelihood of an encounter of an encounter

Smith Mountain Lake Smith Mountain Lake ModelModel

AssumptionsAssumptions Closed system – no reproductionClosed system – no reproduction Introduce one infected fish into the populationIntroduce one infected fish into the population Once infected always infectedOnce infected always infected Loss of parasite only through the death of a fishLoss of parasite only through the death of a fish

Probability FractionProbability Fraction

Is a built-in probability that an Is a built-in probability that an encounter with another fish would encounter with another fish would result in the transmitting of the parasiteresult in the transmitting of the parasite

The chance of actually contracting the The chance of actually contracting the parasite is dependent on the ratio of parasite is dependent on the ratio of infected fish to the entire populationinfected fish to the entire population

ParametersParameters

bb : Encounter rate : Encounter rate 0.90.9

vv : Death rate of the infected : Death rate of the infected 0.25/120.25/12

dd : Death rate of the : Death rate of the susceptiblesusceptible 0.1/120.1/12

SensitivitySensitivity Sensitivity of parametersSensitivity 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 These values do not have to be correct to gain correct assumption about our

model model

Keeping parameters Keeping parameters dd,,vv, constant, while changing the values of , constant, while changing the values of bb, gives , gives us an idea its sensitivityus an idea its sensitivity d = .1d = .1 v = .25v = .25

b = 1b = 1 b = .5 b = .5 b=.1b=.1

ResultsResults What can be done to solve this problem?What can be done to solve this problem?

Stocking ratesStocking rates Introduce a new fish with a lower interactionIntroduce a new fish with a lower interaction

Stocking Rates:Stocking Rates:21 fish per acre21 fish per acre 7 fish per acre 7 fish per acre no stock no stock

Stock a different type of Stock a different type of fish?fish?

Interaction rates:Interaction rates: 90%90% 10% 10%

The effects of stocking a type of fish The effects of stocking a type of fish with a low interaction ratewith a low interaction rate

Schooling fish vs. territorial fishSchooling fish vs. territorial fish

ConclusionsConclusions Under all conditions about 18 months Under all conditions about 18 months

until appearance in the population no until appearance in the population no matter the size of the initial populationmatter the size of the initial population

Fish behavior (contact) most significant Fish behavior (contact) most significant parameter for spread of parasiteparameter for spread of parasite

Low stocking rates may be the best Low stocking rates may be the best management strategy to minimize management strategy to minimize spread of parasite and fish contactspread of parasite and fish contact

¿Questions?¿Questions?

> restart:> with(plots):> b:=.9; d:=.25/12; v:=.5/12; IntS:=1000000; IntI:=100000; New:=145000; years:=12; j=0;> plot1:=array(0..years); Years2:=(years-1); stock:=array(0..Years2,[145000,145000,145000,145000,145000,145000,145000,145000,145000,145000,145000,145000]); season:=array(0..Years2,[.9,.9,.9,.9,.1,.1,.1,.1,.9,.9,.9,.9]);

Graphing ConclusionsGraphing Conclusions

t ( )i t b ( )s t

( )i t( )s t ( )i t v ( )i t

territorial fishterritorial fish

Interaction rates:Interaction rates:

Stocking RatesStocking Rates