using the hawk-dove model and ordinary differential equation systems to study asian carp invasion
DESCRIPTION
Using the Hawk-Dove Model and Ordinary Differential Equation Systems to Study Asian Carp Invasion. Yvonne Feng and Kelly Pham. Outline. Background Motivation Introduction to our models Different Invasion Problems Limitations of our models Future Work. Background . Native habitat: China - PowerPoint PPT PresentationTRANSCRIPT
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Using the Hawk-Dove Model and Ordinary Differential Equation
Systems to Study Asian Carp InvasionYvonne Feng and Kelly Pham
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OutlineBackgroundMotivationIntroduction to our modelsDifferent Invasion ProblemsLimitations of our modelsFuture Work
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Background Native habitat: ChinaProlific (spawns rapidly)Eats planktonEats approximately 6.6-11.3% of their body
weight
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Invasion ProblemsAsian carp introduced to US in 1970’sMigrated to Mississippi RiverCompetes with native species for food50% of total catch in 2008Currently threatening the Great Lakes
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Why Research This?To study and understand the
interaction between the native and invasive species
To study the speed of the invasion with aims to identify parameters to slow down or to stop the invasion
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Game Theory ModelHawk-Dove as basic modelRepresent it as an ODE system
(normalized)
Choose V = 2 and C = 4
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Diffusion- Reaction ModelDivide river into n cells and add spatial
component
Formula: ∂w/∂t = F(w) + D∆ww is the 2n x 1 vector that represents the
population fractions in each cell F is the change of population fractions over
time in each cell (our ODE model)D∆ is the 2n x 2n matrix that contains the
Laplacian matrix and the diagonal matrix of diffusion coefficients
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Davenport
Initial Conditions (Carp) : w0 =(0.2, 0.1, 0)
La Crosse
Saint Louis
Carp Native Fish
Carp -1 2
Native Fish
0 1
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Popu
latio
n Fr
actio
n of
Asi
an
Car
ps
Time Step(Chosen automatically by matlab)Cell # (each cell represent a spot in the
river)
Plot of Asian Carps Population in Cell r at Time t
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Modeling the ImplementationsElectric Fence
Change diagonal entry of coefficient matrix to 0.000001
Targeted RemovalAdd matrix to payoff to matrix A for the
cells where targeted removal is happening
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ProblemsAsian Carps are introduced in certain spots in the river
Asian Carps heavily invade the entire river
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Assumptions Fish in each spot is either an Asian carp
or a native fish All carps act like Hawks; all native fish act
like DovesTotal biomass in each spot is conservedThe carrying capacity of the river is
constantFish dispersal is independent of
temperature, amount of food, flow
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Problem: Prevent Future InvasionAsian Carps are introduced in cell #1-3(ex. Cell 1: 025, Cell2: 0.1, Cell3: 0.05)
Electric Fence: 16 million dollars eachTargeted Fishing: 2 million dollars each set
Goal: Find the best fishing strategy to prevent Asian Carps from invading into other areas(Cell4 – Cell 10)
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Results Beginning of Invasion:
Cell 1
Cell 2
Cell 3
Cell 4
Cell 5
Cell 6
Cell 7
Cell 8
Cell 9
Cell 10
0
0.1
0.2
0.3
0.4
0.5
0.6
No Treat-mentFence be-tween Cell #3 and 4
Fish Cell 4 - 7
Popu
lati
on F
ract
ion
of A
sian
C
arp
Final Population Fraction of Asian Carps
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DiscussionIf the Targeted Fishing is as good as
our assumption, with the given initial Asian Carps Population Fractions:
Fishing Strategy:Cell#4-7 Least Population of Asian Carps that
invade cell #4 to 10More Money efficient than
implementing Electric Fence
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Problem: During InvasionRandom Asian Carps Initial
Population FractionsResources: 2 sets of targeted fishingAverage Invasion Index: Average of
the sum of Asian Carps Population after targeted fishing over 20 iterations
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#1 Group of Targeted Fishing in Cell#
#1
Gro
up o
f Ta
rget
ed F
ishi
ng in
C
ell#
Average Invasion Index of 20 random Asian Carps Initial Conditions
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DiscussionPutting all of the targeted fishing groups
in one cell is a bad strategyWith the current 20 random initial Asian
Carps population iterations, and given two groups of targeted fishing:
results suggest that placing the two fishing groups in separate cells between the center and end of the invasion domain is a good strategy
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Limitations Native and invasive fish interactions are
most likely more complicated than represented in the Hawk-Dove mode
Most likely, there will be a change in biomass
In addition to fish dispersal, fish also exhibit active movement towards food sources and favorable environmental conditions
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Future WorkAdd a Retaliator to our Hawk-Dove
model
Incorporate a term for active movement of fish
Reassess results for later time points
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Thank you!
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Any Questions?