Invasion of the Asian Carp
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Transcript Invasion of the Asian Carp
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
Prolific (spawns rapidly)
Eats plankton
Eats approximately 6.6-11.3% of their body weight
Invasion Problems
Asian carp introduced to US in 1970’s
Migrated to Mississippi River
Competes with native species for food
50% of total catch in 2008
Currently threatening the Great Lakes
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
Game Theory Model
Hawk-Dove as basic model
Represent it as an ODE system
(normalized)
Choose V = 2 and C = 4
Diffusion- Reaction Model
Divide river into n cells and add spatial component
Formula: ∂w/∂t =
F(w) + D∆w
w 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
La Crosse
Davenport
Initial Conditions
(Carp) : w0 =(0.2, 0.1, 0)
Saint
Louis
Carp
Native
Fish
Carp
-1
2
Native
Fish
0
1
Population Fraction of Asian Carps
Plot of Asian Carps Population in Cell r at Time t
Modeling the Implementations
Electric Fence
Change diagonal entry of coefficient matrix to
0.000001
Targeted Removal
Add matrix to payoff to matrix A for the cells
where targeted removal is happening
Problems
Asian Carps are introduced in
certain spots in the river
Asian Carps heavily invade the
entire river
Assumptions
Fish in each spot is either an Asian carp or a native
fish
All carps act like Hawks; all native fish act like
Doves
Total biomass in each spot is conserved
The carrying capacity of the river is constant
Fish dispersal is independent of temperature,
amount of food, flow
Problem: Prevent Future Invasion
Asian Carps are introduced in cell #1-3
(ex. Cell 1: 025, Cell2: 0.1, Cell3: 0.05)
Electric Fence: 16 million dollars each
Targeted Fishing: 2 million dollars each set
Goal: Find the best fishing strategy to prevent
Asian Carps from invading into other
areas(Cell4 – Cell 10)
Results
Beginning of Invasion:
Population Fraction of Asian Carp
Final Population Fraction of Asian Carps
0.6
0.5
0.4
No
Treatment
0.3
0.2
Fence
between
Cell #3 and
4
0.1
0
Cell 1 Cell 2 Cell 3 Cell 4 Cell 5 Cell 6 Cell 7 Cell 8 Cell 9 Cell 10
Discussion
If 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 10
More Money efficient than implementing
Electric Fence
Problem: During Invasion
Random Asian Carps Initial Population
Fractions
Resources: 2 sets of targeted fishing
Average Invasion Index: Average of the sum
of Asian Carps Population after targeted
fishing over 20 iterations
#1 Group of Targeted Fishing in Cell#
Average Invasion Index of 20 random Asian Carps Initial Conditions
#1 Group of Targeted Fishing in Cell#
Discussion
Putting all of the targeted fishing groups in
one cell is a bad strategy
With 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
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
Future Work
Add a Retaliator to our Hawk-Dove model
Incorporate a term for active movement of
fish
Reassess results for later time points
Thank you!
Any Questions?