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 ID: 182050
Download Presentation The PPT/PDF document "Using the Hawk-Dove Model and Ordinary D..." is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
Using the Hawk-Dove Model and Ordinary Differential Equation Systems to Study Asian Carp Invasion
Yvonne Feng and Kelly PhamSlide2
Outline
BackgroundMotivationIntroduction to our models
Different Invasion Problems
Limitations of our models
Future WorkSlide3
Background
Native habitat: ChinaProlific (spawns rapidly)Eats planktonEats approximately 6.6-11.3% of their body weightSlide4Slide5Slide6
Invasion Problems
Asian carp introduced to US in 1970’sMigrated to Mississippi RiverCompetes with native species for food50% of total catch in 2008
Currently threatening the Great LakesSlide7
Why Research This?
To study and understand the interaction between the native and invasive speciesTo study the speed of the invasion with aims to identify parameters to slow down or to stop the invasionSlide8
Game Theory Model
Hawk-Dove as basic modelRepresent it as an ODE system (
normalized
)
Choose V = 2 and C = 4Slide9
Diffusion- Reaction Model
Divide river into n cells and add spatial componentFormula:
∂
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 coefficientsSlide10
Davenport
Initial Conditions (Carp) :
w
0
=(0.2, 0.1, 0)
La Crosse
Saint
Louis
Carp
Native Fish
Carp
-1
2
Native Fish
0
1Slide11
Population Fraction of Asian Carps
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 tSlide12
Modeling the Implementations
Electric FenceChange diagonal entry of coefficient matrix to 0.000001
Targeted Removal
Add matrix to payoff to matrix A for the cells where targeted removal is happeningSlide13Slide14
Problems
Asian Carps are introduced in certain spots in the river
Asian Carps heavily invade the entire riverSlide15
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 conserved
The carrying capacity of the river is constant
Fish dispersal is independent of temperature, amount of food, flowSlide16
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
Targete
d Fishing: 2 million dollars each set
Goal: Find
the best fishing strategy to prevent Asian Carps from invading into other areas(Cell4 – Cell 10) Slide17
Results
Beginning of Invasion:
Population Fraction of Asian Carp
Final Population
Fraction
of Asian CarpsSlide18
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 FenceSlide19Slide20
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 iterationsSlide21
#1 Group of Targeted Fishing in Cell#
#1 Group of Targeted Fishing in Cell#
Average Invasion Index of 20 random Asian Carps Initial ConditionsSlide22
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 strategySlide23
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 conditionsSlide24
Future Work
Add a Retaliator to our Hawk-Dove modelIncorporate a term for active movement of fish
Reassess results for later time pointsSlide25
Thank you!Slide26
Any Questions?