Yvonne Feng and Kelly Pham. Outline Background Motivation Introduction to our models Different Invasion Problems Limitations of our models Future Work.

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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

Davenport Initial Conditions (Carp) : w 0 =(0.2, 0.1, 0) La Crosse Saint Louis Carp Native Fish Carp2 Native Fish 01

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 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

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

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!

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