1 / 26

Using the Hawk-Dove Model and Ordinary Differential Equation Systems to Study Asian Carp Invasion

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

harrison
Download Presentation

Using the Hawk-Dove Model and Ordinary Differential Equation Systems to Study Asian Carp Invasion

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Using the Hawk-Dove Model and Ordinary Differential Equation Systems to Study Asian Carp Invasion Yvonne Feng and Kelly Pham

  2. Outline • Background • Motivation • Introduction to our models • Different Invasion Problems • Limitations of our models • Future Work

  3. Background • Native habitat: China • Prolific (spawns rapidly) • Eats plankton • Eats approximately 6.6-11.3% of their body weight

  4. 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

  5. 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

  6. Game Theory Model • Hawk-Dove as basic model • Represent it as an ODE system (normalized) • Choose V = 2 and C = 4

  7. 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

  8. Initial Conditions (Carp) : w0 =(0.2, 0.1, 0) La Crosse Davenport Saint Louis

  9. Plot of Asian Carps Population in Cell r at Time t Population Fraction of Asian Carps Cell # (each cell represent a spot in the river) Time Step(Chosen automatically by matlab)

  10. 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

  11. Problems • Asian Carps are introduced in certain spots in the river • Asian Carps heavily invade the entire river

  12. 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

  13. 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)

  14. Results Final Population Fraction of Asian Carps Beginning of Invasion: Population Fraction of Asian Carp

  15. 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

  16. 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

  17. Average Invasion Index of 20 random Asian Carps Initial Conditions #1 Group of Targeted Fishing in Cell# #1 Group of Targeted Fishing in Cell#

  18. 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

  19. 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

  20. Future Work • Add a Retaliator to our Hawk-Dove model • Incorporate a term for active movement of fish • Reassess results for later time points

  21. Thank you!

  22. Any Questions?

More Related