1 / 28

CEE262C Lecture 4: Phase line analysis and NPZ models

CEE262C Lecture 4: Phase line analysis and NPZ models. Overview. Phase line analysis Logistic equation Allee effect model Q-logistic model Nutrient-phytoplankton-zooplankton (NPZ) models

roland
Download Presentation

CEE262C Lecture 4: Phase line analysis and NPZ models

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. CEE262C Lecture 4: Phase line analysis and NPZ models Overview • Phase line analysis • Logistic equation • Allee effect model • Q-logistic model • Nutrient-phytoplankton-zooplankton (NPZ) models References: Mooney & Swift, Ch 5.2-5.3; Paper: Truscott, J. E., and J. Brindley (1994), "Ocean Plankton Populations as Excitable Media", Bull. Math. Biol.56, 981-998. CEE262C Lecture 4: Phase line analysis and NPZ models

  2. Levels of ODE models: Linear O(x1) CEE262C Lecture 4: Phase line analysis and NPZ models

  3. Logistic equation O(x2) CEE262C Lecture 4: Phase line analysis and NPZ models

  4. Improved predator-prey Noncompetitive parts CEE262C Lecture 4: Phase line analysis and NPZ models

  5. q-logistic model CEE262C Lecture 4: Phase line analysis and NPZ models

  6. Phase directions for the logistic equation Do small populations always recover as this model implies? CEE262C Lecture 4: Phase line analysis and NPZ models

  7. Allee-effect equation O(x3) CEE262C Lecture 4: Phase line analysis and NPZ models

  8. Phase directions for the Allee-effect equation CEE262C Lecture 4: Phase line analysis and NPZ models

  9. Allee-effect equation K=1,T=0.25,r=0.75 K=1,T=0.15,r=0.5 Carrying capacity (K) K=1,T=0.25,r=0.5 Threshold populations (T) CEE262C Lecture 4: Phase line analysis and NPZ models

  10. Example: Fixed harvesting CEE262C Lecture 4: Phase line analysis and NPZ models

  11. CEE262C Lecture 4: Phase line analysis and NPZ models

  12. Example: Harvesting effort CEE262C Lecture 4: Phase line analysis and NPZ models

  13. CEE262C Lecture 4: Phase line analysis and NPZ models

  14. Higher-order functions: Modeling phytoplankton blooms CEE262C Lecture 4: Phase line analysis and NPZ models

  15. Phytoplankton blooms or "red tides":model requirements: • Existence of two states • equilibrium P-Z level – stable, can remain throughout the red-tide season • outbreak P-Z level – quasi-stable, can remain for weeks or months • Rapid outbreaks followed by slow relaxation: implies 2 time scales • Trigger mechanism • Cyclic nature – both triggering and restoring mechanism CEE262C Lecture 4: Phase line analysis and NPZ models

  16. Modified Predator-Prey CEE262C Lecture 4: Phase line analysis and NPZ models

  17. Model for the grazing rate G(P,Z) CEE262C Lecture 4: Phase line analysis and NPZ models

  18. All F(P)1 as P ; Which function to use? Functional forms of G(P,Z)=RmZ F(P) CEE262C Lecture 4: Phase line analysis and NPZ models

  19. Behavior of Nonzero fixed points: 1 Stable at P=K 1 unstable Nonzero fixed points: 1 Stable at P=K 1 unstable Nonzero fixed points: 2 Stable! 1 unstable CEE262C Lecture 4: Phase line analysis and NPZ models

  20. The phytoplankton bloom model CEE262C Lecture 4: Phase line analysis and NPZ models

  21. Behavior of P2/(a2+P2) a is the "Predation response concentration" Predators respond and start grazing when prey population is roughly P=a. Low a: Predators respond quickly to low P High a: Predators respond more slowly and wait for P to increase. CEE262C Lecture 4: Phase line analysis and NPZ models

  22. Nondimensionalize CEE262C Lecture 4: Phase line analysis and NPZ models

  23. Nullclines and fixed points CEE262C Lecture 4: Phase line analysis and NPZ models

  24. CEE262C Lecture 4: Phase line analysis and NPZ models

  25. Excitability based on initial conditions npzdemo.m CEE262C Lecture 4: Phase line analysis and NPZ models

  26. CEE262C Lecture 4: Phase line analysis and NPZ models

  27. Excitability of the red tide depends on F(P) CEE262C Lecture 4: Phase line analysis and NPZ models

  28. CEE262C Lecture 4: Phase line analysis and NPZ models

More Related