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Non-local Dispersal Models for a Population under Climate Change

Non-local Dispersal Models for a Population under Climate Change. (Joy) Ying Zhou, Mark Kot Department of Applied Mathematics University of Washington. Cartoon of a Range Shift. Global mean: 0.42km/yr. Population Dynamics Matter. Cartoon of a Range Shift. Talk Outline.

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Non-local Dispersal Models for a Population under Climate Change

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  1. Non-local Dispersal Models for a Population under Climate Change (Joy) Ying Zhou, Mark Kot Department of Applied Mathematics University of Washington

  2. Cartoon of a Range Shift

  3. Global mean: 0.42km/yr

  4. Population Dynamics Matter Cartoon of a Range Shift

  5. Talk Outline Population Models on Range Shifts under: Constant-speed climate change Accelerated climate change

  6. Organisms of Interest • Well-defined life stages (growth, dispersal) • Growth and dispersal occur in separate time periods • Non-overlapping generations Seedling Egg mass Dispersal Dispersal Seed Adult Larvae Flower Growth Growth Cocoon

  7. Integrodifference equation Assuming no Allee effects Integrodifferenceeqn (IDE) kernel

  8. How To Mathematize Climate Warming?

  9. Climatically Suitable Habitat Habitat shifts Combination of two classical problems Zhou and Kot 2011 Theoretical Ecology

  10. Two Classic IDE Models

  11. Two Classic IDE Models

  12. A Steady Range Shift For Small c What Population Dynamics Will We Observe? Zhou and Kot 2011 Theoretical Ecology

  13. Extinction When c Large Zhou and Kot 2011 Theoretical Ecology

  14. Critical Speed “c*”

  15. Eigenvalue Problem Net reproductive rate Analytic method for “separable” kernels Numerical method “Nystrom’s method” Delves and Wash 1974

  16. Larger Net ReproductiveRate Helps Zhou and Kot 2011 Theoretical Ecology

  17. More Dispersal, But Not Over-dispersal radius Dispersal radius Zhou and Kot 2011 Theoretical Ecology

  18. Lockwood et al. 2002

  19. Clark 1998 Mean deviation Schultz 1998

  20. The “Tail” of The Dispersal Kernel Result for a typical platykurtic kernel Result for a typical leptokurtic kernel Result for a typical leptokurtic kernel Zhou and Kot 2011 Theoretical Ecology

  21. Heterogeneous Habitat Suitability Climatically Suitable Habitat Climatically Suitable Habitat Habitat shifts Habitat quality function Latore et al. 1999

  22. Consider linearized equation For normally distributed habitat quality a Gaussian dispersal kernel

  23. and a special initial condition (Gaussian initial profile), then we have an ansatz Latore et al. 1999 : peak of the pulse : amplitude of the pulse

  24. “climate deficit”

  25. Declining population if

  26. Accelerated Climate Change Same ansatz

  27. The mean of the Gaussian ansatz

  28. The “climate deficit”

  29. Speed Time T

  30. Comparison of climate deficit vs. For large t

  31. Summary • An integrodifference equation model with shifting boundaries • Critical speed • Acceleration may hurt a lot (more than average)

  32. Thank you! Questions?

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