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ELUDING CATASTROPHIC SHIFTS - Paula Villa Martín, Juan A. Bonachela,, Simon A. Levin, Miguel A. Muñoz

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ELUDING CATASTROPHIC SHIFTS - Paula Villa Martín, Juan A. Bonachela,, Simon A. Levin, Miguel A. Muñoz

  1. 1. ELUDING CATASTROPHIC SHIFTS miércoles, 22 de junio de 16
  2. 2. Juan A. Bonachela ELUDING CATASTROPHIC SHIFTS Paula Villa Martín Miguel A. Muñoz Simon A. Levin miércoles, 22 de junio de 16
  3. 3. Catastrophic shifts Are large, abrupt, persistent changes towards a completely different system state Kéfi, S., Dakos, V., Scheffer, M., Van Nes, E. H., & Rietkerk, M. (2013). Early warning signals also precede non-catastrophic transitions. Oikos, 122(5), 641-648. miércoles, 22 de junio de 16
  4. 4. Catastrophic shifts Are large, abrupt, persistent changes towards a completely different system state Kéfi, S., Dakos, V., Scheffer, M., Van Nes, E. H., & Rietkerk, M. (2013). Early warning signals also precede non-catastrophic transitions. Oikos, 122(5), 641-648. miércoles, 22 de junio de 16
  5. 5. Catastrophic shifts Are large, abrupt, persistent changes towards a completely different system state Importance: They can abruptly affect biodiversity Kéfi, S., Dakos, V., Scheffer, M., Van Nes, E. H., & Rietkerk, M. (2013). Early warning signals also precede non-catastrophic transitions. Oikos, 122(5), 641-648. miércoles, 22 de junio de 16
  6. 6. Catastrophic shifts Lakes Coral reefs Woodlands Deserts Also markets Oceans Herbicides... Hurricanes... Fires, tree cuting... Overgrazing, climate... Climatic events... miércoles, 22 de junio de 16
  7. 7. Catastrophic shifts miércoles, 22 de junio de 16
  8. 8. Catastrophic shifts Jumps in time series Features: miércoles, 22 de junio de 16
  9. 9. Catastrophic shifts Features: Jumps in time series Bistability miércoles, 22 de junio de 16
  10. 10. Catastrophic shifts Features: Jumps in time series Bistability Hysteresis miércoles, 22 de junio de 16
  11. 11. Catastrophic shifts Features: Jumps in time series Bistability Hysteresis Patterns ... miércoles, 22 de junio de 16
  12. 12. Catastrophic shifts Features: Condit Veget Condit First order transition Vegetation Conditions (water...) Jumps in time series Bistability Hysteresis Patterns ... miércoles, 22 de junio de 16
  13. 13. Catastrophic shifts Features: Condit Veget Condit Vegetation Conditions (water...) First order transition Jumps in time series Bistability Hysteresis Patterns ... miércoles, 22 de junio de 16
  14. 14. Catastrophic shifts Features: Condit Veget Condit Vegetation Conditions (water...) First order transition Jumps in time series Bistability Hysteresis Patterns ... miércoles, 22 de junio de 16
  15. 15. Catastrophic shifts Features: Condit Veget Condit Vegetation Conditions (water...) First order transition Jumps in time series Bistability Hysteresis Patterns ... miércoles, 22 de junio de 16
  16. 16. Catastrophic shifts Features: Condit Veget Condit Vegetation Conditions (water...) First order transition Jumps in time series Bistability Hysteresis Patterns ... miércoles, 22 de junio de 16
  17. 17. Catastrophic shifts Condit Veget Condit Vegetation Conditions (water...) Condit Veget ConditConditions (water...) Vegetation First order transition Second order transition Smooth and easily reversible! Abrupt and hardly reversible! miércoles, 22 de junio de 16
  18. 18. Simplest deterministic equation @t⇢(t) = a⇢(t) + b⇢2 (t) c⇢3 (t) miércoles, 22 de junio de 16
  19. 19. : Vegetation, coral abundance... or “Activity” Simplest deterministic equation ⇢ @t⇢(t) = a⇢(t) + b⇢2 (t) c⇢3 (t) miércoles, 22 de junio de 16
  20. 20. : Vegetation, coral abundance... or “Activity” Simplest deterministic equation ⇢ a : Growth rate @t⇢(t) = a⇢(t) + b⇢2 (t) c⇢3 (t) miércoles, 22 de junio de 16
  21. 21. with the strength of “facilitation” : Vegetation, coral abundance... or “Activity” Simplest deterministic equation ⇢ a : Growth rate b = a @t⇢(t) = a⇢(t) + b⇢2 (t) c⇢3 (t) miércoles, 22 de junio de 16
  22. 22. with the strength of “facilitation” : Vegetation, coral abundance... or “Activity” Simplest deterministic equation ⇢ a : Growth rate b = a @t⇢(t) = a⇢(t) + b⇢2 (t) c⇢3 (t) Vegetation Rain (Allee effect) miércoles, 22 de junio de 16
  23. 23. with the strength of “facilitation” : Vegetation, coral abundance... or “Activity” Simplest deterministic equation ⇢ a : Growth rate : Carrying capacity b = a c @t⇢(t) = a⇢(t) + b⇢2 (t) c⇢3 (t) Vegetation Rain (Allee effect) miércoles, 22 de junio de 16
  24. 24. Simplest deterministic equation @t⇢(t) = a⇢(t) + b⇢2 (t) c⇢3 (t) miércoles, 22 de junio de 16
  25. 25. Simplest deterministic equation Our stochastic equation Gaussian demographic noise Spatial diffusion @t⇢(t) = a⇢(t) + b⇢2 (t) c⇢3 (t) @t⇢(x, t) = a⇢(x, t) + b⇢2 (x, t) c⇢3 (x, t) + Dr2 ⇢(x, t) + p ⇢(x, t)⇠(x, t) miércoles, 22 de junio de 16
  26. 26. High diffusion ( )D Our stochastic equation Low noise ( ) “Almost deterministic parameters”: @t⇢(x, t) = a⇢(x, t) + b⇢2 (x, t) c⇢3 (x, t) + Dr2 ⇢(x, t) + p ⇢(x, t)⇠(x, t) miércoles, 22 de junio de 16
  27. 27. miércoles, 22 de junio de 16
  28. 28. D miércoles, 22 de junio de 16
  29. 29. D much smoother and easily reversible! miércoles, 22 de junio de 16
  30. 30. * Further understand catastrophic shifts. * Contribute to the discussion about the possibility of preventing such shifts. Presented ideas can help: miércoles, 22 de junio de 16
  31. 31. Thank you very much! Elsa Wikander miércoles, 22 de junio de 16

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