QUANTITATIVE LAWS June 13 -June 24

1. ELUDING
CATASTROPHIC SHIFTS
miércoles, 22 de junio de 16

2. Juan A.
Bonachela
ELUDING
CATASTROPHIC SHIFTS
Paula
Villa Martín
Miguel A.
Muñoz
Simon A.
Levin
miércoles, 22 de junio de 16

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. 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. 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. 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. Catastrophic shifts
miércoles, 22 de junio de 16

8. Catastrophic shifts
Jumps in time series
Features:
miércoles, 22 de junio de 16

9. Catastrophic shifts
Features:
Jumps in time series
Bistability
miércoles, 22 de junio de 16

10. Catastrophic shifts
Features:
Jumps in time series
Bistability
Hysteresis
miércoles, 22 de junio de 16

11. Catastrophic shifts
Features:
Jumps in time series
Bistability
Hysteresis
Patterns
...
miércoles, 22 de junio de 16

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. 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. 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. 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. 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. 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. Simplest deterministic equation
@t⇢(t) = a⇢(t) + b⇢2
(t) c⇢3
(t)
miércoles, 22 de junio de 16

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. : 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. 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. 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. 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. Simplest deterministic equation
@t⇢(t) = a⇢(t) + b⇢2
(t) c⇢3
(t)
miércoles, 22 de junio de 16

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. 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. miércoles, 22 de junio de 16

28. D
miércoles, 22 de junio de 16

29. D
much
smoother
and easily
reversible!
miércoles, 22 de junio de 16

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. Thank you very much!
Elsa Wikander
miércoles, 22 de junio de 16