eluding catastrophic shifts - paula villa martín, juan a. bonachela,, simon a. levin, miguel a....
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ELUDING CATASTROPHIC SHIFTS
miércoles, 22 de junio de 16
Juan A. Bonachela
ELUDING CATASTROPHIC SHIFTS
Paula Villa Martín
Miguel A. Muñoz
Simon A. Levin
miércoles, 22 de junio de 16
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
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
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
Catastrophic shiftsLakes Coral reefs Woodlands
Deserts Alsomarkets
Oceans
Herbicides... Hurricanes... Fires, tree cuting...
Overgrazing, climate...
Climatic events...
miércoles, 22 de junio de 16
Catastrophic shifts
miércoles, 22 de junio de 16
Catastrophic shifts
Jumps in time series
Features:
miércoles, 22 de junio de 16
Catastrophic shifts
Features:
Jumps in time series
Bistability
miércoles, 22 de junio de 16
Catastrophic shifts
Features:
Jumps in time series
Bistability
Hysteresis
miércoles, 22 de junio de 16
Catastrophic shifts
Features:
Jumps in time series
Bistability
Hysteresis
Patterns
...
miércoles, 22 de junio de 16
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
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
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
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
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
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
Simplest deterministic equation
@t⇢(t) = a⇢(t) + b⇢2(t)� c⇢3(t)
miércoles, 22 de junio de 16
: Vegetation, coral abundance... or “Activity”
Simplest deterministic equation
⇢
@t⇢(t) = a⇢(t) + b⇢2(t)� c⇢3(t)
miércoles, 22 de junio de 16
: 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
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
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
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
Simplest deterministic equation
@t⇢(t) = a⇢(t) + b⇢2(t)� c⇢3(t)
miércoles, 22 de junio de 16
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
High diffusion ( )�
D
Our stochastic equation
Low noise ( )
“Almost deterministicparameters”:
@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
�
miércoles, 22 de junio de 16
� D
miércoles, 22 de junio de 16
� D
much smoother and easily reversible!
miércoles, 22 de junio de 16
* 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
Thank you very much!
Elsa Wikander
miércoles, 22 de junio de 16
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