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

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