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


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.


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.


https://en.wikipedia.org/wiki/Biodiversity#Species_loss_rates

https://en.wikipedia.org/wiki/Biodiversity#Species_loss_rates

Catastrophic shiftsLakes Coral reefs Woodlands

Deserts Alsomarkets

Oceans

Herbicides... Hurricanes... Fires, tree cuting...

Overgrazing, climate...

Climatic events...


Catastrophic shifts


Catastrophic shifts

Jumps in time series

Features:


Catastrophic shifts

Features:


Bistability


Catastrophic shifts

Features:


Bistability

Hysteresis


Catastrophic shifts

Features:


Bistability

Hysteresis

Patterns

...


Catastrophic shifts

Features:

Condit

Veget

Condit

First order transition

Vegetation

Conditions (water...)


Bistability

Hysteresis

Patterns

...


Catastrophic shifts

Features:

Condit

Veget

Condit

Vegetation

Conditions (water...)



Bistability

Hysteresis

Patterns

...


Catastrophic shifts

Condit

Veget

Condit

Vegetation

Conditions (water...)Condit

Veget

ConditConditions (water...)

Vegetation


Second order transition

Smooth and easily reversible! Abrupt and hardly reversible!


Simplest deterministic equation

@t⇢(t) = a⇢(t) + b⇢2(t)� c⇢3(t)


: Vegetation, coral abundance... or “Activity”


⇢

@t⇢(t) = a⇢(t) + b⇢2(t)� c⇢3(t)




⇢

a : Growth rate

@t⇢(t) = a⇢(t) + b⇢2(t)� c⇢3(t)


with the strength of “facilitation”



⇢

a : Growth rate

b = a� � �

@t⇢(t) = a⇢(t) + b⇢2(t)� c⇢3(t)





⇢

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




⇢

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


@t⇢(t) = a⇢(t) + b⇢2(t)� c⇢3(t)



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)


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)


�


� D


� D

much smoother and easily reversible!


* Further understand catastrophic shifts.

* Contribute to the discussion about the possibility of preventing such shifts.

Presented ideas can help:


Thank you very much!

Elsa Wikander


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

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