Janine Bolliger Swiss Federal Research Institute WSL/FNP,
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Transcript of Janine Bolliger Swiss Federal Research Institute WSL/FNP,
Janine Bolliger
Swiss Federal Research Institute WSL/FNP,
Birmensdorf, Switzerland
A case study for self-organized criticality and complexity in forest landscape ecology
Funding
Wisconsin DNRUSGS – BRD
US Forest ServiceUniversity of Wisconsin
Swiss Science Foundation
People
Julien C. Sprott David J. Mladenoff
David J. Albers Monica G. Turner Forest Landscape Ecology Laboratory at UW Madison
Heike Lischke
Acknowledgements
Goals• Understand spatial and temporal features of ecosystems• Predict spatial and temporal features of ecosystems• Determine how much of the ecosystem complexity is a result of variations in external
conditions and how much is a natural consequence of internal interactions
• Effects of specific environmental proces- ses on the observed pattern (autecology)• Externally imposed heterogeneity• Detailed model parameters
• Variation and feedback between biotic units creates pattern (synecology) • Spontaneous symmetry braking and self- organization• Simple model parameters
Points of view
Living trees
Dead trees
Exogeneous models
Observation Landscape pattern with and without biotic units (e.g., trees)
Endogeneous models
fire
soildisease
Research questions
• Can the landscape pattern be statistically explained by simple rules?
• Does the evolution of the landscape show symmetry breaking and self-organization?
• Are the simulations sensitive to perturbations?
Landscape of early southern Wisconsin
Cellular automaton (CA)
r
• Cellular automaton: square array of cells where each cell takes one of the n values representing the landscape
• Evolving single-parameter model: a cell dies out at random times and is replaced by a cell chosen randomly within a circular radius r (1<r<10).
• Conditions: - boundary: periodic and reflecting
- initial: random and ordered
Random
Initial conditions
Ordered
Smallest unit of organization: Cluster probability
• A point is assumed to be part of a cluster if its 4 nearest neighbors are the same as it is
• CP (Cluster probability) is the % of total points that are part of a cluster
Center point is part of cluster
Evolving cellular automaton: Self-organization due to internal dynamics
Animation
Comparison between simulated and observed landscape
• Fractal dimension
• Cluster probability
• Measure for complexity (algorithmic)
Is there any particular spatial scale?
Simulated landscapeObserved landscape
SCALE INVARIANT
Initial conditions = random
r = 1
r = 3
r = 10
experimental value
Is there any particular temporal scale?
Initial conditions = ordered
r = 1
r = 3
r = 10experimental value
Is there any particular temporal scale?
Fluctuations in cluster probabilities
r = 3
Number of generations
Clus
ter p
roba
bilit
y
Is the temporal variation universal? (1)
Power laws (1/f d) for r=1 and r=3
slope (d) = 1.58
r = 3
Frequency
Powe
r
SCALE INVARIANT
Power law !
Is the temporal variation universal? (2)Po
wer
Frequency
No power law (1/f d) for r = 10
r = 10
Power law ?
Measure for complexity of landscape pattern
One measure of complexity is the size of the smallest computer program that can replicate the pattern
A GIF file is a maximally compressed image format. Therefore the size of the file is a lower limit on the size of the program
Observed landscape: 6205 bytes
Random model landscape: 8136 bytes
Self-organized model landscape: Radius = 3 6782 bytes
Data set:- Proportional variation for input data (+ 20%, +50% )
Cellular automaton:- Initial conditions (random, ordered)- Boundary conditions (periodic, reflecting)- Sensitvity to perturbations- Rule variations (uncorrelated, correlated)
Model results are robust towards these tests
Tests for simulation robustness
Summary: Simulated versus experimental landscapes
– Power-law behavior across spatial and temporal scales
– Power laws are footprints of self-organization to a critical state– Self-organized criticality is a universal phenomenon:
• Earthquakes (Gutenberg and Richter 1957)• Sand-pile models (Bak et al. 1987) • Plasma transport (Carreras, et al. 1996)• Forest fires (Bak, et al. 1990)• Rainforests (Sole and Manrubia 1997)• Stock prices (Mandelbrot 1997) • Traffic jams (Nagel and Herrmann 1993• Biological evolution (Bak and Sneppen 1993)
Conclusions for modeling complex forest landscapes
• External spatial heterogeneity may not be required for aspects of spatio-temporal diversity
• Homogenous systems far from equilibrium spontaneously break symmetry and self-organize
• The resulting spatio-temporal patterns are scale-invariant
• Thus it may not be necessary to model accurately the biological processes when performing landscape simulations