Evolvable by Design Panos Oikonomou James Franck Institute Institute of Biophysical Dynamics The...
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Evolvable by Design
Panos Oikonomou
James Franck InstituteInstitute of Biophysical Dynamics
The University of Chicago
Philippe Cluzel
How topology affects network evolution
NetSci07
Introduction
• Some features are ubiquitous in nature and artificial systems • Which are the consequences/advantages of such organizations?
• How do such systems evolve?
Is there an evolutionary advantage in topological features?
US Human Genome Project Yeast protein net, Jeong et al (2001)Internet map
• Dynamical rules for each node
• Dynamics of network
• Evolutionary Game: Genotype, Phenotype, Fitness,
Mutations & Selection • Results:
Random vs. scale-free
• Interpretation and heuristic explanation
Outline
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0)( if 0
0)( if 1
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i
K
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K
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K
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Boolean Threshold Dynamics
Network Dynamics
• N nodes in two states: ON/OFF
• Updated according to boolean rules
• Starting from random initial conditions
• Performs Cycle of length L
Target “Phenotype”
Output Signal:Boolean time series
The target Perform robustly a cycle behavior of length Lc
The fitness average hamming distance over time
ParametersNet. Size~500 nodesLc= 1-50μ= 0.001-0.1
Random networks
Discontinuous evolution:
• Long fitness plateaus & sudden advantageous jumps
• Networks change by neutral mutations
• Convergence depends on rare advantageous mutative events. Each independent population converges differently from the average.
Scale-free networks
Continuous evolution:
• Diversity: the population consists of many different phenotypes
• Evolvability capacity to produce many different heritable phenotypes.
• All populations follow the same trend and are able to converge
Continuous vs. Discontinuous Evolutionary paths
Probability that a mutation affects an output node:
xdynPP
2.5 5 7.5 10 12.5 15 17.5
0.2
0.4
0.6
0.8
1Random
‹K›
‹P›
‹P›
‹K›
Scale-free
2.5 5 7.5 10 12.5 15 17.5
0.0001
0.001
0.01
0.1
1
)()( iisdyn kPkpP
Different topologies give different evolutionary behaviors!
Topology pre-determines the evolutionary paths of networks
evolution "at the edge of chaos“?
random networks exhibit chaotic behavior for K > Kc= 3.83 and scale-free networks exhibit chaotic behavior for exponents γ < γc= 2.42.
Conclusions
Homogeneous random networks and scale-free networks exhibit drastically different evolutionary paths.
Topology pre-determines the evolutionary paths of networks.
Possible implications in design and evolutionary strategies…
Oikonomou et al, Nature Physics, 2 (8), 2006.