local replicator dynamics
DESCRIPTION
Local Replicator Dynamics. Philippe Uyttendaele (joint work with Mandy Tak, Frank Thuijsman, Ronald Westra). Global Replicator Dynamics. Local Replicator Dynamics. Field represent a torus. Local Replicator Dynamics. Random starting field. Local Replicator Dynamics. Focus on a cell. - PowerPoint PPT PresentationTRANSCRIPT
Local Replicator Dynamics
Philippe Uyttendaele(joint work with Mandy Tak, Frank Thuijsman, Ronald Westra)
Global Replicator Dynamics
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Local Replicator Dynamics
• Field represent a torus
Local Replicator Dynamics
• Random starting field
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Local Replicator Dynamics
• Focus on a cell
Local Replicator Dynamics
• Interaction with each neighbors
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Local Replicator Dynamics
• Interaction with each neighbors
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Local Replicator Dynamics
• Interaction with each neighbors
Local Replicator Dynamics
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• Total fitness in a cell
Local Replicator Dynamics
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36Total 36 48 84
• Same procedure for entire field
Local Replicator Dynamics
• Next generation
Global Replicator Dynamics
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Local Replicator Dynamics
• The GRD predicts to take over
• Is there a possibility for this not to happen?
Local Replicator Dynamics
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• Stable pattern
In LRD all survive, in GRD not
• This is a rare event in random simulations
• Especially weak if mutations allowed
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LRD
• Are there other possible stable structures?
• Can we find an easy Toy example like the Prisoner’s Dilemma?
In GRD all survive, in LRD not
• Asymptotically stable for the GRD:
(0.75 , 0.25)
• Asymptotically stable for the LRD:
(1 , 0)
01
30
LRD – Change in time/space
00)2cos(2
0
)2cos(200
k
xt
k
xt
LRD – Resource Model• Fitness depends on availability of local resources• Looks like predator prey models• Populations moving around
Multiple Populations Multiple Fields
1, 2
0, 0 2, 1
R1
Y2Y1
R2
Directional Patterns
• Aligned Interactions
x
x
x
x
What to do next?
• Go deeper in the analysis of each scenario
• Adapt the model based on the current one
• Have a better understanding– What leads to “stable” situations?– Can we define stability?– What are the key features in the matrices?
Questions ?
Beware, the snails are taking over the population