Local Replicator Dynamics Philippe Uyttendaele (joint work with Mandy Tak, Frank Thuijsman, Ronald Westra)
Local Replicator Dynamics
Feb 02, 2016
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 Presentation
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Local Replicator Dynamics
Philippe Uyttendaele(joint work with Mandy Tak, Frank Thuijsman, Ronald Westra)
Global Replicator Dynamics
1713
0012
060
Local Replicator Dynamics
• Field represent a torus
Local Replicator Dynamics
• Random starting field
1713
0012
060
1713
0012
060
Local Replicator Dynamics
• Focus on a cell
Local Replicator Dynamics
• Interaction with each neighbors
1713
0012
060
Local Replicator Dynamics
• Interaction with each neighbors
1713
0012
060
1713
0012
060
Local Replicator Dynamics
• Interaction with each neighbors
Local Replicator Dynamics
12
1713
0012
060
• Total fitness in a cell
Local Replicator Dynamics
12
12
12
12
30
54
36Total 36 48 84
• Same procedure for entire field
Local Replicator Dynamics
• Next generation
Global Replicator Dynamics
1713
0012
060
Local Replicator Dynamics
• The GRD predicts to take over
• Is there a possibility for this not to happen?
Local Replicator Dynamics
2424
24
12
12
12
12
12
1224
24 2418
18 18
18
18 18
18 18
18
12 12
12
1212
12
• Stable pattern
In LRD all survive, in GRD not
• This is a rare event in random simulations
• Especially weak if mutations allowed
1713
0012
060
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
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