Mutation, selection, and ancestry in the deterministic limit of the Moran model

101 Pages·2017·2.46 MB·English

Moranmodel Ancestries References
Mutation, selection, and ancestry in the
deterministic limit of the Moran model
Sebastian Hummel
basedonjointwork(inprogress)withEllenBaakeandFernandoCorderoand
thankstomanydiscussionswithAntonWakolbinger
BielefeldUniversity
Genealogies of Interacting Particle Systems
08.08.2017
Mutation,selection,andancestryinthe
deterministiclimitoftheMoranmodel SebastianHummel BielefeldUniversity 08.08.2017 1/39
Moranmodel Ancestries References
Mutation, selection, and ancestry in the deterministic limit
of the Moran model
1 2-type Moran model and its deterministic limit
2-type Moran model
Deterministic limit
Properties of deterministic limit
2 Ancestries in the Moran model and in the deterministic limit
Ancestral selection graph
Killed ancestral selection graph
Pruned lookdown ancestral selection graph
Mutation,selection,andancestryinthe
deterministiclimitoftheMoranmodel SebastianHummel BielefeldUniversity 08.08.2017 2/39
Moranmodel Ancestries References
Mutation, selection, and ancestry in the deterministic limit
of the Moran model
1 2-type Moran model and its deterministic limit
2-type Moran model
Deterministic limit
Properties of deterministic limit
2 Ancestries in the Moran model and in the deterministic limit
Ancestral selection graph
Killed ancestral selection graph
Pruned lookdown ancestral selection graph
Mutation,selection,andancestryinthe
deterministiclimitoftheMoranmodel SebastianHummel BielefeldUniversity 08.08.2017 3/39
Moranmodel Ancestries References
at rate s
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at rate 1
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Mutation,selection,andancestryinthe
deterministiclimitoftheMoranmodel SebastianHummel BielefeldUniversity 08.08.2017 4/39
Moranmodel Ancestries References
1
Mutation,selection,andancestryinthe
deterministiclimitoftheMoranmodel SebastianHummel BielefeldUniversity 08.08.2017 5/39
Moranmodel Ancestries References
1
Mutation,selection,andancestryinthe
deterministiclimitoftheMoranmodel SebastianHummel BielefeldUniversity 08.08.2017 5/39
Moranmodel Ancestries References
1 1
Mutation,selection,andancestryinthe
deterministiclimitoftheMoranmodel SebastianHummel BielefeldUniversity 08.08.2017 5/39
Moranmodel Ancestries References
0
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deterministiclimitoftheMoranmodel SebastianHummel BielefeldUniversity 08.08.2017 6/39
Moranmodel Ancestries References
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Mutation,selection,andancestryinthe
deterministiclimitoftheMoranmodel SebastianHummel BielefeldUniversity 08.08.2017 6/39
Moranmodel Ancestries References
at rate 𝑢𝑣
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Mutation,selection,andancestryinthe
deterministiclimitoftheMoranmodel SebastianHummel BielefeldUniversity 08.08.2017 7/39