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

101 Pages·2017·2.46 MB·English

Moran model Ancestries References
Mutation, selection, and ancestry in the
deterministic limit of the Moran model
Sebastian Hummel
based on joint work (in progress) with Ellen Baake and Fernando Cordero and
thanks to many discussions with Anton Wakolbinger
Bielefeld University
Genealogies of Interacting Particle Systems
08.08.2017
Mutation, selection, and ancestry in the
deterministic limit of the Moran model Sebastian Hummel Bielefeld University 08.08.2017 1 / 39
Moran model 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, and ancestry in the
deterministic limit of the Moran model Sebastian Hummel Bielefeld University 08.08.2017 2 / 39
Moran model 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, and ancestry in the
deterministic limit of the Moran model Sebastian Hummel Bielefeld University 08.08.2017 3 / 39
at rate s
at rate 1
1
0
Moran model Ancestries References
1 1
0
Mutation, selection, and ancestry in the
deterministic limit of the Moran model Sebastian Hummel Bielefeld University 08.08.2017 4 / 39
1
Moran model Ancestries References
Mutation, selection, and ancestry in the
deterministic limit of the Moran model Sebastian Hummel Bielefeld University 08.08.2017 5 / 39
1
Moran model Ancestries References
Mutation, selection, and ancestry in the
deterministic limit of the Moran model Sebastian Hummel Bielefeld University 08.08.2017 5 / 39
1 1
Moran model Ancestries References
Mutation, selection, and ancestry in the
deterministic limit of the Moran model Sebastian Hummel Bielefeld University 08.08.2017 5 / 39
0
Moran model Ancestries References
Mutation, selection, and ancestry in the
deterministic limit of the Moran model Sebastian Hummel Bielefeld University 08.08.2017 6 / 39
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Moran model Ancestries References
Mutation, selection, and ancestry in the
deterministic limit of the Moran model Sebastian Hummel Bielefeld University 08.08.2017 6 / 39
at rate 𝑢𝑣
0
Moran model Ancestries References
Mutation, selection, and ancestry in the
deterministic limit of the Moran model Sebastian Hummel Bielefeld University 08.08.2017 7 / 39