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 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 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