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 0 1 at rate 1 1 1 0 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 Mutation,selection,andancestryinthe deterministiclimitoftheMoranmodel SebastianHummel BielefeldUniversity 08.08.2017 6/39 Moranmodel Ancestries References 0 Mutation,selection,andancestryinthe deterministiclimitoftheMoranmodel SebastianHummel BielefeldUniversity 08.08.2017 6/39 Moranmodel Ancestries References at rate 𝑢𝑣 0 Mutation,selection,andancestryinthe deterministiclimitoftheMoranmodel SebastianHummel BielefeldUniversity 08.08.2017 7/39