Speaker
Description
Collaborators:
Hannah Dopmeyer (Bielefeld University, Germany),
Fernando Cordero (BOKU University, Vienna, Austria).
Abstract:
We consider the two-type Moran model of population genetics with frequency-dependent neutral reproduction. Relying on the model's graphical representation in terms of a particle system, we establish a (factorial) moment dual. Moment duals are usually related to the genealogy of the population, but in this case, the connection is mysterious. This is because the natural ancestral graph of the model (the so-called ancestral influence graph, AIG) exhibits a complicated hierarchical structure, whereas the moment dual is a simple density-dependent branching process. We solve this mystery by starting from the fact that moment duality is a property in expectation; it need not hold pathwise. This provides the freedom to construct what we call the Frankenstein process by tracing back sample configurations and piecing them together across different realisations of the AIG. This leads to the dual process and resolves the mystery.
