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Genealogical structures under interactive neutral reproduction: factorial moment duality via a Frankenstein process
Ellen Baake, Fernando Cordero, Hannah Dopmeyer
We establish a genealogical framework for an existing analytical moment duality between a Wright--Fisher type SDE and a counting process with interaction. To achieve this, we const…
Critical multitype branching: a functional limit theorem and ancestral processes
Ellen Baake, Fernando Cordero, Sophia-Marie Mellis +1
We consider the long-term behaviour of critical multitype branching processes conditioned on non-extinction, both with respect to the forward and the ancestral processes. Forward i…
Killing versus catastrophes in birth-death processes and an application to population genetics
Ellen Baake, Fernando Cordero, Enrico Di Gaspero +1
We establish connections between the absorption probabilities of a class of birth-death processes with killing, and the stationary tail of a related class of birth-death processes…
Solving the migration-recombination equation from a genealogical point of view
Frederic Alberti, Ellen Baake, Ian Letter +1
We consider the discrete-time migration-recombination equation, a deterministic, nonlinear dynamical system that describes the evolution of the genetic type distribution of a popul…