"Genealogies in multitype frequency-dependent branching processes"André, MathildeOur work delves into the universality class of some very celebrated entities in population genetics: Lambda-coalescents. These objects catalog the genealogies of constant-sized and exchangeable population models known as Cannings models, see Pitman and Sagitov (1999) and serve as baseline models for panmictic, neutral populations in population genetics studies. We establish a broad class of multitype frequency-dependent models that extends beyond exchangeable and fixed population models, yet for which the scaling limit of the genealogies sampled at a given time is still Kingman’s coalescent. Thus, this work strides towards refining the intuition that neutral, Cannings-like genealogies can arise from complex interactions. We prove convergence in distribution of the genealogies for the Gromov-Weak topology, using a method of moments and the multiple spine decomposition formalism developed by Foutel-Rodier and Schertzer (2023). The underlying purpose of this work is to formulate a general methodology for deriving the scaling limits of genealogies within regulated populations. This method streamlines computations on forest-valued processes to a fine-grained analysis of the simpler stochastic process driving the type frequencies in the population. This is joint work with Félix Foutel-Rodier and Emmanuel Schertzer. |
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