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Pré-Publication, Document De Travail Année : 2018

The genealogy of an exactly solvable Ornstein-Uhlenbeck type branching process with selection

Généalogie d'un modèle résoluble de processus de branchement avec sélection de type Ornstein-Uhlenbeck

Aser Cortines
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Résumé

We study the genealogy of a solvable population model with N particles on the real line which evolves according to a discrete-time branching process with selection. At each time step, every particle gives birth to children around a times its current position, where a > 0 is a parameter of the model. Then, the N rightmost newborn children are selected to form the next generation. We show that the genealogical trees of the process converge to those of a Beta coalescent as N → ∞. The process we consider can be seen as a toy-model version of a continuous-time branching process with selection, in which particles move according to independent Ornstein-Uhlenbeck processes. The parameter a is akin to the pulling strength of the Ornstein-Uhlenbeck motion.
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Dates et versions

hal-01790945 , version 1 (14-05-2018)
hal-01790945 , version 2 (18-05-2019)

Identifiants

  • HAL Id : hal-01790945 , version 1

Citer

Aser Cortines, Bastien Mallein. The genealogy of an exactly solvable Ornstein-Uhlenbeck type branching process with selection. 2018. ⟨hal-01790945v1⟩
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