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Pré-Publication, Document De Travail Année : 2013

A Wright-Fisher model with indirect selection

Résumé

We define and study two mathematical models of a surprising biological strategy where some individuals adopt a behaviour that is harmful to others without any direct advantage for themselves. The first model covers a single reproductive season, and is mathematically a mix between samplings with and without replacement; its analysis is done by a sort of "reverse numerical analysis", viewing a key recurrence relation as a discretization scheme for a PDE. This model is then used as a building block for a variant of the classical Wright-Fisher model. In the large population limit, we prove the convergence of the renormalized process to a diffusion with a frequency dependent drift. This allows a quantitative comparison of the indirect selective advantage with the direct one classically considered in the Wright-Fisher model.
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Dates et versions

hal-00925744 , version 1 (13-01-2014)
hal-00925744 , version 2 (16-01-2014)
hal-00925744 , version 3 (17-03-2015)

Identifiants

  • HAL Id : hal-00925744 , version 1

Citer

Ludovic Goudenège, Pierre-André Zitt. A Wright-Fisher model with indirect selection. 2013. ⟨hal-00925744v1⟩
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