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SUMMARY:Asymptotic analysis of an integro-differential model from quantita
 tive genetics
DTSTART:20250610T091500Z
DTEND:20250610T101500Z
DTSTAMP:20260517T215800Z
UID:indico-event-12288@indico.math.cnrs.fr
DESCRIPTION:Speakers: Sepideh Mirrahimi\n\nWe provide an asymptotic analys
 is of a nonlinear integro-differential equation which describes the evolut
 ionary dynamics of a population which reproduces sexually and which is sub
 ject to selection and competition. The sexual reproduction is modeled via 
 a nonlinear integral term\, known as the 'infinitesimal model'. Considerin
 g a   small  variance regime\, we prove that the phenotypic distribution
  remains close to a Gaussian profile with a fixed small variance and we ch
 aracterize the dynamics of the mean phenotypic trait via an ordinary diffe
 rential equation. While similar properties were already proved for a close
 ly related model using a Hopf-Cole transformation and perturbative analysi
 s techniques\, we provide an alternative proof which simplifies considerab
 ly the analysis. Our method relies on a direct study of the dynamics of th
 e moments of the phenotypic distribution and a Lipschitz property of the W
 asserstein distance. This is a joint work with J. Guerand and M. Hillairet
 .\n\nhttps://indico.math.cnrs.fr/event/12288/
LOCATION:Salle J. Cavailles (IMT)
URL:https://indico.math.cnrs.fr/event/12288/
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