Williams' decomposition of the Lévy continuous random tree and simultaneous extinction probability for populations with neutral mutations

Abstract : We consider an initial Eve-population and a population of neutral mutants, such that the total population dies out in finite time. We describe the evolution of the Eve-population and the total population with continuous state branching processes, and the neutral mutation procedure can be seen as an immigration process with intensity proportional to the size of the population. First we establish a Williams' decomposition of the genealogy of the total population given by a continuous random tree, according to the ancestral lineage of the last individual alive. This allows us give a closed formula for the probability of simultaneous extinction of the Eve-population and the total population.
Type de document :
Article dans une revue
Stochastic Processes and their Applications, Elsevier, 2008, 119, pp.1124-1143
Liste complète des métadonnées

Littérature citée [17 références]  Voir  Masquer  Télécharger

https://hal.archives-ouvertes.fr/hal-00141154
Contributeur : Jean-François Delmas <>
Soumis le : mardi 24 mars 2009 - 11:08:15
Dernière modification le : jeudi 3 mai 2018 - 15:32:06
Document(s) archivé(s) le : mercredi 22 septembre 2010 - 12:27:00

Fichiers

williams_05_08.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-00141154, version 2
  • ARXIV : 0704.1475

Collections

Citation

Romain Abraham, Jean-François Delmas. Williams' decomposition of the Lévy continuous random tree and simultaneous extinction probability for populations with neutral mutations. Stochastic Processes and their Applications, Elsevier, 2008, 119, pp.1124-1143. 〈hal-00141154v2〉

Partager

Métriques

Consultations de la notice

331

Téléchargements de fichiers

126