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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.
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https://hal.archives-ouvertes.fr/hal-00141154
Contributor : Jean-François Delmas <>
Submitted on : Tuesday, March 24, 2009 - 11:08:15 AM
Last modification on : Thursday, May 3, 2018 - 3:32:06 PM
Document(s) archivé(s) le : Wednesday, September 22, 2010 - 12:27:00 PM

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

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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⟩

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