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

Romain Abraham; Jean François Delmas

doi:10.1016/j.spa.2008.06.001

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

Romain Abraham
, Jean François Delmas

conventionnée avec l'Université d'Orléans

Research output: Contribution to journal › Article › peer-review

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 continuum random tree, according to the ancestral lineage of the last individual alive. This allows us to give a closed formula for the probability of simultaneous extinction of the Eve-population and the total population.

Original language	English
Pages (from-to)	1124-1143
Number of pages	20
Journal	Stochastic Processes and their Applications
Volume	119
Issue number	4
DOIs	https://doi.org/10.1016/j.spa.2008.06.001
Publication status	Published - 1 Apr 2009

Keywords

Continuous state branching process
Continuum random tree
Immigration
Neutral mutation
Probability of extinction
Williams' decomposition

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10.1016/j.spa.2008.06.001

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title = "Williams' decomposition of the L{\'e}vy continuum 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 continuum random tree, according to the ancestral lineage of the last individual alive. This allows us to give a closed formula for the probability of simultaneous extinction of the Eve-population and the total population.",

keywords = "Continuous state branching process, Continuum random tree, Immigration, Neutral mutation, Probability of extinction, Williams' decomposition",

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T1 - Williams' decomposition of the Lévy continuum random tree and simultaneous extinction probability for populations with neutral mutations

AU - Abraham, Romain

AU - Delmas, Jean François

PY - 2009/4/1

Y1 - 2009/4/1

N2 - 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 continuum random tree, according to the ancestral lineage of the last individual alive. This allows us to give a closed formula for the probability of simultaneous extinction of the Eve-population and the total population.

AB - 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 continuum random tree, according to the ancestral lineage of the last individual alive. This allows us to give a closed formula for the probability of simultaneous extinction of the Eve-population and the total population.

KW - Continuous state branching process

KW - Continuum random tree

KW - Immigration

KW - Neutral mutation

KW - Probability of extinction

KW - Williams' decomposition

UR - https://www.scopus.com/pages/publications/61849179718

U2 - 10.1016/j.spa.2008.06.001

DO - 10.1016/j.spa.2008.06.001

M3 - Article

AN - SCOPUS:61849179718

SN - 0304-4149

VL - 119

SP - 1124

EP - 1143

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 4

ER -

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

Abstract

Keywords

UN SDGs

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