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

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:119

Article

Delmas, Jean-Francois¹ 

[1] Univ Paris Est, CERMICS, F-77455 Marne La Vallee, France

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

DOI  :  10.1016/j.spa.2008.06.001

来源: Elsevier

【 摘 要 】

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. (C) 2008 Elsevier B.V. All rights reserved.

【 授权许可】

Free