Mathematics – Probability
Scientific paper
2007-04-11
Stochastic Processes and their Applications 119 (2008) 1124-1143
Mathematics
Probability
Scientific paper
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.
Abraham Romain
Delmas Jean-François
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