Uniform sampling in a structured branching population
Abstract
We are interested in the dynamic of a structured branching population where the trait of each individual moves according to a Markov process. The rate of division of each individual is a function of its trait and when a branching event occurs, the trait of the descendants at birth depends on the trait of the mother and on the number of descendants. In this article, we explicitly describe the penalized Markov process, named auxiliary process, corresponding to the dynamic of the trait along the spine by giving its associated infinitesimal generator. We prove a ManytoOne formula and a ManytoOne formula for forks. Furthermore, we prove that this auxiliary process characterizes exactly the process of the trait of a uniformly sampled individual in the large population approximation. We detail three examples of growthfragmentation models: the linear growth model, the exponential growth model and the parasite infection model.
 Publication:

arXiv eprints
 Pub Date:
 September 2016
 DOI:
 10.48550/arXiv.1609.05678
 arXiv:
 arXiv:1609.05678
 Bibcode:
 2016arXiv160905678M
 Keywords:

 Mathematics  Probability