Ancestral lineages and uniform sampling in populations with density-dependent interactions
Madeleine KUBASH
Ecole Polytechnique
Date(s) : 06/01/2026 iCal
14h30 - 15h30
Résumé : We study a density-dependent Markov jump process describing a population where each individual is characterized by a type, and reproduces at rates depending both on its type and on the population type distribution. We are interested in the ancestral lineage of a uniformly sampled individual. We exhibit a time-inhomogeneous Markov process, which allows to capture the behavior of a sampled lineage in the population process. This is achieved through a many-to-one formula, which translates the expected value of a functional evaluated over the lineages in the population process into the expectation of the functional evaluated along the spine. This provides a direct interpretation of the underlying survivorship bias, as illustrated on a minimalistic population process.
Emplacement
I2M Saint-Charles - Salle de séminaire
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