Genealogies and Increasing Propagation of Chaos For Feynman-Kac and Genetic Models

A path-valued interacting particle systems model for the genealogical structure of genetic algorithms is presented. We connect the historical process and the distribution of the whole ancestral tree with a class of Feynman-Kac formulae on path space. We also prove increasing and uniform versions of propagation of chaos for appropriate particle block size and time horizon yielding what seems to be the first result of this type for this class of particle systems.