The foundations and the first rigorous analysis on the convergence of genetic type models and mean field Feynman-Kac particle methods are due to Pierre Del Moral in 1996. Branching type particle methods with varying population sizes were also developed in the end of the 1990s by Dan Crisan, Jessica Gaines and Terry Lyons, and by Dan Crisan, Pierre Del Moral and Terry Lyons. The first uniform convergence results with respect to the time parameter for mean field particle models were developed in the end of the 1990s by Pierre Del Moral and Alice Guionnet for interacting jump type processes, and by Florent Malrieu for nonlinear diffusion type processes.