  The paper discusses a family of Markov processes that represent many particle
systems, and their limiting behaviour when the number of particles go to
infinity. The first part concerns model of biological systems: a model for
sympatric speciation, i.e. the process in which a genetically homogeneous
population is split in two or more different species sharing the same habitat,
and models for swarming animals. The second part of the paper deals with
abstract many particle systems, and methods for rigorously deriving mean field
models.
