In this contribution several probabilistic tools to study population dynamics are developed.
The focus is on scaling limits of qualitatively different stochastic individual based models
and the long time behavior of some classes of limiting processes. Structured population
dynamics are modeled by measure-valued processes describing the individual behaviors and taking
into account the demographic and mutational parameters and possible interactions between
individuals. Many quantitative parameters appear in these models and several relevant
normalizations are considered leading to infinite-dimensional deterministic or stochastic
large-population approximations. Biologically relevant questions are considered such as
extinction criteria the effect of large birth events the impact of environmental catastrophes
the mutation-selection trade-off recovery criteria in parasite infections genealogical
properties of a sample of individuals. These notes originated from a lecture series on
Structured Population Dynamics at Ecole polytechnique (France). Vincent Bansaye and Sylvie
Méléard are Professors at Ecole Polytechnique (France). They are a specialists of branching
processes and random particle systems in biology. Most of their research concerns the
applications of probability to biodiversity ecology and evolution.
