The Eco Evolutionary Mathematics unit links mathematicians and biologists in the study of the interactions between the stochasticity of individual-level processes and non-linear population-level feedbacks. It is well-known that demographic variability and population genetics profoundly affect the structure and dynamics of the environment, from single populations to the community of interacting species. At the same time, the dynamics of the environment produces the signals that individuals respond to as well as the selective pressures experienced by successive generations. This feedback between individuals and their environment is studied using new mathematical approaches. The modeling techniques that this gives rise to can be applied to a vast range of applications, which the EEM unit explores in a number of directions: the evolution of biodemographical strategies and their plasticity, the evolution of the cooperation and interspecific mutualisms. the evolution of host-parasite interactions, the non-linear dynamics of invasions and epidemics, the dynamics of small populations and the prediction of extinction risk.