  We consider a stochastic individual based model where each predator searches
during a random time and then manipulates its prey or rests. The time
distributions may be non-exponential. An age structure allows to describe these
interactions and get a Markovian setting. The process is characterized by a
measure-valued stochastic differential equation. We prove averaging results in
this infinite dimensional setting and get the convergence of the slow-fast
macroscopic prey predator process to a two dimensional dynamical system. We
recover classical functional responses. We also get new forms arising in
particular when births and deaths of predators are affected by the lack of
food.
