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We present two approaches to study invasion in growth-fragmentation-deathmod- els. The first one is based on a stochastic individual based model, whichis a piecewise deterministic branching process with a continuum of types, andthe second one is based on an integro-differential model. The invasion of thepopulation is described by the survival probability for the former model and byan eigenproblem for the latter one. We study these two notions of invasionfitness, giving different characterizations of the growth of the population,and we make links between these two complementary points of view. In particularwe prove that the two approaches lead to the same crite- rion of possibleinvasion. Based on Krein-Rutman theory, we also give a proof of the existenceof a solution to the eigenproblem, which satisfies the conditions needed forour study of the stochastic model, hence providing a set of assumptions underwhich both approaches can be carried out. Finally, we motivate our work in thecontext of adaptive dynamics in a chemostat model.

Links between deterministic and stochastic approaches for invasion in growth-fragmentation-death models