Parasite-host systems often include an obligatory environmental stage in the parasite life-cycle, which can be transmitted between successive populations. Complexity even increases if immunity only gradually develops upon re-infection. For a better understanding of such systems we study Eimeria spp. in chickens, a protozoan parasite transmitted through oocysts on the floor. This paper deals with dynamics within and between successive cohorts of chickens by coupling a within-host description of the parasite life-cycle (with immunity) to re-uptake of oocysts from the environment. First the initial environmental oocyst level is related to the maximum infection load within a cohort, as a measure of production damage, from which we conclude that minimum damage levels can be observed with intermediate oocyst levels. Then we relate the initial to the final oocyst level of a cohort, and study the dynamics between cohorts in relation to an oocyst cleaning efficiency after each cohort. The resulting unstable dynamics lead to the conclusion that it will often be impossible to minimize damage by repeatedly cleaning with the same effort: it may be necessary to artificially increase oocyst levels in the shed before each chicken cohort.