Discrete stage-structured prey and prey-predator models are considered. Regarding the former, we prove that the models at hand
are permanent (i.e., the population will neither go extinct nor exhibit explosive oscillations) and, moreover, that the transfer from
stability to nonstationary behaviour always goes through a supercritical Neimark−Sacker bifurcation.The prey model covers species
that possess a wide range of different life histories. Predation pressure may both stabilize and destabilize the prey dynamics but the
strength of impact is closely related to life history. Indeed, if the prey possesses a precocious semelparous life history and exhibits
chaotic oscillations, it is shown that increased predation may stabilize the dynamics and also, in case of large predation pressure,
transfer the population to another chaotic regime
