Persistence and permanence in a metapopulation model with space-limited recruitment

In this paper we analyze a metapopulation model with space-limited recruitment. The model describes the population dynamics of sessile adult and planktonic larvae in a common larval pool. We introduce the basic reproduction number of each species which is the expected number of future larvae reproduced by one larva. We consider the conditions for the persistence of the multi-species and multi-habitats model and the permanence of the single-species model. Subsequently, we consider the conditions for the existence of the non-trivial steady state of the single-species model and its global stability, and the permanence of the two species and two habitats model.