Attraction to equilibria in discrete population models with delayed feedbacks: stage-structure versus age-structure.

Abstract

Time delays and stage structure are common features of most biological populations. This paper aims to describe the influence of these features through simple models. Regarding the role of time delays, we discuss the dynamical differences between populations where the main intraspecific competition episodes occur during the reproduction period or during a different one. The conclusion is that the second situation is generally more prone to generate long-term oscillations. Regarding the role of the stage structure, we show that the shape of the adult recruitment plays a key role. Particularly, adult recruitments associated with contest-type intraspecific competitions do not produce long-term oscillations. From a mathematical point of view, we offer two general criteria of global attraction in discrete systems valid for non-monotone models.