Modelos discretos para dinâmica hospedeiro-parasitoide-predador

Abstract

In this work, we formulate discrete models, described by Difference Equations and Coupled Map Lattices, in order to analize the local and spatio-temporal dynamics of hostparasitoid- predator dynamics. We firstly consider that the three species reproduce in the same time scale so that the dynamics is described by three difference equations. In the second model, we assume that the predator time scale for reproduction is much slower than the time scale for reproduction of the host and parasitoid species. In this way, the predator density is constant and the dynamics and be modelled in terms of two difference equations. We analyze the order of the events of host reproduction, predation, parasitism and consumers growth for both models. All the proposed models assume the Beverton- Holt function for host growth and Holling type III functional response for parasitism and predation; both consumers are considered specialists. By means of numerical simulations, we found biestability and triestability, besides finding periodic solutions. We finally introduced the spatial variable and studied the spatio-temporal dynamics. We obtained homogeneous as well as heterogeneous spatial distribution. The three species local model forecasts regarding the species persistence are maintained by the corresponding spatial model. For the model in the wich the predator density is constant, the spatial model produces heterogeneous distributions generated by three simultaneously stable equilibria. Keywords: Difference equations, Coupled Map Lattices, Host-parasitoid-predator dynamics, Biestability