Modelos de competição e predação em ambientes fragmentados

Abstract

In this thesis, we consider two models of ecological interactions: one for competition and another for predation. We study the effects of dynamic fragmentation on an ecosystem in which species compete for resources and also the role played by habitat heterogeneity in one model in which a predator coexists with two prey. The competition model has as main feature the fact that different species have distinct efficiencies in the use of resources. Each site of a square lattice can be occupied by only one individual, which dies with a fixed rate. Habitat heterogeneity is introduced through the distribution of resources. We investigate the relationship between species diversity and area, as well as habitat heterogeneity. To perform the fragmentation we use the Fractional Brownian Motion, which produces landscapes in which the roughness can be controlled by the parameter of Hurst, H. We observed that diversity presents a unimodal relationship with spatial heterogeneity, where a peak is observed for intermediate heterogeneities. We verified two power law regimes for the species-area relationship, one for small areas and another for large areas. We observed that the dynamic fragmentation generated from very rough landscapes allows the coexistence of a greater number of species when compared to that generated from smooth landscapes. In the predation model, we consider the interaction of three species, one predator and two species of prey. In this model, each site of the spatial structure in which the species are inserted can only have one of four possible states, namely, occupied by prey type 1, occupied by prey type 2, occupied by predator or empty. Interactions occur locally, in which an individual occupying a randomly chosen site can only interact with one of the four neighbors adjacent to it. As in the case of competition, the way resources are distributed determines the heterogeneity of the environment. In this lattice, each site has only two resources. The reproduction rate of prey species is calculated through a resource adaptability function. Our goal in this model is to verify the influence of environmental heterogeneity on the final state of the system. We observed that environmental heterogeneity favors the coexistence of the three species. We verified that for intermediate heterogeneities, the probability of coexistence increases.