Abstract: A community is a collection of populations of different species living in the same geographical area. Species interact with each other in the community and this interaction affects species distribution, abundance, and even evolution [5]. Species interact in various ways, for instance through competition, predation, parasitism, mutualism, and commensalism. Mutualism is an interaction between individuals of different species in which both individuals benefit. Examples include plants and nitrogen fixing bacteria, pollination of flowering plants by an insect, lichen between a species of algae and fungus [53]. Commensalism is a type of relationship among organisms in which one organism is benefited while the other organism is neither benefited nor harmed. For example, some birds live among cattle to eat the insects stirred up by the cows. Predation is an interaction in which one organism consumes either all or part of another living organism (the prey), causing direct negative effect on the prey [6]. The individuals of one species is benefited while individuals of the other species is harmed. Parasitism is considered as a special case of (or analogous to) predation [47]. Individuals compete with each other for limited resources. This is a negativenegative interaction, that is, each individual adversely affects another. Historically, competition has been viewed as an important species interaction. Now, competition is recognized as one of many interacting factors that affect community structure. We have two focuses in this thesis. One focus is analyzing the dynamical behaviors of the discretization systems of the Lotka-Volterra predator-prey model. It is well known that the dynamics of the logistic map is more complex compared with logistic differential equation. Period doubling and the onset of chaos in the sense of Li-York occur for some values. Inspired by this, we analyze the dynamical behaviors of the discretization systems of the Lotka-Volterra predator-prey model (articles I and II). In article I, we show that the system undergoes fold bifurcation, flip bifurcation and Neimark-Sacker bifurcation, and has a stable invariant cycle in the interior of R + for some parameter values. In article II, we show that the unique positive equilibrium undergoes flip bifurcation and Neimark-Sacker bifurcation. Moreover, system displays much interesting dynamical behaviors, including period-5, 6, 9, 10, 14, 18, 20, 25 orbits, invariant cycles, cascade of period-doubling, quasi-period orbits and the chaotic sets. We emphasize that the discretization of continuous models (articles I and II) are not acceptable as a derivation of discrete predator-prey models [26]. A discrete predatorprey model is also formulated in Section 2. We analyze the dynamics (articles I and II) from the mathematical point of view instead of biological point of view. The other focus is disease-competition in an ecological system. We propose a model combining disease and competition and study how a disease affects the two competing species (article III). In our model, we assume that only one of the species is susceptible to an SI type disease with mass action incidence, and that infected individuals do not reproduce but suffer from additional disease induced death. We further assume that infection does not reduce the competitive ability of the infected. We show that infection of the superior competitor enables the inferior competitor to coexist, either as a stable steady state or limit cycle. In the case where two competing species coexist without the disease, the introduction of disease is partially determined by the basic