Stochastic processes are a central issue in Statistical Physics (Gardiner 2009). In most realmodels, the deterministic prediction is only an estimate of the system’s actual behavior since random factors affect it. Specifically, problems with significant historical relevance, such as Brownian motion (Brown 1828; Einstein 1905), could not be correctly studied until the development of the stochastic processes theory. In this thesis, we study the effect of stochastic factors on populations within an ecosystem, classically modeled with deterministic growth equations (Cotgreave and Gotelli 2006). There are random fluctuations in natural ecosystems, which can change the model’s behavior, evencausing the extinction of an otherwise stable population in the deterministic case. The variability affecting a population can be modeled as a stochastic process with spatial and/or temporal correlation.We begin by introducing the state of the art in ecology and stochastic processes. In Chapter 1,we introduce well-known deterministic dynamic equations for a single species, emphasizing on the Allee effect dynamic equation (Allee and Rosenthal 1949), for which the population has negative growth when its size is below a certain minimum threshold. Besides, we include metapopulation models to represent dispersal…