In this paper, we discuss a hierarchical model, based on a Ricker competition model. The species considered are competing for resources and may be subject to an Allee effect due to mate limitation, anti-predator vigilance or aggression, cooperative predation or resource defense, or social thermoregulation. The species may be classified into a more dominant species and less dominant or “wimpy” species or just as a predator and prey. The model under consideration also has components taking into account immigration and emigration in both species and a more structured Holling type II functional response. Local and global stability analyses are discussed and simulations are provided. Demographic stochasticity on the species due to environmental fluctuations in the form of Wiener processes are considered and we show that there are conditions under which a global solution and stationary distributions exist, and conditions under which strong persistence in mean of the species is possible. We also use the Wasserstein distance to show empirically that stochasticity can act as a bifurcation parameter.