Mathematical models of predator–prey interactions are interesting dynamical systems that exhibit fascinating complex phenomena. Competition models on the contrary may possess simple dynamics. The well-known competitive exclusion principle in ecology states that two populations competing for the same limited resources cannot coexist. One competitor will always overcome the other, leading the less competitive competitor to either extinction or an evolutionary shift towards a different ecological niche [3]. The Allee effect, referring to the reduced fitness or the decline in population growth at low population densities or sizes, was first observed by Allee [1]. It has significant impact on population survival when the population is at low level [6]. There are many natural populations with Allee effects that are also pests. Biological control is the reduction of pest populations by natural enemies, also known as the biological control agents. Very often biological control involves supplemental release of natural enemies. Relatively few natural enemies may be released at a critical time of the season (inoculative release) or literally millions may be released in a single time (inundative release) [8]. Several discrete-time mathematical models have been proposed to study the dynamical effects of external stocking, or the inoculative release of the control agents. See AlSharawi and Rhouma [2], Elaydi and Yakubu [7], Kulenovc ´ and Nurkanovic ´ [16] and references cited therein. In particular, the classical Leslie–Gower model with stocking in one of the twopopulations is analysed in [16] and the Ricker-type competition system with stocking occurring in one of the two competing population is studied in [7], while [2] investigates a multi-species population model with constant harvesting/stocking. Since ecosystems are complex and often involve many populations, we propose a model of three interacting populations, x; y and z, to study the impact of Allee effects and stocking on population interactions. Specifically, populations x and y engage in competition while populations y and z are in predator–prey type relation. Population x is regarded as a pest population and is also subject to Allee effects. Its competitor, population y, is used as a control agent so that a constant level of the external population is released into the interaction at each generation. Furthermore, population y is the host population for its parasitoids, population z. To avoid parasitism, the stocking is implemented at each generation after parasitism has occurred. These result in a system of three equations that are linked by different biological mechanisms. We study dynamics of this threedimensional system of first-order difference equations. In the following sections, competition subsystem is analysed in Section 2. Using the tools of planar monotone systems, we provide basins of attractions of the local attractors and of the non-hyperbolic fixed points. Section 3 studies the predator–prey subsystem by deriving conditions for uniform persistence and for the Neimark–Sacker bifurcation. The full model is analysed in Section 4, where sufficient conditions for the existence of interior steady states and for persistence based on the initial population size of the population with Allee effects are derived. The final section provides a brief summary and discussion.