Abstract: An important biological concern is to understand the changes in a species' population over time. The two major factors that influence these changes are the species' dispersal mechanisms and environmental conditions (like resource availability, growth or proliferation rate and other limiting factors).  Considering dispersal mechanisms, random walk (local diffusion)  and long-range dispersal (nonlocal dispersal) are among the most prevalent strategies. Environmental factors could be homogeneous or exhibit seasonal variations. However, nature is typically heterogeneous, and even when seasonal, the variations could exhibit disproportionate periods. The nonlocal dispersal equation has been effective in modeling the dynamics of species that exhibit long-range dispersal strategy.

In this talk, we will discuss the Lotka-Volterra competition system with nonlocal dispersal under different environmental conditions. We shall examine different biological scenarios that employ the nonlocal dispersal strategy with the Lotka-Voltera-type competition. In particular, we shall explore these models under the almost periodic environment condition and discuss the persistence and extinction dynamics of the species.