Modeling mixotroph-bacterium dynamics: Spatial homogeneity vs heterogeneity

This paper explores two mixotroph-bacterium interaction dynamic models in different eutrophic aquatic environments. One is the spatially homogeneous ordinary differential equation model in a well-mixed aquatic environment. The other is the spatially heterogeneous reaction-diffusion-advection model in a poorly-mixed aquatic environment. Dynamical properties of the two models are investigated containing dissipativity, equilibria, steady states, and uniform persistence. The ecological reproductive indices are developed to characterize mixotrophs or bacteria invasion. We also explore the effects of light, autotrophic behavior of mixotrophs, turbulent diffusion, and advection on population dynamics. Numerical simulations reveal that two mixotroph-bacterium interaction dynamic models display bistability dynamics. Furthermore, our findings indicate that sufficient light and a high proportion of autotrophic behavior of mixotrophs contribute to the coexistence of mixotrophs and bacteria.