Abstract:   In a vertical water column, the movements of obligately photosynthetic phytoplankton are not only affected by turbulence in the vertical direction, but also by light exposure. Considering the influence of light on phytoplankton growth, we propose a nonlocal reaction-diffusion-advection model for the competition between mixotrophic 
and obligately photosynthetic phytoplankton in this paper. We first prove the stability of semitrivial steady state of system by using eigenvalue theory. Then we prove the existence and boundedness of the solution of system and establish a priori estimates of the solution for the steady state system. Our research indicates successful invasion is determined by the interplay of physiological traits and movement strategies: species with extreme growth 
advantages can invade unconditionally, while those with intermediate competitiveness must adopt a vertical migration strategy that either contrasts with the dominant species or enables precise positioning at an optimal depth.

Key words:  Reaction-diffusion-advection system, Phytoplankton, Stability, Existence