Dynamics of autotroph–mixotroph interactions with the intraguild predation structure

A mathematical model with the intraguild predation structure is proposed to describe the interactions of autotrophs and mixotrophs containing light and nutrients in a well-mixed aquatic ecosystem. The dissipation, existence and stability of equilibria of the model are proved, and the ecological reproductive indexes for the extinction, survival and coexistence of autotrophs and mixotrophs are established. We also consider the influence of Holling type functional responses and abiotic factors on the coexistence and biomass of autotrophs and mixotrophs. It is shown that the intraguild predation structure is beneficial to phytoplankton biodiversity and provides an explanation for the phytoplankton paradox.