<p>This study introduces a two-species mathematical model to investigate the dynamical behavior of toxin producing phytoplankton and zooplankton interactions, incorporating phytoplankton harvesting and additional food for zooplankton. Analytical results establish the boundedness of solutions, the existence of equilibrium points, and their local stability. The occurrence of Hopf and transcritical bifurcations is examined to identify the control parameters. To explore spatiotemporal dynamics, the model is extended into a reaction-diffusion system, wherein the conditions for Turing instability are analytically established. Numerical simulations validate analytical outcomes and examine the effects of various parameters on the temporal and spatial model systems. In the temporal model, high rate of toxin release and insufficient additional food lead to the extinction of zooplankton species. In spatial model, the effects of cross diffusion, time iteration, toxin release, and additional food on the density distribution of species are discussed, showing that higher cross diffusion can induce Turing instability, forming a mixture of circular and rectangular spots. Thus, for the conservation of aquatic biodiversity and the coexistence of species, it is essential to control the key parameters (additional food and the rate of toxin release) that have a significant influence on the system dynamics.</p>