A phytoplankton-zooplankton prey-predator model has been investigated for temporal, spatial and spatio-temporal dissipative pattern formation in a deterministic and noisy environment, respectively. The overall carrying capacity for the phytoplankton population depends on the nutrient level. The role of nutrient concentrations and toxin producing phytoplankton for controlling the algal blooms has been discussed. The local analysis yields a number of stationary and/or oscillatory regimes and their combinations. Correspondingly interesting is the spatio-temporal behaviour, modelled by stochastic reaction-diffusion equations. The present study also reveals the fact that the rate of toxin production by toxin producing phytoplankton (TPP) plays an important role for controlling oscillations in the plankton system. We also observe that different mortality functions of zooplankton due to TPP have significant influence in controlling oscillations, coexistence, survival or extinction of the zoo-plankton population. External noise can enhance the survival and spread of zooplankton that would go extinct in the deterministic system due to a high rate of toxin production.