It has been reported that the minimal spatially extended phytoplankton-zooplankton system exhibits both tem-poral regular/chaotic behaviour, and spatiotemporal chaos in a patchy environment. As a further investigation by means of computer simulations and theoretical analysis, in this paper we observe that the spiral waves may exist and the spatiotcmporal chaos emerge when the parameters are within the mixed Turing Hopf bifurcation region, which arises from the far-field breakup of the spiral waves over a large range of diffusion coefficients of phytoplankton and zooplankton. Moreover, the spatiotemporal chaos arising from the far-field breakup of spiral waves does not gradually invade the whole space of that region. Our results arc confirmed by nonlinear bifurcation of wave trains. We also discuss ecological implications of these spatially structured pattes.