Heterosigma akashiwo does not serve as prey and chloroplast donor for the toxic dinoflagellate, Dinophysis acuminata

•Dinophysis acuminata does not prey on Heterosigma akashiwo in lab culture.•Growth rates declined for Dinophysis acuminata when grown with Heterosigma akashiwo.•A microscope method was developed to investigate accessory pigments in algal cells.•There is no evidence of plastids from Heterosigma in Dinophysis cells.•Abundance of Dinophysis acuminata correlates with Heterosigma akashiwo in the field.