We consider the role played by the heterogeneous distribution of heat-producing elements (HPE) in time-dependent mantle convection. Petrological studies, especially those associated with hotspots, indicate significant variations of the amount of HPE, ranging several to several tens times that of chondrite. The spatial extent of HPE anomalies in the mantle is uncertain, though some inferences from the morphologies of subducting slabs, geochemical and seismological studies suggest the possibility of the existence of HPE anomalies with dimensions which range from several to a few hundreds of kilometers thick and several to thousands of kilometers wide. Correlation between hotspot magmas and geochemical heterogeneities, especially the enrichment of incompatible elements in hotspot magmas, raises certain issues concerning the relationship between HPE anomalies and plume dynamics. The major questions arise: (1) the onset of plume instabilities excited by HPE, and (2) plume-plume interactions. We find that, HPE anomalies result in more rapid growth of plumes, and there exists the possibility that the plumes with HPE may dominate over the other thermal plumes. The dynamical effects of plume-plume interactions are to prevent plumes from being sheared by the large-scale background flow, and they also provide an efficient mode for transporting heat and HPE anomalies. From these two-dimensional calculations, we propose a dynamical model in which the generation and persistence of plumes are strongly controlled by HPE anomalies and plume-plume interactions.