The development of U-Th-Pb and Sm-Nd isotopic signatures in a convecting mantle is studied using a numerical convection model with melting-induced differentiation and tracking of major and trace elements. The models include secular cooling and the decay of heat-producing elements, a rudimentary self-consistent treatment of plate tectonics, and both olivine system and garnet-pyroxene system phase transitions. The system self-consistently evolves regions with a high ¿(=U/Pb) (HIMU)-like Pb signature and regions with low 143Nd/144Nd. However, the isotopic age determined from the slope in (207Pb/204Pb)--(206Pb/204Pb) space is much larger than observed. Several hypotheses are examined to explain this discrepancy. Sampling length scale has a minimal effect on age. The extent of crustal settling above the core-mantle boundary makes some difference but not enough. More frequent remelting is a possible explanation but requires the rate of crustal production to have been much higher in the past. Not introducing HIMU into the mantle prior to 2.0--2.5 Gyr before present, because of a change in the surface oxidization environment or subduction zone processes, can account for the difference, but its effect on other isotope systems needs to be evaluated. Improved treatment of the stretching of heterogeneities, which reduces them to length scales at which they cease to be identifiable magma sources, greatly reduces the Pb-Pb age. The mantle develops substantial chemical stratification from a homogeneous start, including stratification around 660 km caused by the two-component phase transitions. A deep layer of subducted crust may provide storage for some of the missing heat-producing elements. Magmatic heat transport is important in the first 2 Gyr of model time.