Parameterized models of mantle flow and melting are used to examine two problems in ocean-island and mid-ocean ridge basalt (OIB, MORB) geochemistry: (1) the causes of variations in He, Sr, Nd, and Pb isotopes with one another and with age of the surrounding seafloor and (2) the origin of geochemical distinctions between OIB and MORB. We assume the mantle is a mixture of different isotopic components that have different solidus temperatures and are expressed in magmas to varying degrees depending on mantle temperature, lithospheric thickness, and shallow mantle flow. Isotopic variations along the Hawaiian hot spot chain support the possibility that lithospheric thickness controls magma composition primarily by limiting the melting of the most refractory, depleted mantle (DM) component. For Hawaii and a collection of other hot spots, calculations of melt extraction trajectories reproduce the strong correlations often seen among Sr-Nd-Pb isotopes together with the more variable and weaker correlations involving 3He/4He. The latter are predicted to be a direct consequence of only one mantle component with high 3He/4He. We show that both OIB and MORB can arise out of the same heterogeneous mantle layer if three conditions are met: the high-3He/4He source begins melting deeper than DM, DM is ≥85% of the mantle, and the concentration of He in the high-3He/4He source is comparable to that in DM.