We present the results of a series of numerical geodynamic experiments designed to characterize the thermal and compositional evolution of the sub-arc mantle in response to spreading in the back-arc. We find large changes in both the temperature and composition of the sub-arc mantle with time as the BASC migrates away from the arc. In particular, the sub-arc mantle becomes increasingly more depleted with time following the onset of spreading, as mantle that has experienced decompression melting and melt extraction beneath the BASC is gradually drawn beneath the arc plate by slab-induced corner flow. The rate at which this depletion increases during the ∼2 Myr immediately following the onset of spreading is controlled by the spreading rate at the BASC, with faster spreading leading to a more rapid increase in depletion. Following this initial period, depletion within the sub-arc mantle continues to increase at a somewhat slower pace. During this phase, the rate at which depletion increases is chiefly dictated by the subduction rate, with faster subduction leading to a more rapid increase in depletion beneath the arc. Depletion within the sub-arc mantle is also found to increase with increasing mantle potential temperature, decreasing age of the overriding plate, and decreasing distance between the initial location of the BASC and the arc. Predicted changes in the depletion of the sub-arc mantle with time are shown to be consistent with observations of systematic along-strike geochemical variations within a portion of the Tonga Arc adjacent to the Eastern Lau Spreading Center.