As a river bed of heterogeneous gravel degrades, previously buried material becomes exposed on the surface and thus available for transport. As the river aggrades, surface material and bedload becomes buried, resulting in a transfer of material to the substrate. Any predictive treatment of bed variation in gravel-bed rivers must account for this process in terms of an appropriate transfer, or exchange function at the interface between the surface layer and substrate. In the case of degradation it has long been recognized that substrate is incorporated directly into the surface layer. In the case of aggradation, however, existing formulations are based on little more than educated speculation. Here data from a large-scale experiment on the aggradation and selective deposition of gravel are used to back-calculate a form for the transfer function. The empirical relation so derived suggests that material transferred to the substrate can be represented as a weighted average of bedload and surface material, with a bias toward bedload.