The phenomenon of downstream fining has been attributed to both particle abrasion and selective particle sorting; the latter is generally considered to play the dominant role within resistant lithologies. It has been recognized that tributaries can disrupt fining patterns; however, few downstream-fining studies have considered the entire fluvial network structure. Here we combine a theory for selective transport with a model of river-basin evolution in order to simulate the dynamics of selective sorting throughout a drainage network. Previous numerical modeling studies of single-thread or braided channels have treated downstream fining as a phenomenon driven by differential deposition rates. We show, however, that in an eroding drainage network, downstream fining emerges as a natural dynamic adjustment to variable water, sediment, and energy inputs, even under conditions of uniform size distribution in sediment flux. Thus, although selective deposition and abrasion clearly can and do play a role in some fluvial systems, neither is necessary to produce downstream fining within a drainage network.