Traditionally, ion selectivity in nanopores and nanoporous membranes is understood to be a consequence of Debye overlap, in which the Debye screening length is comparable to the nanopore radius somewhere along the length of the nanopore(s). This criterion sets a significant limitation on the size of ion-selective nanopores, as the Debye length is on the order of 1-10 nm for typical ionic concentrations. However, the analytical results we present here demonstrate that surface conductance generates a dynamical selectivity in ion transport, and this selectivity is controlled by so-called Dukhin, rather than Debye, overlap. The Dukhin length, defined as the ratio of surface to bulk conductance, reaches values of hundreds of nanometers for typical surface charge densities and ionic concentrations, suggesting the possibility of designing large-nanopore (10-100 nm), high-conductance membranes exhibiting significant ion selectivity. Such membranes would have potentially dramatic implications for the efficiency of osmotic energy conversion and separation techniques. Furthermore, we demonstrate that this mechanism of dynamic selectivity leads ultimately to the rectification of ionic current, rationalizing previous studies, showing that Debye overlap is not a necessary condition for the occurrence of rectifying behavior in nanopores.