Scanning tunneling microscopy (STM) has been used to investigate the nucleation and growth of Ag islands on the fivefold surface of an icosahedral Al-Pd-Mn quasicrystal. Analysis of the data as a function of deposition temperature, from 127 K to 300 K, reveals that island density is constant, while at higher temperature it decreases. To model this behavior, we first show that the potential energy surface describing bonding of Ag at various locations on the surface is complex, with a few sites acting as traps for clusters of adatoms. We then develop a rate equation model which incorporates enhanced nucleation at trap sites relative to nucleation at regular sites on terraces. It recovers the temperature dependence of the island density, plus previous flux-scaling data. Our model suggests that the critical size for both types of nucleation sites is large—corresponding to stable clusters of at least 6 Ag atoms—and that binding between atoms at trap sites is significantly stronger than at free terrace sites. The data and the model, combined, provide guidance about the conditions of temperature and flux under which saturation of trap sites can be expected. This, in turn, provides a general indicator of the conditions that may favor localized pseudomorphic growth at low coverage, here and in other systems.