The self-assembly of polypeptides into amyloid structures is associated with a range of increasingly prevalent neurodegenerative diseases as well as with a select set of functional processes in biology. The phenomenon of self assembly results in species with dramatically different sizes, from small oligomers to large fibrils; however, the kinetic relationship between these species is challenging to characterize. In the case of prion aggregates, these structures can self replicate and act as infectious agents. Here we use single molecule spectroscopy to obtain quantitative information on the oligomer populations formed during aggregation of the yeast prion protein Ure2. Global analysis of the aggregation kinetics reveals the molecular mechanism underlying oligomer formation and depletion. Quantitative characterization indicates that the majority of Ure2 oligomers are relatively short-lived, and their rate of dissociation is much higher than their rate of conversion into growing fibrils. We identify an initial metastable oligomer, which can subsequently convert into a structurally distinct oligomer, which in turn converts into growing fibrils. We also show that fragmentation is responsible for the autocatalytic self-replication of Ure2 fibrils, but that preformed fibrils do not promote oligomer formation, indicating that secondary nucleation of the type observed for peptides and proteins associated with neurodegenerative disease does not occur at a significant rate for Ure2. These results establish a framework for elucidating the temporal and causal relationship between oligomers and larger fibrillar species in amyloid forming systems, and provide insights into why functional amyloid systems are not toxic to their host organisms.