Nestedness of species assemblages occurs when thebiotas of sites with lower numbers of species tend to be subsets of the biotas at richer sites. We develop new quantitative and statistical techniques for measuring, testing, and comparing nestedness, and apply these methods to data from the literature. Significantly nonrandom nestedness was present in all 27 assemblages examined, and tended to be stronger in systems dominated by extinction, such as landbridge islands. Sets of assemblages that were very strongly nested were more likely to have greater species richness on one or a few large sites than on several smaller sites of equivalent total area - that is, to fall toward the "single large" side of the "Single Large Or Several Small" (SLOSS) continuum. Our analysis indicates that nestedness, when quantified as a single number for a presence-absence matrix, measures community-wide differences in incidence (the frequency of occurrence or "distribution" of species). Factors that lead to consistent differences among species in immigration or extinction rates cause strong patterns of nestedness of species assemblages. Nestedness is negatively related to beta diversity: nestedness is low when beta diversity is high, and vice versa. Conservation managers will thus seek to minimize nestedness and the development of nested structure in systems of nature reserves.