Complex networks of interactions are ubiquitous and are particularly important in ecological communities, in which large numbers of species exhibit negative (for example, competition or predation) and positive (for example, mutualism) interactions with one another. Nestedness in mutualistic ecological networks is the tendency for ecological specialists to interact with a subset of species that also interact with more generalist species. Recent mathematical and computational analysis has suggested that such nestedness increases species richness. By examining previous results and applying computational approaches to 59 empirical data sets representing mutualistic plant-pollinator networks, we show that this statement is incorrect. A simpler metric--the number of mutualistic partners a species has--is a much better predictor of individual species survival and hence, community persistence. Nestedness is, at best, a secondary covariate rather than a causative factor for biodiversity in mutualistic communities. Analysis of complex networks should be accompanied by analysis of simpler, underpinning mechanisms that drive multiple higher-order network properties.