We combine mathematical models, simulations, and data set analysis to address fundamental and applied questions in ecology. Our current major research interest focuses on the structure and dynamics of ecological networks. This complements main approaches to biodiversity research that neglect species interactions or assume these are homogeneously distributed. As an example, our application of network theory to the study of mutualisms among free-living species has provided a quantitative framework to address mutualistic interactions at the community level. Our work has shown that these networks of mutual dependencies between plants and animals present general architectural patterns that maximize the number of coexisting species and increase the range of perturbations that can be withstood before one or more species goes extinct.