This project will advance the theoretical framework of network analysis aimed toward the study of ecological communities, in order to answer basic and applied questions concerning the impacts of extinctions and invasions on community stability and biodiversity. The investigators have introduced a dynamic Boolean network model of plant-pollinator mutualistic ecosystems that describes their formation and stability. They will expand the model to examine perturbations to ecosystem structure, specifically the permanent or temporary removal (extinction) or introduction (invasion) of one or more species. This will allow for assessment of which species and ecosystem properties contribute to the susceptibility of an ecosystem to catastrophic failure, and which contribute most to stability. The project will make use of high-performance computing to model the formation and dynamics of diverse ecological communities. The results of the dynamic simulations will be distilled into novel graph theoretical analyses and measures. This project will also inform a number of related theoretical studies on the importance of transient species (those absent from stable communities, but temporarily present during dynamical re-equilibration), the role of other mutualistic and natural enemy interactions, composite interactions, and context-dependent interactions. This project is based upon an application of dynamic network theory to mutualistic ecological networks, the unique challenges of which will also expand the body of knowledge concerning network theory's general applications and uses. The need to address the impacts of environmental perturbations is increasingly urgent; the addition or loss of species to existing ecological communities can have far-reaching consequences for both the community and the greater ecosystem in which the community is embedded. For example, the recent, rapid decline in pollinator levels poses a serious risk to global agriculture and food security. This project will advance our knowledge of how these complex systems function; only if we can anticipate the effects of environmental perturbations can we act to prevent or ameliorate undesired outcomes. This project will not only address species and community structures that are critical to community stability, but will also facilitate assessment of community manipulations, such as floral resource provisioning for native bees to benefit fruit growers, that bring about desired management outcomes in the face of perturbations.