In this dissertation, new theory and its applications are developed to predict three properties of complex ecological communities: stability, equilibrium response, and non-equilibrium dynamics. First, a graph-theoretic analysis identifies the interconnections in a complex ecosystem that promote or diminish stability (Chapter 2). The hierarchy of interactions that influences stability and...
This work sets forth a reformulation of Levins' loop analysis for the qualitative modeling of complex dynamical systems. Relationships between members of ecological communities can be analyzed through a qualitatively specified community matrix, whereby +1, -1, or 0 represent effects of one species upon another. A contribution is made to...
