Book Description

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 feedback processes can guide resource allocation for environmental monitoring, investigate alternative management strategies, and help formulate novel research hypotheses. Second, a combined graph-theoretic and probabilistic approach evaluates the potential for long-term changes in equilibrium (Chapter 3). Conditional probabilities of long-term increase and decrease in variables are transferred from the graph-theoretic models into a Bayesian network. The Bayesian network allows researchers both to predict how an ecosystem might change given a perturbation and to diagnose which model structure best matches empirical observations. Third, a threshold index predicts whether or not largemagnitude short-term transitory changes in disease prevalence can occur (Chapter 4). The concept of reactivity is used to derive a threshold index for epidemicity, E0, which gives the maximum number of new infections produced by an infective individual at a disease free equilibrium. This index provides a threshold that determines whether or not major epidemics are possible. The relative importance of parameters differs between control strategies that seek to reduce endemicity and those that seek to reduce epidemicity. The index E0 therefore is an important measure of epidemic potential that may assist efforts to control epidemics. Together these approaches provide new theory that help bridge the gap between our need to understand complex ecological systems and the empirical data available for their characterization.