Spatial and Behavioral Models for Ecological Management
This dissertation focuses on developing mathematical and statistical models to address important problems in ecological management, in particular relating to spatial and behavioral processes. The first chapter considers the optimal spatial management of fisheries where fishing activity can result in benthic habitat damage (e.g., from trawls or dredges). We develop a multi-patch fisheries model and use approximate dynamic programming methods to find (near)-optimal policies of dynamic and fixed spatial closures. Our work shows that dynamic closures can achieve greater harvests and more habitat protection than fixed closures in many scenarios, especially when fish respond strongly to habitat quality. In the second chapter, we develop a general spatial survival model for analyzing time-to-event data arising from animal telemetry. The model can contribute to the management of fish and wildlife by characterizing how mortality risks vary across space alongside estimating conventional non-spatial risk factors. The model is demonstrated with several simulated examples and two animal telemetry case studies. Finally, we develop models to study how behavioral avoidance can affect host-pathogen dynamics for waterborne diseases of fish and wildlife. Through a stability and bifurcation analysis, we show that learned avoidance has the potential for complex dynamics (e.g. disease persistence for R_0 < 1) that are not found under innate avoidance. Furthermore, simulations show that management to induce learned behavioral avoidance may be an effective strategy for increasing host population size.