Hierarchical models for the anlaysis of species distributions and abundances: development and applications

There is a strong need for statistical methods that can maximize the utility of ecological data while providing accurate estimates of species abundances and distributions. This dissertation aims to build on current statistical models using Bayesian hierarchical approaches to advance these methods. Chapters one, two, and three utilize a multi-species modeling framework to estimate species occurrence probabilities. Chapter one presents a model to assess the community response of breeding birds to habitat fragmentation. The results demonstrate the importance of understanding the responses of both individual, and groups of species, to environmental heterogeneity while illustrating the utility of hierarchical models for inference about species richness. Chapter two demonstrates how the multi-species modeling framework can be used to evaluate conservation actions through a component that incorporates species-specific responses to management treatments. In Chapter three, I develop a method for validating predictions generated by the multi-species model that accounts for detection biases in evaluation data. I build competing models using wetland breeding amphibian data and test their abilities to predict occupancy at unsampled locations. Chapters four and five develop count models that are used to estimate population abundances in relation to environmental and climate variables. In Chapter four, I employ a Poisson regression designed to determine how climate affects the annual abundances of migrating monarch butterflies. I incorporate the climate conditions experienced both during a spring migration phase, as well as during summer recruitment. In Chapter five, I analyze sea duck data to characterize the spatial and temporal distributions along the U.S. and Canadian Atlantic coast. I model count data for five species using a zero-inflated negative binomial model that includes latitude, habitat covariates, and the North Atlantic Oscillation. The results from these two chapters demonstrate how Bayesian models can be used to elucidate complicated species-climate relationships. The chapters of this dissertation illustrate creative development and application of advanced statistical methods to complex biological systems. These applications provide a practical framework for dealing with highly aggregated species and uneven species distributions in community analyses, as well as a method for evaluating occurrence estimates that accounts for detection biases. My results highlight the dynamic relationships between population and community structure, habitat, and climate