Abstract:
Wavelet analysis is an analytical and modeling tool for optimizing sampling efficiency and accuracy, particularly in the context of designing long-term, large-scale monitoring plans. As a pattern analysis method that accommodates and preserves non-stationarity, wavelet analysis provides novel visualization and analytical capabilities for increased insight into interactions between multi-scalar heterogeneous pattern and sampling design. Effective monitoring must involve sampling designs sufficiently detailed to detect ecologically significant patterns at multiple scales, yet logistically tractable and
resource-efficient for sustained use. For this reason, methods that help optimize these
objectives and contribute to the design of more efficient sampling prior to implementation are important for successful large-scale monitoring. The main objectives in this dissertation were: (1) to explore Complexity Theory as a framework for pattern analysis in ecological monitoring for conservation of species and habitat; (2) to examine the relative capabilities of semivariogram, Fourier analysis, and onedimensional wavelet analysis to detect and classify spatio-temporal pattern in a comparison of stochastic processes, deterministic simulations, and empirical species range data for Western Meadowlarks; (3) to illustrate pattern detection and
reconstruction capabilities of two-dimensional wavelet analysis in three bird species (Neotropical migrants) with varying degrees of heterogeneity (Field Sparrow, Brewer's Sparrow, and Red-eyed Vireo); and (4) to compare statistical and ecological inference and examine these approaches within the context of the statistical analyses in landscape ecology. The sampling properties and behavior of these spatial statistics are described and illustrated in a comparison of spatio-temporal patterns in species range data from the Breeding Bird Surveys. Both one- and two-dimensional wavelet analyses were better suited than semivariogram and Fourier analysis in separating signal from noise to identify and characterize ecological pattern in the Neotropical migrants. Wavelet
analysis accommodates non-stationarity, compares multi-scalar pattern, localizes
detected pattern to original data, provides flexibility in choice of analyzing filter, and retains the context of the pattern to view the system as a complex space-time volume. Monitoring within the framework of Complexity Theory for conservation of species and habitats will be increasingly important as we progress into the Twenty-first Century.
