View AbstractAbstract: The interface between basic ecology and applied mathematics is robust, and results from this interface are often critical to effective conservation. In this Probability/Applied Math seminar, I will focus on one part of this interface whereby ecological observations and datasets have created new opportunities for a variety of mathematical tools and approaches. For instance, datasets derived from efforts to track the movements of wild animals (e.g., using GPS-satellite devices) have presented new applications for research on stochastic processes. As technology has improved and datasets have expanded, autocorrelations in both animal position and animal velocity have become key features that can no longer be ignored. Instead there is a need to embrace the information content of the autocorrelation structure of tracking datasets and use that information to obtain biological understanding. Examples include applications of semi-variograms, which identify multiple movement modes and solve the sampling rate problem for tracking data, and autocorrelated kernel density estimators, which provide valuable new approaches for delineating animal home ranges.