Spline Modeling and Localized Mutual Information Monitoring of Pairwise Associations in Animal Movement

to a new era of remote sensing and geospatial analysis. In environmental science and conservation ecology, biotelemetric data recorded is often high-dimensional, spatially and/or temporally, and functional in nature, meaning that there is an underlying continuity to the biological process of interest. GPS-tracking of animal movement is commonly characterized by irregular time-recording of animal position, and the movement relationships between animals are prone to sudden change. In this dissertation, I propose a spline modeling approach for exploring interactions and time-dependent correlation between the movement of apex predators exhibiting territorial and territory-sharing behavior. A measure of localized mutual information (LMI) is proposed to derive a correlation function for monitoring changes in the pairwise association between animal movement trajectories. The properties of the LMI measure are assessed analytically and by simulation under a variety of circumstances. Advantages and disadvantages of the LMI measure are assessed and alternate measures of LMI are proposed to handle potential disadvantages. The proposed measure of LMI is shown to be an effective tool for detecting shifts in the correlation of animal movements, and seasonal/phasal correlatory structure