Quantifying spatio-temporal interactions of animals using probabilistic space-time prisms

Probabilistic space-time prisms are a recent development in time geography. They can be used to determine the probability of an object's location at any time given tracking data that record information about its whereabouts periodically. This paper extends this approach in order to quantify probabilities of interaction for two or more individuals that have tracking data for overlapping time periods. The method relies on using a voxel-based representation of the probabilistic space-time prism. Equations for computing interaction probabilities from the intersection of overlapping space-time prisms are formulated for single voxels, each time step, each raster cell, and for the tracking duration overall. The approach is illustrated using tracking data for three zebras. Probabilistic space-time prisms are mapped simultaneously for all three zebras, and the resulting interactions are summarized using probability clocks and maps. The results show when and where each pair of zebras, or all three zebras, were most likely to have physically interacted with one another. Implications of this research in GIScience, ecology, and other disciplines are also discussed.