Tests of Spatial and Temporal Interaction Among Animals

I report a method for analyzing interaction between two animals around a common object or resource (simple association) or within a shared area (spatial—temporal interaction in home range overlap). The pair's association is reduced to binomial events forming a 2 x 2 classification; each is either present or not in the shared area. For the most common home range overlap description, observed frequencies of presence and absence for each animal are compared to expected frequencies based on two null hypotheses of spatially independent home range use by each animal relative to the other, and one null hypothesis of temporally independent home range use by the two animals. The procedure uses any statistically derived, two—dimensional home range representation that allows spatial overlap to be delineated for each animal pair. The temporal order of simultaneous pairs of locations for the two animals can then be evaluated for a pattern of use regarding the area of overlap (shared area). The window of "simultaneity" is dictated by the animal's primary sensory mode and mobility. An overall chi—squared test with three degrees of freedom is partitioned into spatial "main effects" and temporal "interaction," analogous to analysis of variance. The two main effects are each animal's purely spatial attraction to or avoidance of the shared area. When interaction effects are significant, it is possible to interpret temporal attraction to or avoidance of the shared area. This temporal response is in terms of the pair's simultaneous vs. solitary occupation of the shared area relative to overall home range use. Experimental design and assumptions are discussed because degree of adherence affects the validity of inferences and influences interpretation. Detailed examples of analysis and interpretation from North American badgers (Taxidea taxus) and from mule deer (Odocoileus hemionus) interacting with domestic cattle (Bos taurus) illustrate the range of complexity inherent to even this simple form of interaction analysis.