Spatial distribution of dominant animals within a group: comparison of four statistical tests of location

We considered statistical methods of testing the hypothesis of spatial centrality of animals in a herd when individuals were classified into one of two mutually exclusive categories. For ease in presentation, we assumed the binary classification was based on individuals' dominance ranking within a herd (dominant or subordinate). One of the main problems in attempting to determine how the spatial structure within a herd correlates with the dominance hierarchy is determining the appropriate measure for testing the spatial distribution. A related difficulty is the definition of what constitutes the centre of a herd. We compared four methods for assessing and testing centrality of dominant animals within a herd. Using simulations, we manipulated several criteria for describing study populations, including herd size, proportion of a herd that was dominant, the method of designation for being on the periphery and the spatial arrangement of animals in a herd. In addition, we considered tests based on different sample sizes. The simulation study indicated that the best test was often dependent on the particular population under study and less so on the sample size. The best test was one based on circular statistics; it had the highest or close to the highest power for every combination of manipulated factors. The tests based on distance to nearest neighbour or distance from the geometric centre behaved poorly under many conditions.