Geographic boundaries are generated by biological and physical processes that are of great interest to environmetnal scientists. However, many existing methods for identifying boundaries are ad-hoc, involving subjective criteria for identifying boundary links. This paper porposes two new tests, based on local and global statistics, for identifying statistically significant geographic boundaries. the statistics have several advantages. First, they account for connection criteria, gradient aspect and gradient magnitude simultaneously. Second, they provide a statistic to reference distributions under realistic null hypotheses. Third, they are appropriate whether boundaries are crisp or fuzzy. The statistics find the locations of crisp boundaries, or the core of fuzzy boundaries. We evalauted the statistics using simulation studies, and, based on these simualtions, the new statistics correctly identify large-scale boundaries when they are indeed present. the new tests thus provide a solid theoretical foundation for boundary detection that, until now, has been lacking.
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