Consensus in the search for areas of endemism



For ambiguous data sets, methods to determine areas of endemism based on an optimality criterion may result in large numbers of candidate areas, and thus some kind of consensus technique is required to summarize those results. This paper presents a formal description of two possible algorithms or rules for area consensus, which merge candidate areas if they share a user-defined percentage of the species that define each candidate area. The two consensus rules summarize ambiguity in different ways. Applying the ‘tight’ rule will result in consensus areas defined by species present in nearly all cells, but in cases where there is significant conflict the result may be a high number of distinct consensus areas. The ‘loose’ consensus rule is more agglomerative and will result in fewer consensus areas, combining areas when overlapping distribution patterns exist. Depending on the aim and scale of the analysis, the two consensus rules can be used either to delimit areas of endemism with sharp boundaries or to identify diffuse and gradually replacing biogeographical patterns. These two different approaches are discussed and demonstrated using real data.