A statistical method for idiographic analyses in biogeographical research

Idiographic analyses (i.e. detailed analyses of single species ranges) can be criticized for subjective and speculative reasoning. Medoid partition is suggested here as a method to perform a statistically supported idiographic analysis. The medoid algorithms attempt to group objects into clusters by finding a set of representative objects called medoids. If areas are the objects that are clustered using species occurrences (0/1) as variables, each cluster will be characterized by a medoid area. The species that characterize each medoid are representative of the entire cluster to which the medoid belongs and can be regarded as (statistically supported) species `characteristic' of the main distributional patterns observed in the study system and can be used to draw idiographic observations. To illustrate the issues involved, the Coleoptera Tenebrionidae of the Aegean Islands (Greece) were analysed. Two species appeared to be characteristic of the Balkan cluster, while eight species were characteristic of the Anatolian one, and two species were equally distributed in both areas. Idiographic considerations based on these species outlined the importance of a Balkano-Anatolian discontinuity in the Aegean that prevented species dispersal between the two landmasses. This study illustrates that medoid analysis may help the researcher to find some representative patterns from a puzzling distribution. Traditional idiographic analyses can be biased by the fact that species are selected ad hoc. Thus, one cannot establish if results are truly objective or if the author intentionally selected, from a wider array of species, those that supported some preferred patterns. Medoid clustering uses the full array of species to find clusters of areas. After clusters are objectively defined, their medoids are examined to find species that mostly contributed to cluster definition, and the distribution patterns of these species are interpreted.