Integrating fuzzy logic and statistics to improve the reliable delimitation of biogeographic regions and transition zones.

This study uses the amphibian species of the Mediterranean basin to develop a consistent procedure based on fuzzy sets with which biogeographic regions and biotic transition zones can be objectively detected and reliably mapped. Biogeographical regionalizations are abstractions of the geographical organization of life on Earth that provide frameworks for cataloguing species and ecosystems, for answering basic questions in biogeography, evolutionary biology, and systematics, and for assessing priorities for conservation. On the other hand, limits between regions may form sharply defined boundaries along some parts of their borders, whereas elsewhere they may consist of broad transition zones. The fuzzy set approach provides a heuristic way to analyse the complexity of the biota within an area; significantly different regions are detected whose mutual limits are sometimes fuzzy, sometimes clearly crisp. Most of the regionalizations described in the literature for the Mediterranean biogeographical area present a certain degree of convergence when they are compared within the context of fuzzy interpretation, as many of the differences found between regionalizations are located in transition zones, according to our case study. Compared with other classification procedures based on fuzzy sets, the novelty of our method is that both fuzzy logic and statistics are used together in a synergy in order to avoid arbitrary decisions in the definition of biogeographic regions and transition zones.