Metapopulation Patterns of Iberian Butterflies Revealed by Fuzzy Logic.

Metapopulation theory considers that the populations of many species are fragmented into patches connected by the migration of individuals through an interterritorial matrix. We applied fuzzy set theory and environmental favorability (F) functions to reveal the metapopulational structure of the 222 butterfly species in the Iberian Peninsula. We used the sets of contiguous grid cells with high favorability (F ≥ 0.8), to identify the favorable patches for each species. We superimposed the known occurrence data to reveal the occupied and empty favorable patches, as unoccupied patches are functional in a metapopulation dynamics analysis. We analyzed the connectivity between patches of each metapopulation by focusing on the territory of intermediate and low favorability for the species (F < 0.8). The friction that each cell opposes to the passage of individuals was computed as 1-F. We used the r.cost function of QGIS to calculate the cost of reaching each cell from a favorable patch. The inverse of the cost was computed as connectivity. Only 126 species can be considered to have a metapopulation structure. These metapopulation structures are part of the dark biodiversity of butterflies because their identification is not evident from the observation of the occurrence data but was revealed using favorability functions.