A new procedure for extrapolating turnover regionalization at mid-small spatial scales, tested on British butterflies

Biotic regionalization provides fundamental information for biogeography and conservation. The current consensus is to couple turnover indices and clustering methods to identify regions with distinct biotic composition. Nevertheless, turnover indices can produce large numbers of zero and tied dissimilarity values generating multiple clustering solutions which vary according to the arbitrary order of cases in the input matrix. Zero and tied values are particularly numerous at mid-small spatial scales where low signals for turnover occur. Turnover patterns can be also obscured by incomplete sampling. We have designed a new method (recluster.region) based on the creation of a new dissimilarity matrix involving a continuous consensus of cell clustering among different random trees. This matrix minimizes the bias produced by zero and tied values before the final clustering. We created virtual data sets with a priori generated turnover areas and compared the power of the new and of classic methods in recognizing regionalization patterns on the basis of several evaluators (consistency among runs, correct attribution, mean silhouette width and explained dissimilarity) for different levels of sampling intensity [collection completeness (CC)]. We also used a real data set of British butterflies recorded for 10 × 10 km2 cells to test our method. All methods were sensitive to the order of cases in the dissimilarity matrix. Some methods (UPGMA, UPGMC, WPGMA, WPGMC and single linkage) also produced ineffective clustering solutions. Our recluster.region procedures had higher consistency compared to classic clustering and performed best in recognizing the a priori determined regions in virtual data sets (mostly when in association with Ward clustering). Moreover, for the real butterfly data set, recluster.region associated with Ward method and to a lesser extent with DIANA and complete linkage resulted in stable solutions, which largely agreed with the distribution of a set of species identified as responsible for generating the turnover pattern. The Ward method also performed best with low CC. Regionalization can be greatly improved by using the recluster.region algorithm. For the data set of butterflies, it clearly revealed the occurrence of three faunistic regions, supporting the existence of a Holocene climatic refuge and a current Anthropocene refuge in northern and western Britain.