Spatial genetic pattern in the land mollusc Helix aspersa inferred from a ‘centre-based clustering’ procedure

The present work provides the first broad-scale screening of allozymes in the land snail Helix aspersa. By using overall information available on the distribution of genetic variation between 102 populations previously investigated, we expect to strengthen our knowledge on the spread of the invasive aspersa subspecies in the Western Mediterranean. We propose a new approach based on a centre-based clustering procedure to cluster populations into groups following rules of geographical proximity and genetic similarity. Assuming a stepping-stone model of diffusion, we apply a partitioning algorithm which clusters only populations that are geographically contiguous. The algorithm used, which is actually part of leading methods developed for analysing large microarray datasets, is that of the k-means. Its goal is to minimize the within-group variance. The spatial constraint is provided by a list of connections between localities deduced from a Delaunay network. After testing each optimal group for the presence of spatial arrangement in the genetic data, the inferred genetic structure was compared with partitions obtained from other methods published for defining homogeneous groups (i.e. the Monmonier and SAMOVA algorithms). Competing biogeographical scenarios inferred from the k-means procedure were then compared and discussed to shed more light on colonization routes taken by the species.