Gradients in the number of species at reef-seagrass ecotones explained by gradients in abundance

[EN] Gradients in the composition and diversity (e.g. number of species) of faunal assemblages are common at ecotones between juxtaposed habitats. Patterns in the number of species, however, can be confounded by patterns in abundance of individuals, because more species tend to be found wherever there are more individuals. We tested whether proximity to reefs influenced patterns in the composition and diversity (‘species density’ = number of species per area and ‘species richness’ = number of species per number of individuals) of prosobranch gastropods in meadows of two seagrasses with different physiognomy: Posidonia and Amphibolis. A change in the species composition was observed from reef-seagrass edges towards the interiors of Amphibolis, but not in Posidonia meadows. Similarly, the abundance of gastropods and species density was higher at edges relative to interiors of Amphibolis meadows, but not in Posidonia meadows. However, species richness was not affected by proximity to reefs in either type of seagrass meadow. The higher number of species at the reef-Amphibolis edge was therefore a consequence of higher abundance, rather than species richness per se. These results suggest that patterns in the composition and diversity of fauna with proximity to adjacent habitats, and the underlying processes that they reflect, likely depend on the physiognomy of the habitat.

Normalized Frobenius condition number of the orthogonal projections of the identity

[EN]This paper deals with the orthogonal projection (in the Frobenius sense) AN of the identity matrix I onto the matrix subspace AS (A ? Rn×n, S being an arbitrary subspace of Rn×n). Lower and upper bounds on the normalized Frobenius condition number of matrix AN are given. Furthermore, for every matrix subspace S ? Rn×n, a new index bF (A, S), which generalizes the normalized Frobenius condition number of matrix A, is defined and analyzed...