A functional data-analytic approach to the classification of species according to their spatial dispersion. Application to a marine macrobenthic community from the Bay of Morlaix (Western English Channel)

We investigate with multivariate methods the behaviour of species collected in a sequence of ecological surveys. The behaviour of the sth species is first characterized by a classical dispersion index. Under the hypothesis (H) of spatial randomness, the probability distribution vs of this index obeys a reference law μ. All the sampled species are then compared through a Principal Components Analysis whose metric structure depends on μ. More precisely, the distance between two species s and s' is an approximation of the μ-centred chi-square distance (Benzecri 1976) between vs and vs'. Thus, while Correspondence Analysis displays departures from independence or homogeneity, the proposed analysis displays departures of the species from (H). As an application, a macrobenthic data time series is analysed, and the obtained species typology is described and discussed. The method enabled us to separate rare species from random ones while rare species could easily be confused with random ones. All the aggregated species were common (or even dominant), and most random ones were moderately abundant. Finally, a group of 23 species showed a mixed random-aggregated behaviour. The repulsive (uniform) behaviour was extremely rare.