Clustering in non-parametric multivariate analyses.

Non-parametric multivariate analyses of complex ecological datasets are widely used. Following appropriate pre-treatment of the data inter-sample resemblances are calculated using appropriate measures. Ordination and clustering derived from these resemblances are used to visualise relationships among samples (or variables). Hierarchical agglomerative clustering with group-average (UPGMA) linkage is often the clustering method chosen. Using an example dataset of zooplankton densities from the Bristol Channel and Severn Estuary, UK, a range of existing and new clustering methods are applied and the results compared. Although the examples focus on analysis of samples, the methods may also be applied to species analysis. Dendrograms derived by hierarchical clustering are compared using cophenetic correlations, which are also used to determine optimum  in flexible beta clustering. A plot of cophenetic correlation against original dissimilarities reveals that a tree may be a poor representation of the full multivariate information. UNCTREE is an unconstrained binary divisive clustering algorithm in which values of the ANOSIM R statistic are used to determine (binary) splits in the data, to form a dendrogram. A form of flat clustering, k-R clustering, uses a combination of ANOSIM R and Similarity Profiles (SIMPROF) analyses to determine the optimum value of k, the number of groups into which samples should be clustered, and the sample membership of the groups. Robust outcomes from the application of such a range of differing techniques to the same resemblance matrix, as here, result in greater confidence in the validity of a clustering approach.

Clustering in non-parametric multivariate analyses.

Non-parametric multivariate analyses of complex ecological datasets are widely used. Following appropriate pre-treatment of the data inter-sample resemblances are calculated using appropriate measures. Ordination and clustering derived from these resemblances are used to visualise relationships among samples (or variables). Hierarchical agglomerative clustering with group-average (UPGMA) linkage is often the clustering method chosen. Using an example dataset of zooplankton densities from the Bristol Channel and Severn Estuary, UK, a range of existing and new clustering methods are applied and the results compared. Although the examples focus on analysis of samples, the methods may also be applied to species analysis. Dendrograms derived by hierarchical clustering are compared using cophenetic correlations, which are also used to determine optimum  in flexible beta clustering. A plot of cophenetic correlation against original dissimilarities reveals that a tree may be a poor representation of the full multivariate information. UNCTREE is an unconstrained binary divisive clustering algorithm in which values of the ANOSIM R statistic are used to determine (binary) splits in the data, to form a dendrogram. A form of flat clustering, k-R clustering, uses a combination of ANOSIM R and Similarity Profiles (SIMPROF) analyses to determine the optimum value of k, the number of groups into which samples should be clustered, and the sample membership of the groups. Robust outcomes from the application of such a range of differing techniques to the same resemblance matrix, as here, result in greater confidence in the validity of a clustering approach.

Simple procedures to assess and compare the ecological niche of species

Hutchinson's (1957; Cold Spring Harbour Symp Quant Biol 22:415-427) niche concept is being used increasingly in the context of global change, and is currently applied to many ecological issues including climate change, exotic species invasion and management of endangered species. For both the marine and terrestrial realms, there is a growing need to assess the breadth of the niches of individual species and to make comparisons among them to forecast the species' capabilities to adapt to global change. In this paper, we describe simple non-parametric multivariate procedures derived from a method originally used in climatology to (1) evaluate the breadth of the ecological niche of a species and (2) examine whether the niches are significantly separated. We first applied the statistical procedures to a simple fictive example of 3 species separated by 2 environmental factors in order to describe the technique. We then used it to quantify and compare the ecological niche of 2 key-structural marine zooplankton copepod species, Calanus finmarchicus and C. helgolandicus, in the northern part of the North Atlantic Ocean using 3 environmental factors. The test demonstrates that the niches of both species are significantly separated and that the coldwater species has a niche larger than that of its warmer-water congeneric species.

Seasonal plankton dynamics along a cross-shelf gradient off northern Spain

The development of population models able to reproduce the dynamics of zooplankton is a central issue when trying to understand how a changing environment would affect zooplankton in the future. Using 10 years of monthly data on phytoplankton and zooplankton abundance in the Bay of Biscay from the IEO's RADIALES time-series programme, we built non-parametric Generalized Additive Models (GAMs) able to reproduce the dynamics of plankton on the basis of environmental factors (nutrients, temperature, upwelling and photoperiod). We found that the interaction between these two plankton components is approximately linear, whereas the effects of environmental factors are non-linear. With the inclusion of the environmental variability, the main seasonal and inter-annual dynamic patterns observed within the studied plankton assemblage indicate the prevalence of bottom-up regulatory control. The statistically deduced models were used to simulate the dynamics of the phytoplankton and zooplankton. A good agreement between observations and simulations was obtained, especially for zooplankton. We are presently developing spatio-temporal GAM models for the North Sea based on the Continuous Plankton Recorder database.