A new procedure to optimize the selection of groups in a classification tree

Agglomerative cluster analyses encompass many techniques, which have been widely used in various fields of science. In biology, and specifically ecology, datasets are generally highly variable and may contain outliers, which increase the difficulty to identify the number of clusters. Here we present a new criterion to determine statistically the optimal level of partition in a classification tree. The criterion robustness is tested against perturbated data (outliers) using an observation or variable with values randomly generated. The technique, called Random Simulation Test (RST), is tested on (1) the well-known Iris dataset [Fisher, R.A., 1936. The use of multiple measurements in taxonomic problems. Ann. Eugenic. 7, 179–188], (2) simulated data with predetermined numbers of clusters following Milligan and Cooper [Milligan, G.W., Cooper, M.C., 1985. An examination of procedures for determining the number of clusters in a data set. Psychometrika 50, 159–179] and finally (3) is applied on real copepod communities data previously analyzed in Beaugrand et al. [Beaugrand, G., Ibanez, F., Lindley, J.A., Reid, P.C., 2002. Diversity of calanoid copepods in the North Atlantic and adjacent seas: species associations and biogeography. Mar. Ecol. Prog. Ser. 232, 179–195]. The technique is compared to several standard techniques. RST performed generally better than existing algorithms on simulated data and proved to be especially efficient with highly variable datasets.

Variation in elemental stoichiometry of the marine diatomThalassiosira weissflogii(Bacillariophyceae) in response to combined nutrient stress and changes in carbonate chemistry

The combined consequences of the multi-stressors of pH and nutrient availability upon the growth of a marine diatom were investigated. Thalassiosira weissflogii was grown in N- or P-limited batch culture in sealed systems, with pH commencing at 8.2 (extant conditions) or 7.6 (ocean acidification [OA] conditions), and then pH was allowed to either drift with growth, or was held fixed. Results indicated that within the pH range tested, the stability of environmental pH rather than its value (i.e., OA vs. extant) fundamentally influenced biomass accumul-ation and C:N:P stoichiometry. Despite large changes in total alkalinity in the fixed pH systems, final biomass production was consistently greater in these systems than that in drifting pH systems. In drift systems, pH increased to exceed pH 9.5, a level of alkalinity that was inhibitory to growth. No statis-tically significant differences between pH treatments were measured for N:C, P:C or N:P ratios during nutrient-replete growth, although the diatom expre-ssed greater plasticity in P:C and N:P ratios than in N:C during this growth phase. During nutrient-deplete conditions, the capacity for uncoupled carbon fixa-tion at fixed pH was considerably greater than that measured in drift pH systems, leading to strong contrasts in C:N:P stoichiometry between these treatments. Whether environmental pH was stable or drifted directly influenced the extent of physiological stress. In contrast, few distinctions could be drawn between extant versus OA conditions for cell physiology.