No abstract

Context. The diversification of galaxies is caused by transforming events such as accretion, interaction, or mergers. These explain the formation and evolution of galaxies, which can now be described by many observables. Multivariate analyses are the obvious tools to tackle the available datasets and understand the differences between different kinds of objects. However, depending on the method used, redundancies, incompatibilities, or subjective choices of the parameters can diminish the usefulness of these analyses. The behaviour of the available parameters should be analysed before any objective reduction in the dimensionality and any subsequent clustering analyses can be undertaken, especially in an evolutionary context. Aims. We study a sample of 424 early-type galaxies described by 25 parameters, 10 of which are Lick indices, to identify the most discriminant parameters and construct an evolutionary classification of these objects. Methods. Four independent statistical methods are used to investigate the discriminant properties of the observables and the partitioning of the 424 galaxies: principal component analysis, K-means cluster analysis, minimum contradiction analysis, and Cladistics. Results. The methods agree in terms of six parameters: central velocity dispersion, disc-to-bulge ratio, effective surface brightness, metallicity, and the line indices NaD and OIII. The partitioning found using these six parameters, when projected onto the fundamental plane, looks very similar to the partitioning obtained previously for a totally different sample and based only on the parameters of the fundamental plane. Two additional groups are identified here, and we are able to provide some more constraints on the assembly history of galaxies within each group thanks to the larger number of parameters. We also identify another "fundamental plane" with the absolute K magnitude, the linear diameter, and the Lick index Hβ. We confirm that the Mg b vs. velocity dispersion correlation is very probably an evolutionary correlation, in addition to several other scaling relations. Finally, combining the results of our two papers, we obtain a classification of galaxies that is based on the transforming processes that are at the origin of the different groups. Conclusions. By taking into account that galaxies are evolving complex objects and using appropriate tools, we are able to derive an explanatory classification of galaxies, based on the physical causes of the diverse properties of galaxies, as opposed to the descriptive classifications that are quite common in astrophysics.

Minimum contradiction matrices are a useful complement to distance-based phylogenies. A minimum contradiction matrix represents phylogenetic information under the form of an ordered distance matrix Yi, jn. A matrix element corresponds to the distance from a reference vertex n to the path (i, j). For an X-tree or a split network, the minimum contradiction matrix is a Robinson matrix. It therefore fulfills all the inequalities defining perfect order: Yi, jn ≥ Yi,kn, Yk jn ≥ Yk, In, i ≤ j ≤ k < n. In real phylogenetic data, some taxa may contradict the inequalities for perfect order. Contradictions to perfect order correspond to deviations from a tree or from a split network topology. Efficient algorithms that search for the best order are presented and tested on whole genome phylogenies with 184 taxa including many Bacteria, Archaea and Eukaryota. After optimization, taxa are classified in their correct domain and phyla. Several significant deviations from perfect order correspond to well-documented evolutionary events.

Distance-based approaches to phylogeny use estimations of the evolutionary distance between sequences to reconstruct an evolution tree. If the evolution can be represented by an X-tree, the different sequences can be ordered so that the distance matrix , n i j Y , representing the distance from a leaf n to the path (i, j ), is perfectly ordered meaning that ,After ordering of the sequences, the distance matrix Y i j n , permits to visualize phylogenetic relationships between taxa and to localize deviations from perfect order. The effect of perturbations resulting from lateral gene transfer or crossover can be modeled probabilistically. The order is shown to be quite robust against many perturbations. We have developed algorithms to minimize the level of contradiction in the order of the sequences. These algorithms are tested on the SSU rRNA data for Archaea. The degree of contradiction after optimization is for most taxa quite low. Regions in the taxa space with deviations from perfect order were identifi ed.

We describe the conditions under which a set of continuous variables or characters can be described as an X-tree or a split network. A distance matrix corresponds exactly to a split network or a valued X-tree if, after ordering of the taxa, the variables values can be embedded into a function with at most a local maximum and a local minimum, and crossing any horizontal line at most twice. In real applications, the order of the taxa best satisfying the above conditions can be obtained using the Minimum Contradiction method. This approach is applied to 2 sets of continuous characters. The first set corresponds to craniofacial landmarks in Hominids. The contradiction matrix is used to identify possible tree structures and some alternatives when they exist. We explain how to discover the main structuring characters in a tree. The second set consists of a sample of 100 galaxies. In that second example one shows how to discretize the continuous variables describing physical properties of the galaxies without disrupting the underlying tree structure.