Evolutionary rank analysis

Methods for evolutionary rank analysis are explained and discussed in this section. The different approaches of evolutionary rank analysis have in common that the two-way data stmcture is analyzed piece-wise to locally reveal the presence of the analytes. A reference to the review of evolutionary methods by Toft et al. is included in the additional recommended reading list at the end of this chapter. 

J. Toft, Tutorial Evolutionary rank analysis applied to multidetectional chromatographic structures. Chemom. Intell. Lab. Syst., 29 (1995) 189-212. 

Evaluating of the Distribution of Components in the Peak by Local Rank Analysis. Complementary information about the evolution of the components inside the CE peak system can be obtained from local rank analysis. In this case, instead of estimating the rank of the whole D matrix, a succession of smaller submatrices derived from D is analyzed to get the evolution of the mathematical factors throughout the system. The most widely used evolutionary methods are as follows ... 

Basically, we make a distinction between methods which are carried out in the space defined by the original variables (Section 34.4) or in the space defined by the principal components. A second distinction we can make is between full-rank methods (Section 34.2), which consider the whole matrix X, and evolutionary methods (Section 34.3) which analyse successive sub-matrices of X, taking into account the fact that the rows of X follow a certain order. A third distinction we make is between general methods of factor analysis which are applicable to any data matrix X, and specific methods which make use of specific properties of the pure factors. 

It was the analysis of the 16S rRNAs that first revealed the unique evolutionary position of the archaebacteria, and defined the primary evolutionary divisions of life on this planet (4,6). Figure 1 shows an unrooted phylogenetic tree based upon complete 16S rRNA sequences of representatives of the three primary lines of evolutionary descent the archaebacteria, the eubacteria and the eukaryotes. Within these primary lines of descent other major lines of descent have been delineated. Within the eubacteria, for example, some ten major divisions are now recognized. It has been suggested that these be given a systematic rank equivalent to phylum (12). However, this chapter will not elaborate upon the emerging phylogenetic description of life on this planet. The reader is referred to a recent review for a dedicated treatment of this subject (4,12). 

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