# An Introduction to Mathematical Taxonomy by G. Dunn

By G. Dunn

Students of mathematical biology observe smooth tools of taxonomy with this article, which introduces taxonomic characters, the size of similarity, and the research of crucial elements. different subject matters contain multidimensional scaling, cluster research, identity and project innovations, extra. A familiarity with matrix algebra and hassle-free records are the only real prerequisites.

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One possible method is the following: 1. One considers the whole sequence to be a complex character, comprising several unit characters (the individual nueleotides) which can have states U, C, A or G. 2. One aligns the sequences in all possible ways. For example: UCAGCAAUCCGU UCAGCAAUCCGUAAA or UCAGCAAUCCGU UCAGCAAUCCGUAAA or UCAGCAAUCCGU UCAGCAAUCCGUAAA and so on. 3. For each possible alignment one counts the number of unit characters that match in the two aligned fragments. So, for the three alignments given above, the number of matches are one, three and twelve, respectively.

2 26 Measurement of similarity where p is the total number of binary characters studied, a is the number of characters where both OTUs have the code 1, b is the number of characters where OTU i is coded 0 and j 1, and so on. The number of matches is a + d, and the number of mismatches is b + c. This 2 x 2 table as used in numerical taxonomy is primarily a convenient arrangement of the data and should not be confused with conventional 2 x 2 tables which arise as the subject for a test of independence (see Sokal & Sneath, 1963, Chapter 6).

Principal components analysis thus leads to a set of p composite characters that are uncorrelated and are arranged in order of decreasing variance. e. the Y variables) account for most of the variation, it might be possible to use only these in subsequent analyses and thus achieve a considerable simplification. 3 by a brief mathematical account. 1, and clearly the pairs of measurements are highly correlated. H one wished to express the variation in these two characters on a single axis or dimension, what would be the 'best' axis to choose?