QUANTITATIVE METHODS OF TAXONOMY:NUMERICAL TAXONOMY

In 1963, Sokal and Sneath (Sokal, RR and Sneath, P.H.A. 1963-Principles of numerical taxonomy, San Francisco) introduced the new concept of numerical taxonomy. This new approach to taxonomy employs computers and statistical methods for establishing the degree of similarity among taxa. They laid down certain postulates which in their own words are as follows:

1. The greater content of information in the taxa of a classification and the more characters on which it is based, the better a classification will be.

2. A priori (every) character is of equal weight in creating natural taxa.

3. Overall similarity between any two entities is a function of their individuals similarities in each of the many characters in which they are compared.

4. Distinct taxa can be recognized because correlations of character differ in the groups of organisms under study.

5. Phylogenetic inferences can be made from thetaxonomic structures of a group and from character correlations given certain assumptions about evolutionary pathways and mechanisms.

6. Taxonomy is viewed and practised as an empirical science.

7. Classifications are based on phenetic similarity.

In numerical taxonomy it is the computer and not the author who fixes the weightage for the characters. Therefore the subjective element has yielded place to the objective and this is the greatest merit of numerical taxonomy. On par with its merit of objectivity there is also the other merit of being able to handle hundreds of unit characters of extremely diverse kinds taking the help of a computer.

From the foregoing account, it follows that a Numerical Taxonomist has to proceed through the following steps, for the realization of his goals.

1. Choice of units for study: Whether it is an individual or strain or species that is to be the subject of study is first determined. The smallest units figuring within a programme of study are called Operational Taxonomic Units (O.T.U).
2. Character Selection: Each O.T.U. is carefully studied for determining its unit characters, a unit character being one or two or more states, not lending itself for further subdivision. For a fairly satisfactory analysis, at least 50 to 100 such unit characters should be determined. Once the unit characters are fixed, they are coded. In a two state coding the characters are divided into + and – or as 1 and O. The positive characters are recorded as + or as 1 and negative characters as – or as 0.1n case the organ possessing a given character is missing in an organism, the character must be scored NC which means no comparision. The multi-state characters may be either quantitative or qualitative. Quantitative characters can be expressed by a single numerical value corresponding to their range of variation. Qualitative multi-state characters cannot be arranged in some order, and no reliable sequence can be established. In such cases, qualitative characters are conveniently converted into some new characters. The information so secured is used for preparing at X n table, t standing for the number of O.T.U and n for the number of unit characters. This table gives us the Data Matrix. The table below is a data matrix for 4 0.T.Us and 3 unit characters:

3. Measurement of Resemblance: From the data so collected, a comparison of the O.T.U is made and the degree of similarities established. If the similarity is complete it is then expressed as S (100% similar) and if there is no resemblance whatever, the similarity is zero (0). From this data, a similarity table, tabulating the S coefficients, one for each O.T.U. is then constructed which enable us to bring together all those O.T.U whose members have the highest mutual similarity. These constitute clusters or phenons.

4. Cluster analysis: The next logical step is an analysis of the clusters. We may fix arbitrarily certain levels of similarity as appropriate to certain ranks and on the basis of S coefficients running through the members of a cluster. Each members maybe assigned a rank appropriate to it in terms fixed earlier. By arranging the various O.T.U into their respective clusters based on their appropriate ranking, we may draw different phenon lines, each indicating the degree of closeness between the O.T.U. understudy.

5. Discrimination– Once this study is completed, the entire data matrix will show us which characters are more constant and which therefore should be employed for keying and diagnosis.