2.3. Methods of numerical taxonomy

Numerical taxonomy, known also as phonetic, mathematical taxonomy, and multivariate morphometrics (Singh, 2010), is mainly based on the overall affinity (similarity) at any taxonomic level; i.e., species, genus, family, etc. In this study, the similarity or variation will be measured at the species level (represented by specimens). An equal number of specimens of each species (12 specimens) were used. The resemblance between the fundamental taxonomic units is determined in two steps: First, measuring the similarity values (or distance values) between all possible pairs of specimens under study for all of the studied characters and character states. Second, forming the similarity matrix. This matrix was analyzed using the numerical taxonomy technique supplied in the Minitab program, version 17 (Minitab, 2017).

All characters studied, including morphological, scanning, anatomical, in addition to the numerical analysis have been shown in the forms of tables, figures, plates, microphotographic pictures, and dendrograms in order to determine the similarities or dissimilarities between the studied species. The proposed keys will be established based on various posterior characters. The phenetic analysis will be based on overall affinity (resemblance). The presence of a consistent character combination defining a particular taxon is achieved by using as many characters and evidence as possible. Sokal and Sneath (1963) recommended using numerical taxonomy. All of these characters should have equal importance. The weighing of traits may take two forms and the resemblance between the classification modules can be calculated in two steps.