The multidimensional statistical method of cluster analysis permits the creation of clusters of objects on the basis of the similarity of the individual objects, where the distance between these clusters and the manner in which they are gradually immersed in one another express the degree and character of mutual similarity amongst the classified objects. If these objects are individual species of organisms and the degree of mutual similarity consists, for example, in the number of shared traits, then the created system of clusters can be used as a taxonomic system for this group. More serious attempts to create systems of some organisms using the methods of cluster analysis were made only in the middle of the last century (Michner & Sokal 1957). The usefulness of the relevant methods in biology was dependent on the existence of computers, as it required the processing of a large amount of data. This procedure came to be called numerical taxonomy or numerical phenetics. Numerical taxonomists assumed that, if the initial data set contains information on the maximum number of traits for all the studied species, the outputs of the relevant programs would be a hierarchically ordered system of clusters, objectively expressing the existing relationships amongst the studied organisms. Such a system could form a good basis for taxonomic classification of organisms. Experience in the use of the methods of numerical taxonomy has shown that, for a sufficiently large number of traits and using the same methods of cluster analysis, the results obtained are truly objective, i.e. individual taxonomists processing the same group of organisms come to more or less the same results. However, the choice of suitable methods of cluster analysis remains a problem. There are a great many ways of calculating the phenetic distances (or similarities) amongst the classified species on the basis of the individual traits and also a great many methods that can be used to form clusters on the basis of the phenetic distances, where each method usually provides qualitatively different results. Simultaneously, it cannot be stated that one method is the right one and the others are wrong. The choice of methods is a matter for the subjective decision of each taxonomist and thus the consequent taxonomic system is subjective.
When any phenetic taxonomic system is used, it must be constantly borne in mind that the system expresses only the similarity but not the relatedness of the organisms. In a great many systems this does not matter much, for example, if it is necessary to classify species that diverged apart at a single moment a long time ago. At other times, the use of a phenetic approach seems more like the only solution in a bad situation. If no traits are available, on the basis of which we could reconstruct the cladogenesis of the particular group, we will have no choice but to use phenetic classification. Finally, it should be pointed out that, where the input data consisted in selectively neutral traits, which changed during evolution at roughly a constant rate in all the species in the studied line, the obtained phenogram should be identical with the cladogenesis scheme and should allow us to reconstruct the relationships amongst the species of the particular phylogenetic line (see XXIV.6).