A phylogenetic tree can be subdivided according to a monophyletic hierarchical model, in which only monophyletic units figure, or according to a 'Linnaean' hierarchical model in which both mono- and paraphyletic units occur. Most present-day phylogeneticists try to fit the monophyletic model within the set of nomenclatural conventions that fit the Linnaean model. However, the two models are intrinsically incongruent. The monophyletic model requires a system of classification of its own, at variance with currently accepted conventions. Since, however, the monophyletic model is unable to cope with reticulate evolutionary relationships, it is unsuited for the classification of nature. The Linnaean model is to be preferred. This renders the acceptance of paraphyletic supraspecific taxa inevitable.