Cladoendesis is a method of phylogeny analysis opposed to various matrix methods. In contrast to matrix methods, in cladoendesis phylogenetic trees are not built each time as new ones, but are reconstructed based on the previous results. Each character of each taxon is compared with its ancestral condition in the ground-plan of the higher taxon. The revealed part of the phylogeny is represented in a form of hierarchical classification. In addition to the principles of natural classification elaborated by C. Linnaeus, P.-A. Latreille, and others, evolutionary theory elaborated by Ch. Darwin and others, and principles of phylogenetic systematics elaborated by W. Hennig and others, cladoendesis includes rank-free dual nomenclature system (DualNom) and advanced method of text layout elaborated by the author. Important components of cladoendesis are the use of the term "plesiomorphon" and taking into account such important evolutionary events as conservation and deconservation of characters. Cladoendesis allowed the author to make comprehensive revision of the phylogeny of Ephemeroptera, find homology in the structure of the maxillae of adult Aphaniptera, larval maxillae of Neuropteroidea-Birostrata, larval legs of Nannomecoptera, and genital parts of some insect taxa. It also allows understanding the nature and evolution of insect metamorphosis. It is generally believed that initially insect ontogenesis proceeds the shortest way, while such phenomena as substitutions of organs by means of their atrophy and subsequent restoring are secondary. In contrast to this, the flagellum of the antenna of Amyocerata initially grows by addition of proximal segments and simultaneous loss of distal ones; in many taxa, including Metabola (insects with complete metamorphosis), distal segments are not aborted. Some authors tried to explain the origin of complete metamorphosis by various reasons: ecological, morphogenetic, or others. This approach is wrong because all insects with complete metamorphosis constitute the holophyletic taxon Metabola Burmeister 1832, i. e., originate from a single ancestral species which acquired this kind of metamorphosis. If complete metamorphosis could appear in response to some factor, it would appear many times in different species, in which case the taxon Metabola, characterized by complete metamorphosis, would be polyphyletic. The holophyly of Metabola is well proven by cladoendesis but cannot be revealed by any matrix method. Based on understanding of these facts, the author was able to discover the specific features which appeared in the common ancestor of Metabola and then became conserved and were inherited by all its descendants. These features include loss of the scape in the larval antenna (leading to a peculiar transformation of antennae in metamorphosis) and a peculiar mode of leg transformation during molt from larva to pupa. During the larval/pupal molt, the leg loses musculature and gets an immobile knee bend, so that the pupa is unable to use its legs. This conserved feature determines the inactive mode of life of the pupae of most insects. It is usually believed that male coccids (Gallinsecta De Geer 1776) have metamorphosis similar to the complete metamorphosis of Metabola. But the phylogenetic position of Gallinsecta and Metabola, as revealed by cladoendesis, does not allow one to assume common modifications in their metamorphoses. Now, when concrete autapomorphies of Metabola have been found, it becomes possible to compare metamorphoses of Metabola and Gallinsecta. Examination of Orthezia urticae and some other coccids shows that metamorphosis of their males shares no modifications with the true complete metamorphosis. The inactive mode of life of their nymphs is not connected with any anatomical reason, but purely with the fact that in the course of transformation from the feeding wingless larva to the non-feeding winged adult, the nymph has already lost its mouth apparatus and has not yet got functional wings, so it does not need to move. At the same time, actively feeding stages of Gallinsecta, both males and females, have an unusual mode of molt transformation of the legs and antennae; this is a unique autapomorphy of Gallinsecta not found in any other insect taxon.
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