Put forward by Darwin in the middle of the nineteenth century, the idea of the origin of species by natural selection (Darwinism-1) did not initially cause public resonance. Somewhat later Darwinism became the subject of acute controversy, during which time it was reduced to a coarse concept of anthropogenesis (Darwinism-2). The latter was less significant than the more adequate idea of K. Linnaeus concerning the inclusion of Homo in the system of the animal kingdom, but this was deliberately belittled by Linnaeus. The reaction to the lag of historicism in biology was the generalization of Darwin's rather narrow work on the origin of species into an expanded ideological doctrine (Darwinism-3) with an ideological struggle unfolding around it. In the course of this generalization, an idea of micro- and macroevolution was formed (although it does not always differ), the study of which is associated with its own range of problems. By the 20-30s of XX century, fierce discussions around microevolution led to the creation of a synthetic theory of evolution (STE, Darwinism-4), which turned out to be the standard scientific program of neo-Darwinism to demonstrate how macroevolution develops from microevolution. Mathematical models of population genetics, population dynamics, population ecology and related problems became the basis of STE. The study of these models yielded important mathematical results, but their biological meaning and relation to speciation remains unclear without careful meaningful biological interpretation and accurate correlation with the data of empirical biology (an example of which is the work, since the 1960s, of the Biometric Seminar of O.M. Kalinin in Leningrad State University-Saint Petersburg State University). At the same time, a more or less attentive attitude to the species organization in various living beings reveals its great diversity, as well as a radical difference between the overwhelming number of species from the classical «Darwinian» ones, so that Darwinian microevolution (demonstrated on the material of an insignificant fraction of species) proceeds against the background of the microevolution of a disproportionately larger number of non-Darwinian species. Such a disproportionately greater diversity of the organization of microbes (including prokaryotes) and lower organisms (lower plants, invertebrates) also gives more variety to the concepts of microevolution, which is usually substantiated by indirect evidence and supported by research in related fields, while for specific taxa the mechanisms of microevolution appear to be very different and often hypothetical. This requires a different methodology for the study of historical reconstructions of speciation, taking into account the distinction between history and genesis which entailes a variety of mechanisms of change, direction, continuity and discontinuity, etc., which already affects the problems of studying macroevolution.