Frozen Evolution. Or, that’s not the way it is, Mr. Darwin. A Farewell to Selfish Gene.

There are species and entire phylogenetic lines in which anagenetic changes occur very rapidly during evolution. In contrast, other species and other lines developed very slowly or did not change at all over a long time. In addition, the rate of evolution within a single phylogenetic line can change substantially over time – it can be small initially, can grow many fold within a certain interval and can then remain completely or almost completely unchanged. A sudden increase in evolutionary rate is generally connected with adaptive radiation of the given line; however, in many cases the reasons for the change remain unclear.
Where the evolution occurs at the usual rate, it is termed horotelic evolution. If its rate is less than normal, this is termed bradytelic evolution, while that with unusually high rate is termed tachytelic evolution. It is obvious that there are no absolute borderlines between the individual types of evolution and that inclusion of a certain species in one of these categories also depends on the evolutionary lines within which we attempt to define the individual categories in relation to one another. Bradytelic species within a rapidly evolving line can change faster in evolution than tachytelic species in a line in which most species evolve slowly. Simpson originally introduced these terms to categorize the taxonomic rate (see below) and defined its individual types on the basis of the character of categorization of the rates within a particular taxon (Simpson 1944). He demonstrated, for example, that the histograms of the number of genera evolving at a certain rate are highly unsymmetrical, where most of the species form a single, generally narrow peak on the graph and the numbers of genera evolving at slower or faster rates rapidly decrease on both sides of the graph. Simultaneously, especially on the side of more slowly evolving genera (and also frequently on the side of species evolving very rapidly) there is a statistically significant surplus of species in a great many taxa that evolve at a very slow or very fast rate. Simpson emphasized that, because of the statistical character of the method through which the individual categories of evolutionary rate are defined, we cannot speak about a specific bradytelic or tachytelic species, but only of groups of bradytelic or tachytelic species (Simpson 1961).
These terms are currently very frequently used in a broader sense and are also related to the rate of anagenetic changes. One of the attempts to make the individual categories of evolution more objective is based on comparison of the rate of anagenetic changes in a certain line with the theoretical rate of evolutionary changes occurring through the action of genetic drift. Then changes occurring more slowly than the minimum rate corresponding to genetic drift can be termed bradytelic evolution, while changes occurring at a faster rate that the theoretical rate of genetic drift in a population of the given size can be termed tachytelic. Rates falling in the interval between the theoretically minimum and maximum rates of drift can be termed horotelic. If a certain line evolves at a bradytelic rate, it is apparent that genetic drift is prevented by normalized (centripetal) selection or by evolutionary limitations. On the other hand, in cases of tachytelic evolution, it is apparent that the change is caused by directional selection and not genetic drift. This categorization of rates of evolution has the chief disadvantage that it is rather difficult, in practice, calculate the theoretical rate of genetic drift.
Some authors also mention ultrabradytelic evolution as a separate category. Microscopic organisms evolved at ultrabradytelic rates throughout the entire Paleoproterozoic and Mezoproterozoic, i.e. at least in the period 3.5 to 1.1 billion years ago (Schopf 1980). Some studies state that the period of ultrabradytelic evolution lasted to the beginning of the Phanerozoic, i.e. until 600 million years ago (Schopf 1994). During the Phanerozoic, only asexual organisms evolved at ultrabradytelic rates. For example, it is known that a great many blue-green algae described on the basis of microfossils from the Proterozoic are morphologically almost identical with modern species of blue-green algae (Schopf 1994). It is not clear whether ultrabradytelic evolution is specific for only blue-green algae (which are actually not algae at all, but bacteria) or whether it applies to all organisms living at the time of the Proterozoic and whether faster forms of evolution began only with the establishment of sexual reproduction, which could have occurred somewhere at the borderline between the Mezoproterozoic and Neoproterozoic.