Hierarchies: To Rank or Not to Rank?

In the structure of any sufficiently complex system, including the classification one, two basic components can be generally distinguished, hierarchical and non-hierarchical. They relate to each other in a complex manner, manifest themselves in different ways, and their consistent combination in a single classification system is fraught with serious methodological difficulties. All this creates a serious multifaceted hierarchy puzzle in systematics.

A hierarchical component of the structure of the classification system implies a certain subordination of its classification units (taxa, partons) set by a hierarchization scale, which establishes both the sequence and character of this subordination; this scale can be of two kinds. The external scale is borrowed from a certain ordering system independently of the classification system in question; it is universal with respect to its structure and determines an absolute hierarchy in it: classification units can be arranged in this hierarchy independently of each other with reference to this scale. The internal scale is part of the classification system in question; it is local with respect to its structure and determines a relative hierarchy in it: the position of the classification units in such hierarchy is mutually interdependent. These two scales are exemplified by the hierarchy of monophyletic groups in phylogenetic classifications: it can be determined either absolutely with reference to a universal geochronological scale or relatively by a branching sequence within each lineage (see Section 5.7).

Hierarchical ordering is twofold [Salthe 1985, 2012; Knox 1998; Pavlinov 2018]. A linear hierarchy arranges the classification units according to varying degrees of importance; sometimes it is called an exclusive hierarchy. A typical example is the social hierarchy of the “host-clave” kind; in systematics, it occurs in the character ranking (weighting) according to their contribution to the classification. An inclusive (encaptic, nested) hierarchy means subordination of the classification units according to their levels of generality: units of a higher level of generality include units of lower levels of generality. Accordingly, the inclusive hierarchy establishes the relations of the “set-subset” or “whole-part” kind between these units.

A non-hierarchical component of the structure of a classification system means that the classification units are linearly arranged by the gradient of a certain external variable. The latter sets the order of these units along its gradient, but, in contrast to the case of linear hierarchy, nothing like their subordination is presumed. An illustrative example is the Ladder of Nature, in which taxa are arranged according to the complexity of the organisms allocated to them.

In taxonomic terminology, classifications with inclusive hierarchy are customarily designated as “vertical,” while those with a non-hierarchical arrangement are designated as “horizontal”; the latter are sometimes called parametric [Lyubishchev 1923, 1972], its not in the sense of [Subbotin 2001]. These components reflect substantially different aspects of the ordering of organisms and are weakly correlated with each other. As an illustrative example, it is enough to mention two classifications of tetrapods: classifying them by their kinship relation provides an inclusive hierarchy of monophyletic groups, while they are arranged linearly along a scale from cold-blooded to warm-blooded according to the properties of their thermoregulation.

Thus, these components can be reflected by different classifications of the same group of organisms, ordering their overall diversity in significantly different ways. Therefore, it is not possible to combine them consistently in a single taxonomic system; for each of them a particular system is to be construed. This collision gives rise to specific questions about the hierarchy puzzle: if both of these components are objectively inherent in the diversity of living beings and thus equally “natural,” and at the same time they are mutually incompatible, how should a classification be built to make it “globally” natural? If it is impossible to combine them harmoniously, which one should be preferred as the most natural “locally”? This problem evidently relates to the one of different kinds of “locally” natural classifications considered above (see Section 6.1).

Different PTTs answer these questions differently depending on which component of the TD is given the greatest importance. Scholastic systematics and cladistics, aimed at developing strictly “vertical” hierarchical classifications, are at one extreme. In them, the only scale of hierarchization is the branching sequence of the initial tree, either a generic-species scheme or a cladogram, according to which the respective classification units are arranged. The already-mentioned version of onto-rational systematics developing periodic classification systems (see Section 5.2.1) is another extreme. Somewhere between these two extremes are PTTs that pay equal attention to both components of the ordered diversity. Examples include Oken’s organismic natural philosophy, classical (Haeckelian) phylogenetics, and evolutionary taxonomy; they are usually called syncretic because they attempt to combine the uncombinable.

When working with inclusive hierarchies, another specific question about the hierarchy puzzle arises: an inclusive hierarchy can be either ranked or rankless. In the first case, clearly fixed levels of generality are distinguished and denoted by specific terms, and they are called taxonomic ranks: species, genus, family, etc. In the second case, the ranks are neither fixed nor denoted in any way.

Ranked hierarchy is established by a certain ranking scale, according to which both the sequence and number of fixed taxonomic ranks are determined. A set of taxa belonging to one rank constitutes the same taxonomic category, and it is termed the same as its corresponding rank (species, genus, etc.). According to the principle of rank equivalence, taxa of the same level of generality belong to the same rank as members of the same equivalence class, while those of different levels of generality belong to different ranks and are not equivalent in this sense. At an operational level, this principle is complemented by the principle of rank coordination, or the rule of uniform level [Starobogatov 1989; Vasilieva 1992, 1998; Shatalkin 1995; Lyubarsky 1996. 2018].

If the ranking scale is rigidly defined, it generates a strict hierarchy; this condition is usually met in the case of absolute ranking. In this case, the same sequence of taxonomic ranks is observed in different parts of a classification. In contrast, in the case of relative ranking, a non-strict (degenerate) hierarchy appears with its characteristic rank uncertainty [Zarenkov 1988; Pavlinov 2015, 2018]. The latter means that: (a) taxa cannot be unambiguously assigned to a specific rank; and (b) an equivalence of taxa of the same rank is not strict. With this, in the case of relative ranking, the more distantly taxa are located in a classification, the less it is possible to assess their equivalence [Pavlinov 2018]. The strict hierarchy is characteristic of most traditional classifications; typical examples of non-strict hierarchy are as follows. In traditional classifications, this happens in the case of extensional coincidence of the subordinate taxa of different ranks: for example, a monotypic family coincides in its species composition with its only genus [Gregg 1950, 1954; Sklar 1964; Gordon 1999]. In cladistics, non-fixed ranks are permissible, which makes it possible (a) to allocate the taxa with formally different ranks to the same level of generality, and (b) to use “out-of-rank”plesions [Wiley 1979, 1981; Gauthier et al. 1988; Pavlinov 1990,2005; McKenna and Bell 1997].

In the rankless hierarchy, fixed categories are not distinguished and not designated terminologically. In such a hierarchy, a certain sequence of the levels of generality is set depending on a particular research task being solved. One of the most notable examples is the fractal with a scaling hierarchy set by different levels of detail in the description of a complexly structured object; this concept is relevant to systematics [Burlando 1990; Minelli et al. 1991]. A non-strict hierarchy occupies an intermediate position between strict ranked and rankless hierarchies.

The hierarchy of the genus-species scheme of scholastics, which was a starting point for systematics, was rankless (see Section 2.2.2). Fixed ranks with specific names were “invented” in the 18th century; at first there were 4-5 of them, and then during the 19th and 20th centuries their number increased significantly [Stevens 1994; Ereshefsky 1997,2001a; Pavlinov 2015, 2018; Lyubarsky 2018]. With the fragmentation of the ranked hierarchy, the number of categories and their designations increased more and more, especially influenced by cladistics [Hennig 1966; Wiley 1981; de Queiroz and Gauthier 1992; Ereshefsky 2001a, 2001b, 2002], so a kind of “rank inflation” progressed [Stuessy 2008]. As a result, rank uncertainty increased, so the very meaningfulness of the over-complicated ranked hierarchy became doubtful. Based on this, it was proposed to abandon it and build rankless classifications in cladistics; in fact, this suggestion means formally a return to the genus-species scheme .

The coexistence of both traditional and cladistic approaches in contemporary systematics led to the fact that two hierarchical systems, ranked (classical) and rankless (cladistic), function in it almost on an equal footing. A contradiction between them, constituting another point of the hierarchy puzzle, is due to the lack of clear understanding of what fixed ranks might mean, whether they are needed or not, and if they are used, then what for?

To the extent that systematics is engaged in the development of natural classifications in their ontic understanding, the main question in this puzzle can be presented as follows: are there certain aggregations of organisms of different levels of generality really existing in the structure of Nature to which certain taxonomic ranks might correspond? If there are clearly delineated levels in this structure, the respective ranks are “real” in a classical sense; if not, they are nominal. With this, it should to be taken into account that different manifestations of the TD structure can be associated with different internested hierarchies (phylogenetic, biomorphic, typological, etc.), each with its own ranking scale; when considered together as components of the same faceted classification, they yield a kind of polyarchic system [Knox 1998].

Objectification of the ranked hierarchy implicitly presupposes a principal possibility of (or even need for) an absolute ranking scale; the latter is given different substantiations by different PTTs. In typology, it is inferred from an “objective” subdivision of Nature-as-superorganism into partons of different levels of generality [Beklemishev 1994; Lyubarsky 1996, 2018], which is rooted in the organismic natural philosophy of Oken. Similar to this in some respect is substantiation of an objective ranked hierarchy with a few fundamental ranks by reference to a “parallelism” between stages of evolutionary and ontogenetic differentiation of organisms [Ho 1988, 1998; Ho and Saunders 1993; Goodwin 1994; Shatalkin 1995, 2012]; this viewpoint ascends to the epigenetic typology of von Baer. In evolutionary taxonomy, the objectivity of ranks is substantiated by reference to adaptive zones and a kind of “quantum” shifting of evolving groups between them [Simpson 1961; Legendre 1972]. An objective nature of ranked hierarchy in biomorphics [Aleyev 1986] and in onto-rational systematics aimed at distinguishing various natural kinds [Webster and Goodwin 1996; Zakharov 2005] is substantiated in their own ways. The objective species rank is substantiated by reference to specific mechanisms of generating and integrity of species, from their divine creation to breeding mechanisms (see Section

6.7). However, according to the “Ladder” natural philosophy, and phenetic and cla-distic PTTs, there is nothing in Nature that would justify a unified ranked taxonomic hierarchy [Brown 1810; Bentham 1875; Kozo-Polyansky 1922; Sokal and Sneath 1963; Lpvtrup 1977; de Queiroz and Gauthier 1992; Zachos 2011].

Leaving aside a fundamental philosophical consideration of reality vs. nominality of taxonomic ranks as unresolvable under current circumstances, a critical question of the puzzle in question becomes more practical. It can be put as follows: does the ranked hierarchy bring anything important to the solution of some biologically meaningful tasks? A positive answer to it may go as follows. The system of fixed ranks gives classification a certain stability by serving as a kind of rigid frame that provides a specific basis for comparing taxa of different levels of generality [Simpson 1961; Vences et al. 2013]. A possible analogy here can be the Cartesian coordinate system: no one believes that such a system exists in reality— and nevertheless, it is very actively used in a variety of disciplines [Lyubarsky 2018]. Similarly, the ranked hierarchy makes it possible to bring different taxa from very distant fragments of classification into a certain relation to each other by establishing at least some “approximate” equivalence between them. Indeed, when experts speak of, say, orders of insects, mammals, monocotyledonous plants, etc., they usually mean an approximately similar (though hardly “the same”) level of generality different from that of the genera.

From this point of view, the problem of the impossibility of strict rank equivalence loses its acuteness. Ranked hierarchy is used as a special technical tool: though not too precise, it nevertheless allows us to solve some scientifically significant tasks with some approximation. For example, in many ecological studies of natural communities, the species category is of particular significance: it is important for specialists to compare just the species, even if they are theoretically defined differently [Schwarz 1980]. When considering the global evolutionary dynamics of TD, the family rank is most often considered as the main reference level [Smith 1994; Sepkoski 1996]. Excluding ranked hierarchy, all these and similar studies remain without an important basis for comparison.

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