The range of the statistical methods used in comparison and grouping of vegetation data is rich and diverse. The discussed classification method has been initially offered by E.S. Smirnov (1960) for estimation of similarity of biological taxa. It caused great interest and criticism of the scientific community, was included into the methodological reviews on numerical taxonomy, got a mathematical justification and is widely and successfully used in practice of quantitative taxonomy.
The main feature of Smirnov’s method, distinguishing it from other quantitative approaches to classification, is the account of the degree of expressiveness ("weight") of characters: the contribution of a character to the similarity of two taxa is inversely proportional to its weight, ie, the fact that the simultaneous presence of a rare character is more important. The rarity of an attribute is established on frequency of its occurrence in a matrix of compared objects.Initially, the method allowed operating only with binary (qualitative) taxonomical characters. In more recent studies E.S. Smirnov (1969) summarized his proposals and made them available to use attributes, expressed in nominal ordinal and quantitative scales, as well as polymorphisms - the simultaneous presence of two or more states of attribute.
V.M. Schmidt (1970), along with the popularization of Smirnov’s method for the purposes estimation of proper kinship degree of taxa proposed to introduce it in the analysis tools of comparative floristics, in particular, to use it to compare floras in their historical and geographical ties as path to "objective" floristic zoning. In fact it means the possibility of using the method of taxonomic analysis as a variant of comparative Q-analysis - cluster analysis of botanical data in which the objects of comparison are floras and relevés meanwhiletaxa or elements of factors-sets (the last was namely suggested by V.M. Schmidt) are used as characters with the optional expression of their weight in quantitative scale. Important was the fact that such usage maintains all the conceptual apparatus of Smirnov’s method, and the key to its implementation in this new quality became a method of encoding of character modalities. This coding algorithm V.M. Schmidt examined in detail by the example of metering number of species of each historical and geographical elements in structure of compared floras.
The aim of this study was to compare the results of the classification of floras performed using the method of Smirnov’s taxonomic analysis and "traditional" methods of comparative floristics. WPGMA-linkage hierarchical clustering was done in Statistica 8.0. Used binary and quantitative similarity indices: Czekanowski, Cosine and Relativized Sørensen (Pesenko, 1982). Comparisons were made both for complete taxonomic lists and for full and head family-species taxonomic spectra.
Input and storage model floristic lists, calculation of their taxonomic parameters, the construction of the taxonomic spectra , the calculation of similarity matrices of stated above indices, as well as the matrix of paired taxonomic relations between compared floras using Smirnov’s method (hereinafter referred to as "Smirnov index") were performed in software IBIS (Zverev, 2007, 2012).
We used studied earlier by us floras (Ebel, 2011, 2012) of 13 botanical-geographical regions as model data. The regions are located in the north-western part of Altai-Sayan mountain region (ASR), in Northern Sub-Province of Altai-Sayan floristic province (ASP). These regions are as follows: WA, NWA, NA, NEA – Altaic group of regions (West, Northwest, North and Northeast Altai); MS – Mountain Shoria; SR– Salair; KB – Kuznetsk intermountain basin; KAW, KAE, KAN – Kuznetsk Alatau (Western, Eastern and Northern parts); MB – the north-western part of Nazarovsk-Minusinsk intermountain basin; KTW, KTE – Kolyvan-TomskPlateau (Western and Eastern parts).
Joint flora of study area is characterized by the following values: species – 2017, genera – 565, families – 125; the same figure for the most floristically rich region (WA) totaled 1376, 468 and 112, and for the most poor region (KAW) – 773, 348 and 97, respectively.
Comparison of complete species lists using of traditional similarity indices of leads to similar results. Clearly distinguishedis cluster combining 2 Western Altai regions (WA+NWA). Two other regions of the Altai (NA+NEA) are connected rather closely but this cluster also includes KAW and MS. The rest regions are distributed in 2 clusters: "Upper Tchulym" (MB+KAE) and "Kuznetsk" (SR+KB+KTW+KTE+SR). Smirnovindexgives almost the same picture as the "traditional" indices. However, it revealed close relationship between regions (KAW+MS; MB+KAE). This is most clearly using quantitative approach, when taking into account not only the presence of the species, but its occurrence.
Similarity analysis of districts bytaxonomic structure of flora (family-species spectra) produced somewhat different results. The use of Relativized Sørensen allowed to allocate the same 4 cluster. However, geographically dispersed clusters (MB+KAE and WA+NWA) were much closer by the taxonomic structure than by full species composition.
Significantly different pattern was found when comparing the taxonomic structure of floras using Smirnov index and3 clusters were respectively clearly identified: 1) The plain and low mountain regions (KB+MB) + (KTE+KTW+SR); 2) Kuznetsk Upland (excluding the eastern part): KAW+KAN+MS; 3) Altai and Eastern part of the Kuznetsk Alatau: (WA+NWA) + (NEA+NA) + KAE.
Comparison using the head spectra (24 families, accumulating at least one percent of taxa in the average for all regions) using different approaches showed not very stable position of 3 regions: KB, KAE and MB. So, by Smirnov index (absence-presence) MB and KB fall in the "West Altai" cluster (WA+NWA). It can probably be explained by the abundance of Fabaceae species in these regions. However, the set of species in the Altai region and in the MB is significantly different (in particular, due to endemic species)!
This study allows concluding about the prospect of using the method of taxonomic analysis by Smirnov for quantitative processing of floristic data and application of the results for the purposes of floristic and geobotanical zoning.