Description of Divergence of Subpopulations in the Hierarchical System When Analyzing Isonymy: I. Variance as an Indicator of Divergence

Metapopulations typical of human populations with hierarchical subdivision into parts (subpopulations) corresponding to the classification of subpopulations based on administrative-territorial division (for example, village, village council, district, region, and so on) and on a genealogical approach founded on ethnogenesis, as well as on other principles of biological classification are considered. Each level of the hierarchy is a partition of the metapopulation into nonintersecting subpopulations, which in total make up its entirety and, in turn, have a hierarchical structure of subdivision. The properties of the variability of the quantitative trait of subpopulations under the hierarchical structure are studied using the example of such a trait as the concentration of a separate surname. The distribution of the surname concentration over subpopulations, characterized at each level by its mean value and variance, which reflects the surname divergence of subpopulations at the corresponding level, is analyzed. The study of surname divergence is important since, under appropriate assumptions, it reflects the genetic divergence and the genetic structure of the metapopulation. It is shown that a nonnegative contribution to the total variance corresponds to each separate level of the hierarchy, which is equal to the average value of the intragroup variance for the distribution of the surname concentration over its subpopulations. The decomposition of the total variance of the surname concentration in the metapopulation into the contributions of separate levels, which generalizes the addition rule for variances, is obtained. The underestimation value of the total variance, when subpopulations of a higher level (for example, districts) serve as observation units instead of undivided subpopulations of the first level of the hierarchy (for example, villages), is found. This allows one to judge the degree of the genetic divergence underestimation in the metapopulation as a result of ignoring surname variability at any of the hierarchy levels. The entire population is divided into two components with the hierarchical subdivision structure: rural and urban residents. The results of this work are equally applicable to each of them.