Description of the Divergence of Subpopulations in the Hierarchical System under the Analysis of Isonymy. III. Surname Inbreeding Coefficient

The hierarchical structure of metapopulations characteristic of humans with their subdivision into parts (subpopulations), usually classified on the basis of administrative-territorial division, principles of biological systematics, etc., is considered. Attention is focused on the description of surname divergence of subpopulations. The surname inbreeding coefficient Fs is expressed through the divergence indices, which is similar to the traditional inbreeding coefficient in population genetics. Its expansion by hierarchy levels into the sum of increments of the surname inbreeding coefficient corresponding to separate levels is obtained. The relationship between the found decomposition and the decomposition of the dispersion of the distribution of the surname concentration by subpopulations is demonstrated. With an additional assumption about the independence of the concentration of the surname and Fs, the factorization of Fs by hierarchy levels is found in line with the ideas of S. Wright. It is simplified with a small surname divergence of subpopulations when the Fs coefficient of the entire metapopulation is equal to the sum of the average Fs values at individual levels of the hierarchy. The underestimation of surname inbreeding was obtained, when subpopulations of a higher rank serve as units of observation instead of undivided subpopulations of the first level of the hierarchy. These results are statistical characteristics of the hierarchical structure, and not a feature of a particular population system, and do not follow from one or another model of microevolution. They are computationally independent of the hierarchical system under study, but allow characterizing their heterogeneity quantitatively. The results obtained refer to rural and urban hierarchical metapopulations as separate components of the entire population. In an appendix that can be read independently, genetic analogues of the properties found are given without proof in respect to the genetic structure of a metapopulation.