Abstract
A theoretical analysis of the surname state of the population (the vector of namesake concentrations in the male component of the population) and its dynamics as a result of random surname drift is presented. An approximation of such a process by the Wright-Fisher model of a population with non-overlapping generations without selection pressure is used, i.e., an approximation by a sequence of nested random samples with the replacement from fathers’ surnames in the population. The sample size is N/2 according to the size of the male component in the population of size N. In the same population, processes of random drift of both surnames and genes simultaneously occur. Their cardinal difference is that the sample size of surnames is four times smaller than the sample size of autosomal locus alleles. The analysis of random drift is simplified when moving from concentration coordinates to the square roots of them. As generations change, the state receives a sample deviation, measured by angular distance, and its mean square gives the rate of divergence, stabilizing in the new coordinates. An adaptation (in relation to the analysis of surname drift) of a known in population genetics result about the nature of divergence at a stage of a relatively small number of generations compared to the size of the population is given. The divergence of surnames occurs four times faster than the divergence of allele concentrations.