Analysis of population genealogical structure II. using numerical pedigrees for pedigrees for calculation of inbreeding coefficient

摘要

A method for calculation of inbreeding coefficient F in a numerical pedigree with no reference to its graphic representation is suggested. For calculation of F, a formula, that does not take into account inbreeding coefficients of common ancestors and admits intersections in a loop is used. An advantage of this method is that it automatically finds all loops formed by paths to common ancestors. Detecting these loops via their tracing in a graphic pedigree with intersecting lines of descent creates a possibility of errors. A criterion of existence of at least one common link for two numerical paths is presented. It enables one to exclude pairs of paths to common ancestors that do not form loops. The methods considered form computing F in a given pedigree give exact values of the inbreeding coefficient for autosomal and sex-linked loci and generalize the known approximate approaches. The methods are illustrated by examples.