A Generalisation of an Approximate Method to Calculate Inbreeding Coefficients

Where, A is a common ancestor of the parents of X; n is the number of generations from the sire of X to A and n' the number of generations from the dam of X to A. Subsequently, Wright & McPhee (1925) developed a method for calculating an approximate inbreeding coefficient from a pedigree which is completed for only a limited number of generations, the residual pedigree being represented by randomly selected lines of descent. Complete pedigrees are compiled for i generations. Thus 2i individuals are recorded in the ith generation. Only one parent, chosen at random, of each of these 2i individuals is recorded in the {i + I )th generation. Thereafter only one parent of a recorded individual is random· ly selected and recorded in every generation. This procedure is continued with as far back into the ancestry as the research worker wishes to go. The estimated inbreeding coefficient is then obtained by adding the con· tributions of all ties, i.e. all paths joining sire and dam through a common ancestor. Three kinds of ties are distinguished: