Abstract
Mainly for use on high-speed computer, a method of calculating coefficients of inbreeding and relationship is proposed as the one where all the procedures can be proceeded by perfectly mechanistic operations and judgements. This method is preferrable to the path method widely in use in animal and poultry breeding, even when the coefficients are to be calculated by hand, if the pedigrees are so complicated that mistakes might occur in picking up common ancestors and relevant connecting paths on the diagram.
A pedigree line is defined here as the record of a series of ancestors appearing in the process of tracing the pedigree of any individual, say I, back to one ancestor of his, provided that the line include the individual I himself as the first entry. By the pedigree lines for I are meant all the pedigree lines obtained for I by tracing back to each of all the ancestors of a certain number of generations earlier. Comparison of pedigree lines is defined as an operation of comparing one pedigree line for I and one for J and judging if there appears any same individual on the two lines compared. When such individual appears, it be recorded as a common ancestor for I and J, provided that, if more than one of such individuals appear in one comparison, only the one nearest to I and J be recorded. Comparison of pedigree lines between I and J means comparison of pedigree lines for I and those for J in all possible combinations.
The inbreeding coefficient for individual X be calculated by the following formula after making comparison of pedigree lines between the sire and the dam of X:
FX=(1/2)n+n'+1∑iki(1+FAi),
where n and n' are the number of generations over which the sire's and dam's pedigrees trace back, and ki is the number of times common ancestor Ai was recorded in the comparison of pedigree lines.
The coefficient of relationship between X and Y be calculated by the following formula after making comparison of pedigree lines between X and Y:
RXY=(1/2)n+n'∑iki(1+FAi)/√(1+FX)(1+FY)
where n and n' are the number of generations over whicn the pedigrees of X and Y trace back, and ki is the number of times common ancestor Ai was recorded in the comparison of pedigree lines.
A few examples of application are given. Brief comments on the nature of the method and on some practical problems which may occur in the use of the method on high-speed computers are also given.
