For codominant loci, each allele can be associated with one factor. If n alleles are present, the ith allele is represented by a series of n binary codes with a 0 in all locations, except in the ith position, which contains a 1. For example, in a two allele system the allelic codes are:
1 0 (allele 1)
0 1 (allele 2)
The three possible phenotypes are:
1 0 (union of alleles 1 and 1)
1 1 (union of alleles 1 and 2)
0 1 (union of alleles 2 and 2)
An unknown phenotype is coded as 0 0. Spaces between the codes
are very important; they must be included when entering the
phenotypes into the pedigree file as described below.
A locus with three codominant alleles is coded as:
1 0 0 (allele 1)
0 1 0 (allele 2)
0 0 1 (allele 3)
The six possible phenotypes are:
1 0 0 (union of alleles 1 and 1)
1 1 0 (union of alleles 1 and 2)
1 0 1 (union of alleles 1 and 3)
0 1 0 (union of alleles 2 and 2)
0 1 1 (union of alleles 2 and 3)
0 0 1 (union of alleles 3 and 3)
and an unknown phenotype is 0 0 0.
The advantage of the binary factor coding scheme is evident when a recessive disease gene is under study. To code such a system, we could indicate the normal gene by the presence of a single factor (1) and the disease gene by the absence of this factor (0). The phenotype 1 (unaffected) now corresponds to two possible genotypes, either the union of allele 1 and allele 1 (noncarrier) or the union of allele 1 and allele 0 (carrier).
This simple coding is usually not sufficient because both homozygote recessive and unknown phenotypes are coded as 0. To account for this, we introduce a second factor for which a 1 indicates that the phenotype is known, and a 0 that the phenotype is unknown. The allelic codes are:
1 1 (allele 1)
0 1 (allele 2)
and the possible phenotypes are:
1 1 (union of alleles 1 and 1, or alleles 1 and 2)
0 1 (union of alleles 2 and 2)
0 0 (unknown)