Counts of Total Haplotype Pairs Produced by Genotypes
Provide a count of all possible haplotype pairs for each subject, according to the phenotypes in the rows of the geno matrix. The count for each row includes the count for complete phenotypes, as well as possible haplotype pairs for phenotypes where there are missing alleles at any of the loci.
Matrix of alleles, such that each locus has a pair of adjacent columns of alleles, and the order of columns corresponds to the order of loci on a chromosome. If there are K loci, then geno has 2*K columns. Rows represent all observed alleles for each subject, their phenotype.
When a subject has no missing alleles, and has h heterozygous sites, there are 2**(h-1) haplotype pairs that are possible ('**'=power). For loci with missing alleles, we consider all possible pairs of alleles at those loci. Suppose that there are M loci with missing alleles, and let the vector V have values 1 or 0 acccording to whether these loci are imputed to be heterozygous or homozygous, respectively. The length of V is M. The total number of possible states of V is 2**M. Suppose that the vector W, also of length M, provides a count of the number of possible heterozygous/homozygous states at the loci with missing data. For example, if one allele is missing, and there are K possible alleles at that locus, then there can be one homozygous and (K-1) heterozygous genotypes. If two alleles are missing, there can be K homozygous and K(K-1)/2 heterozygous genotypes. Suppose the function H(h+V) counts the total number of heterozygous sites among the loci without missing data (of which h are heterozygous) and the imputed loci (represented by the vector V). Then, the total number of possible pairs of haplotypes can be respresented as SUM(W*H(h+V)), where the sum is over all possible values for the vector V.
Vector where each element gives a count of the number haplotype pairs that are consistent with a subject's phenotype, where a phenotype may include 0, 1, or 2 missing alleles at any locus.
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