5. Frequency Parameters

The probability of a specified genotype for a founder equals the corresponding genotype frequency; this assumes that founders in the pedigrees constitute a random sample of the population. Since the frequencies sum to 1, a constraint reduces the number of parameters; the final frequency (for each locus or total) cannot be estimated.

To assume Hardy-Weinberg equilibrium and linkage equilibrium for the genotype frequencies, use papfqhw. Alternatively, to assume or test for linkage disequilibrium or deviations from Hardy-Weinberg equilibrium, use another PAM in the option list.

1. Allele frequencies

Module papfqd uses linkage disequilibrium D to compute genotype frequencies. D equals the excess of the haplotype frequency over the product of allele frequencies (locus 1, allele 1 and locus 2, allele 1). Therefore, the range of D depends on the allele frequencies; 0 represents equilibrium. Module papfqd restricts the genetic model to two loci with 2 alleles each. You might select this parameterization over papfqc in order to fix the allele frequencies.

Module papfqr2 estimates the squared correlation r² which equals D² divided by the 4 allele frequencies at the 2 loci. Parameter r² ranges from -1 to +1 since the sign of D is preserved for ease of estimation; 0 represents equilibrium. Both papfqd and papfqr2 restrict the genetic model to two loci with 2 alleles each.

2. Conditional allele frequencies

Module papfqc uses conditional allele frequencies in computing the genotype frequencies. Any locus in the model can be conditional on another locus; the locus with conditional frequencies must have 2 alleles. Other loci may have any number of alleles. Equality of the conditional allele frequencies equates to linkage equilibrium; significant differences indicate association between the loci. You might select this parameterization over papfqd for diseases associated with a marker locus. For example, estimate the frequency of the allele for diabetes mellitus (locus 1) conditional on HLA-DR3, conditional on HLA-DR4, and conditional on HLA-DRX (locus 2).

3. Haplotype frequencies

Module papfqh uses haplotype frequencies in computing the genotype frequencies assuming Hardy-Weinberg equilibrium. This parameterization removes any constraints on the numbers of loci or alleles.

4.Genotype frequencies

Module papfqg uses genotype frequencies directly, eliminating all assumptions about relationships between the frequencies.