Single diallelic random mating DS locus models

In this section, we consider a single random mating DS locus with two alleles: a ``disease'' allele, D, and a ``wild-type'' allele, d. Define three penetrance probabilities as follows:

Common models for the penetrances are:

• Strict-recessive: (Thomson and Bodmer [32]);
• Quasi-recessive: (Day and Simons [6]);
• Strict-dominant: (Thomson and Bodmer [32]);
• Quasi-dominant: (Day and Simons [6]);
• Additive: (Motro and Thomson [23]);
• Intermediate: (Spielman et al. [30], Louis et al. [21]).

In general, there are nine different mating types (Table 8), with frequencies denoted by , . Denote the frequencies of alleles D and d in the population of interest by p and q=1-p, respectively. Assume that mating is random at and the three genotypes DD, Dd and dd have the Hardy-Weinberg (HW) frequencies , and , respectively. Note that the models considered in this section may not always be realistic, but are nevertheless useful for studying the coverage of the ASP triangle and the impact of violations of various assumptions.

  
Table 8: Parental mating types, ordered genotypes and their frequencies for a two-allele DS locus with random mating and Hardy-Weinberg equilibrium.

The ASP IBD probabilities at the DS locus only depend on the allele frequency p and on the ratios of penetrances, and .

• Strict-recessive model
• Quasi-recessive model
• Additive model
• Strict-dominant model
• Quasi-dominant model