Final answer:
The disease allele 'S' follows a dominant inheritance pattern, as the phenotype is expressed with only one copy of the allele. In horses, the gray and white alleles for skin color exhibit codominance, resulting in the appaloosa phenotype with both colors visibly expressed.
Step-by-step explanation:
Inheritance Patterns
The disease described in the question follows dominant inheritance because the presence of a single disease allele S results in the disease. This indicates that the allele for the disease ('S') is dominant over the normal allele ('s'). For the phenotype to be displayed in this scenario, just one copy of the 'S' allele is required, regardless of whether the individual is homozygous (SS) or heterozygous (Ss) for the trait.
Regarding the horse color, since an appaloosa horse displays a mix of gray and white patches, it indicates that neither color is completely dominant over the other and that the two alleles for color interact in a unique way. This is an example of codominance, where the gray and white alleles are expressed equally in the phenotype of the horse that is heterozygous for the skin color gene (possessing one allele for gray and one for white).