In sheep, coat color is influenced by two genes. Gene A influences pigment production, while gene B produces black or brown pigment. If two heterozygous white sheep resulted in 12 white sheep, 3 black sheep, and 1 brown sheep, which genotype(s) of the white sheep explain this data?

It is a clear case of dominant epistasis which is in turn a result of gene interaction. In dominant epistasis, dominant allele of one gene masks the expression of another gene which is present at different locus.

When we will cross two heterozygous sheep AaBb x AaBb, progeny with following genotypes will be produced:

1- AABB - White

2- AABb - White

1- AAbb - White

2- AaBB - White

4- AaBb - White

2- Aabb - White

1- aaBB - Black

2- aaBb - Black

1- aabb - brown

In this case, dominant 'allele A' of gene A will mask the expression of gene B. This is the reason why genotype AABB, AABb, AAbb, AaBB, AaBb and Aabb are producing white phenotype. So in total, 12 sheep will produce white phenotype.

But when dominant 'allele A' is absent, then only gene B will be able to express if it is present in dominant form. This is the reason why aaBB and aaBb are producing black phenotype because here dominant allele A is absent and recessive allele a will not be able to mask the expression of gene B because gene B has dominant allele here i.e. BB and Bb. So 3 sheep will produce black phenotype.

But when when dominant 'allele A' is absent and gene B is in recessive form i.e. bb then a third phenotype will be produced which is brown. This is the reason why aabb will produce brown color. So only 1 sheep will produce brown phenotype.