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 were crossed and offspring were produced in a ratio of 12 white sheep to 3 black sheep to 1 brown sheep, what are the genotypes of the offspring?A) The white sheep could be A-B- or aaB-.
B) The white sheep could be A_B_ or aabb.
C) The white sheep could be A_B_ or A_bb.
D) The white sheep must all be aabb.
E) The white sheep must all be A_B_.

C) The white sheep could be A_B_ or A_bb.

Explanation:

Given that in a certain population of sheep, coat color is influenced by two genes, in which:

Gene A: influence pigment production

Gene B: influence black or brown pigment.

Since Gene B influences Black or Brown pigment production and we are given three coat color (white, black and brown), definitely, this implies that Gene A influences White  pigment production.

NOW, If two heterozygous sheep were crossed; definitely we knew our heterozygous genes will be AaBb, so if two of these were crossed;

Offspring that were produced were in the ratio of 12 white: 3 black : 1 brown

So, we are asked to deduce, what is the possible genotype of the offspring:

If a cross occur between AaBb:

i.e AaBb × AaBb

we have the following gametes for the cross: (AB, Ab, aB, ab)

                 AB                       Ab                 aB                     ab

AB            AABB                 AABb              AaBB                AaBb

Ab            AABb                  AAbb              AaBb                Aabb

aB            AaBB                   AaBb              aaBB                aaBb

ab            AaBb                   Aabb                aaBb               aabb

So, since gene A influences white pigment production; if can either be A_B_ or A_bb.

Since gene B influences black or  brown pigment production;

then aaB_ represent Black sheep

and aabb represent homozygous recessive Brown sheep.

So for white sheep; we have the following gene:

( AABB, AABb, AaBB, AaBb, AABb, AAbb, AaBb, Aabb, AaBB, AaBb, AaBb, Aabb ) = 12

Black sheep = (aaBB, aaBb, aaBb) = 3

Brown = (aabb) = 1

Therefore, The white sheep could be A_B_ or A_bb.

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