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Genetics of comb type:
Comb type in chickens is due to two genes, the rose comb gene, R, and the pea comb gene, P. These two genes are on different chromosomes. The lack of these genes is represented with lower-case letters, r and p. More correctly stated, r and p (or r+ and p+ to indicate they are the wild-type genes) are the genes that replace R and P when they are not present. A chicken with a single comb is lacking both R and P genes and so could be represented as (r, r) for rose comb and (p, p) for pea comb. Some authors will combine this notation and write (rrpp) to represent the genes for single comb. I prefer the first way of writing the genes for the purposes of this text.
A chicken with a rose comb will have one of the gene combinations: (R, R) with (p, p), or (R, r) with (p, p). A bird with a pea comb will have (r, r) with (P, P), or (r, r) with (P, p). Since one copy of the rose or pea gene is sufficient for that comb type, these genes can be thought of as dominant. However, they act together to create the walnut comb when both rose and pea comb genes are present.
Poultry with a walnut comb have at least one copy of both the rose comb gene and the pea comb gene. The gene combinations that give walnut comb are: (R, R) with (P, P), (R, r) with (P, P), (R, R) with (P, p) and (R, r) with (P, p).
To explore the genetics of comb type, lets cross a pea comb chicken, (r, r) with (P, p), and a rose comb chicken, (R, r) with (p, p). Because two genes on different chromosomes are involved, there is more bookkeeping than if there were only one gene involved, but the principle is the same and no more difficult. We first have to consider the combinations of the rose comb genes of the two parents, then the combinations of the pea comb genes of the two parents. Then we realize that each of the rose comb combinations can occur with each of the pea comb combinations. In the end there are 16 combinations in all.
The four possible combinations for the rose comb genes from the two parents are: (R, r), (R, r), (r, r) and (r, r). The four combinations for the pea comb genes from the two parents are: (P, p), (P, p), (p, p) and (p, p). Since each of the four rose comb combinations can occur with any of the pea comb combinations, we now have to consider each of the rose comb combinations with each of the pea comb combinations (16).
The figure above shows how to make a helpful drawing. Make a list (column) of the four rose comb gene combinations on one side and the pea comb genes on the other side. The combinations of the first rose comb gene pair with all the pea comb gene pairs is shown in the figure by the connecting arrows. Considering the (A, a) of the drawing to be (R, r), the possible combinations of the first rose comb gene pair with the pea comb gene pairs are: (R, r) with (P, p) twice [we get this combination twice], and (R, r) with (p, p) twice. The second rose comb gene pair with the pea comb genes gives the same combinations: (R, r) with (P, p) twice and (R, r) with (p, p) twice. The third rose comb gene pair with the pea comb gene pairs gives: (r, r) with (P, p) twice and (r, r) with (p, p) twice. The last rose comb gene pair with the pea comb gene pairs gives the same: (r, r) with (P, p) twice and (r, r) with (p, p) twice.
So, of the 16 possibilities, four of them are (R, r) with (P, p) and is walnut comb, four are (R, r) with (p, p) and is rose comb, four are (r, r) with (P, p) and is pea comb, and four are (r, r) with (p, p) which is single comb. We have four out of 16 chances (25% chance) to get a walnut comb from this cross, four out of 16 chances to get rose comb, four out of 16 chances to get pea comb and four out of 16 chances to get single comb.