A poultry farmer hopes to profit from the current craze for keeping egg laying chickens as pets and wishes to increase his stock of interesting and unusual breeds. (a) The farmer crossed a pure-breeding white chicken with a pure-breeding black chicken and found that 100% of their offspring (the F1 generation) were an attractive blue colour. Hoping to get more of these blue chickens he crossed several of the F1 offspring, but found that he had the following numbers of chickens in the F2 generation: ƒ|ƒnBlack, 28 ƒ|ƒnWhite, 30 ƒ|ƒnBlue, 60. Assign symbols to the alleles controlling these colour characters and draw genetic cross diagrams illustrating both crosses . Explain why the mode of inheritance of feather colour in this case means that the farmer will never be able to develop pure-breeding blue chickens.

To understand the mode of inheritance of feather color in this case, we need to assign symbols to the alleles controlling the color characters and analyze the cross diagrams.

Let's assign the following symbols:
- The allele for white color (W)
- The allele for black color (B)

Cross 1: Pure-breeding white chicken (WW) crossed with pure-breeding black chicken (BB)
In this cross, the genotype of the parents can be represented as:
White chicken (WW) x Black chicken (BB)

The F1 generation will have the genotype: WB (since each parent contributes one allele)
This means that all offspring in the F1 generation will have one white allele and one black allele.

Cross 2: Several F1 offspring (WB) crossed with each other
In this cross, the genotype of the F1 offspring can be represented as:
WB x WB

To determine the genotypes and phenotypes of the F2 generation, we can use a Punnett square:

| W | B
----|-----|----
W | WW | WB
----|-----|----
B | WB | BB

The Punnett square shows that if two F1 offspring (WB) are crossed, we can expect the following genotypes and phenotypes:

- 25% probability of getting a white chicken (WW)
- 50% probability of getting a blue chicken (WB)
- 25% probability of getting a black chicken (BB)

Based on the given numbers in the F2 generation: Black (28), White (30), Blue (60), we can deduce that the blue chickens (WB) are the most common in the F2 generation.

Now, let's explain why the mode of inheritance of feather color in this case means that the farmer will never be able to develop pure-breeding blue chickens:

The mode of inheritance here is incomplete dominance, where neither of the alleles (W or B) is completely dominant over the other. Instead, they blend together to produce an intermediate phenotype which is the blue chicken.

In the F2 generation, when blue chickens (WB) are crossed with each other, we get a combination of different genotypes: WW, WB, and BB. This means that no matter how many times the farmer crosses the blue chickens, they will always produce offspring with a mixture of white, blue, and black feathers.

To develop pure-breeding blue chickens, the farmer would need a homozygous genotype consisting of only blue alleles (BB). However, since the blue color is a result of incomplete dominance, such a genotype cannot be achieved through breeding blue chickens.

In summary, due to incomplete dominance, the farmer will not be able to develop pure-breeding blue chickens, and the feather color in subsequent generations will always be a mixture of white, blue, and black.