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: Black, 28 White, 30 Blue, 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, let's assign symbols to the alleles controlling the color characters. We can use "B" for the dominant allele that produces black feathers, "b" for the recessive allele that produces white feathers, and "Bl" for the allele that produces the attractive blue color.

Based on the information given, the original cross was between a pure-breeding white chicken (bb) and a pure-breeding black chicken (BB). Since all the F1 generation chickens were blue, we can conclude that the blue color (Bl) is dominant over both black (B) and white (b).

The cross between several F1 offspring would look like this:

F1 (Blue) x F1 (Blue)

BBBl x BBBl

The F2 generation had the following numbers:

Black: 28
White: 30
Blue: 60

From these numbers, we can deduce the genotypes of the F2 chickens. Let's assign "B" for Black, "b" for White, and "Bl" for Blue:

BB (Black) = 28
Bb (Black) = 0 (none)
bb (White) = 30
BBBl (Blue) = 60

Now, let's analyze the mode of inheritance and why the farmer will never be able to develop pure-breeding blue chickens:

1. Inheritance: In this case, the blue color (Bl) is a result of a heterozygous combination of alleles (BBl). This means that the blue color is not a pure-breeding trait on its own. It requires the presence of both black (B) and white (b) alleles to produce the blue color.

2. F2 generation: The F2 generation results show that there are black (BB) and white (bb) chickens present. If the blue chickens were pure-breeding, we should only see blue chickens in the F2 generation. However, the presence of black and white chickens indicates that the blue chickens are not capable of producing a pure-breeding blue offspring.

3. Crossing blue chickens: If the farmer continues to cross the blue (BBBl) chickens, they will always get a mixture of black (BB), white (bb), and blue (BBBl) chickens in subsequent generations. The blue chickens can never produce a completely pure-breeding blue line.

In summary, the mode of inheritance in this case demonstrates that the blue color is a result of a heterozygous combination of alleles, and therefore, the farmer will not be able to develop pure-breeding blue chickens.