All the females in the first generation would lay a blue egg; since blue is dominate they only need 1 gene to lay a blue egg. You'll start getting white eggs again in second generation crosses from the females that have 2 white genes.
Finding the females that carry 2 white genes is easy, because they'll lay white eggs. it's the males and the females that carry 1 blue and 1 white that would cause you problems because you won't know what they carry unless you test their DNA or do test hatches and wait for their offspring to lay. To do that, you have to pair them with other birds whose genetics you know. For example, you pair a second gen male with female leghorns (you know they have 2 white genes) and hatch a bunch of their eggs. It should be a pretty large sample size, like 30+. If some of the female offspring lay a white egg and some lay blue, you know that the male has 1 white gene. If they all lay white you know he has 2 white genes. If they all lay blue, you know he has 2 blue genes.
This would also work for the second generation females to see if she has 2 blue or 1 blue and 1 white (I'm assuming you wouldn't use any second gen females that lay a white egg if colored eggs are the goal). Just pair them with a male leghorn and test their female offspring. If any of her offspring lay white, you'll know she carries 1 white gene.
Of course you could skip the testing phase but if I were doing it, I'd at least want to make sure that my males carried at least 1 blue gene. I should note that the pea comb has been found to have a connection with the blue egg gene so weeding out any straight combed males would give you a better shot. You could also just pair up second gen birds and see what you get from them.
You can breed full siblings, fathers to daughters, or mothers to sons if they have the traits you want. Because birds have more genetic diversity than mammals inbreeding doesn't usually have adverse effects.
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