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Statistical probabilities with the blue egg gene

For a lot of my project birds, I am working with the blue egg gene to create blue or green eggs. A green egg is just blue, plus some brown color. This gene is tricky to work with for 2 reasons:

  • It is dominant – that means that a hen that lays a blue egg might only have 1 copy of the blue egg gene and so could make a chick that carries no copies.
  • The cockerels never lay eggs, so you can’t tell if they have even 1 copy of this dominant gene

Short of paying for a genetic test, the best I can do is to compute probabilities of having at least 1 copy of the gene. Because there seems to be a shortage of layer chicks this year, and the pullets that I am finished with from my Isabel Welbar project are such great layers, I decided to put them into my Opal Legbar pen. Until last week, there were 5 cockerels in there. Two are homozygous for the blue egg gene and the other 3 are hetereozygous. Some of the pullets lay olive eggs and some lay medium brown eggs, about half and half.

So, for all of us that loved word problems in high school math, here is a chance to apply that. Statistical probabilities are portions of 100%, and this is a binary possibility (lay green eggs or not). So, I’m going to compute the chance of getting non-green and subtract that from 100%.

60% of the fathers have 1 copy of the white egg gene (non-blue), they will have a 50% chance of passing that to their progeny, so the chance of getting a white egg gene from the father is 30% (.5 x .6). The chance of getting a white egg gene is 100% from the brown egg pullets and 50% from the green egg pullets. Given half of the pullets lay brown, the chance of getting a white egg gene for the mother is 75%. To lay a non-green egg, the chick must get a white egg gene from both parents (white is recessive to blue). So we multiply the 2 probabilities (.75 x .3) and get 22.5% (chance of non-green). Subtract that from 100% and we get a 77.5% chance of each chick laying a green egg.

On February 15, I removed the 3 Opal cockerels that have a copy of the white egg gene, leaving only the 2 that have 2 copies of the blue egg gene. It takes some time to ensure the hens are not retaining sperm from the removed cockerels, but once that passes, the probabilities change. Since only 1 copy of the blue egg gene is needed to turn the daughters eggs green, the chance of green eggs will go to 100% very soon.