A group of eccentric old men started their own cattle breed using as their base

Question

A group of eccentric old men started their own cattle breed using as their base the animals that they owned. They named the breed "Heinz 57" because it was believed to consist of genes from 57 different breeds. One of the strange rules of their association was that all matings had to be at random. Everything went well for their group until an undesirable trait (droopy ears) that is inherited as an autosomal recessive started appearing. Six calves in last year's calf crop had the condition. The total number of calves in last year's crop was 150. This group does not have the money to develop a test to identify animals that carry the gene. Therefore, they have hired you to give them some consulting advice. As part of your fee, you have agreed to answer their questions in the space below. If we do nothing, how many calves can we expect to have the condition next year? What assumptions do you have to make to come up with that number? For our cow herd, how many would be expected to be in the heterozygous state? If we do not allow animals with droopy ears to be used as breeding animals, at the of one generation how many calves can we expect to have the condition annually?

Explanation / Answer

1. Out of 150 calves this year you had 6 calves with droopy ears which are about 4% of all the calves you had in this year. If these 6 calves were bred with other calves, in the next generation you would have almost 20% of calves with droopy ears.

2. The droopy ears being a recessive condition when bred with a cow which is not a carrier for this trait, only 1/4th of the progeny would have this trait. In that case, when you breed these calves with calves having a carrier trait, then almost 50% of all the progeny will have this trait. Then the percentage of droopy ears will increase to almost 20% of the population in the next generation.

3. The population would have 50% calves in the heterozygote stage for this trait.

4. If you do not breed these droopy ears calves, you still might still have 10% of the population having this trait. As some of this trait is carried as heterozygotes from the previous generation.

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